A Syntactic Correspondence between Context-Sensitive Calculi and Abstract Machines We present a systematic construction of environment-based abstract machines from context-sensitive calculi of explicit substitutions, and we illustrate it with ten calculi and machines for applicative order with an abort operation, normal order with generalized reduction and call/cc, the lambda-mu-calculus, delimited continuations, stack inspection, proper tail-recursion, and lazy evaluation. Most of the machines already exist but have been obtained independently and are only indirectly related to the corresponding calculi. All of the calculi are new and they make it possible to directly reason about the execution of the corresponding machines.In connection with the functional correspondence between evaluation functions and abstract machines initiated by Reynolds, the present syntactic correspondence makes it possible to construct reduction-free normalization functions out of reductionbased ones, which was an open problem in the area of normalization by evaluation. How does one construct a new semantic artifact? We successively consider call by name: Krivine's machine with call/cc (Section 4) and the λµ-calculus (Section 5); call by value: static and dynamic delimited continuations (Section 6), stack inspection (Section 7), and proper tail-recursion (Section 8); and call by need (Section 9). Towards this end, we first present the λ ρ-calculus and the notion of context-sensitive reduction (Section 2) and then a detailed walkthrough for the λ ρ-calculus with an abort operation (Section 3). The subsequent repetitiveness of Sections 4 to 9 (language, notion of context-sensitive reduction, abstract machine, and formal correspondence) is a deliberate feature, not an inadvertent presentational bug: we apply the same simple method to many situations that have been separately studied so far. Each of these sections can therefore be read independently of the others. This local characterization is not fit for non-local reductions such as one involving a control operator capturing all its surrounding context in one step, or a global state. For these, one needs a notion of context-sensitive reduction, i.e., a binary relation defined both on redexes and on their reduction context instead of only on redexes [40] . This relation is given by context-sensitive contraction rules of the form r, C → c , C , where r, C denotes the decomposition of a program into a potential redex r and its context C .. A one-step reduction relation for a given notion of context-sensitive reduction is defined as follows: A program p reduces in one step to p if decomposing p yields r, C , reducing r, C yields c , C , and plugging c into C yields p . A context-sensitive reduction implicitly assumes a decomposition of the entire program, and therefore it cannot be used locally. One way to recover compatibility in the contextsensitive setting is to add explicit local control delimiters to the language (see Section 6 for an illustration). For a language without explicit control delimiters (as the λ ρ-calculus with call/cc), there is an implicit global control delimiter around the program [41] . We have presented a detailed and systematic derivation of an abstract machine for call-byvalue evaluation in the λ-calculus with an abort operation. We started from the specification of the applicative-order reduction strategy in the λ ρ-calculus with an abort operation and we finished with a formal correspondence between the calculus and tbe abstract machine.. In the next six sections, we apply the same method in a variety of computational situations, each of which has been separately studied and reported in the literature. Our presentation is structured around four elements: language, notion of context-sensitive reduction, abstract machine, and formal correspondence. The rest is mechanical and therefore omitted.. The syntactic correspondence has made it possible to exhibit the calculus corresponding to static delimited continuations as embodied in the functional idiom of success and failure continuations and more generally in the CPS hierarchy, and to show that (the explicit-substitutions version of) Felleisen's calculus of dynamic delimited continuations corresponds to his extension of the CEK machine [41] . Elsewhere, we present the abstract machine [7] and the evaluator [32] corresponding to static delimited continuations and an evaluator [11] corresponding to dynamic delimited continuations. We are now in position to compare them pointwise:. • From a calculus point of view, it seems to us that one is better off with layered contexts because it is immediately obvious whether a notion of reduction is compatible with them (see Section 6.1.3); a context containing marks is less easy to treat. Otherwise, the difference between static and dynamic delimited continuations is tiny (see Section 6.2.2), and located in the rule (Beta C ).. • From a machine point of view, separating between the current delimited context and the other ones is also simpler, as it avoids linear searches, copies, and concatenations (in this respect, efficient implementations, e.g., with an Algol-style display, in effect separate between the current delimited context and the other ones).. • From the point of view of CPS, the abstract machine for dynamic delimited continuations is not in defunctionalized form whereas the abstract machine for static delimited continuations is (and corresponds to a evaluator in CPS). Conversely, defunctionalizing a CPS evaluator provides design guidelines, whereas without CPS, one is on one's own, and locally plausible choices may have unforeseen global consequences which are then taken as the norm. Two cases in point:. 1. in Lisp, it was locally plausible to push both formal and actual parameters at function-call time, and to pop them at return time, but this led to dynamic scope since variable lookup then follows the dynamic link; and 2. here, it was locally plausible to concatenate a control-stack segment to the current control stack ("From this, we learn that an empty context adds no information." [45, p. 58] ), but this led to dynamic delimited continuations since capturing a segment of a concatenated context then gives access to beyond the concatenation point.. Granted, a degree of dynamism makes it possible to write compact programs (e.g., a compositional breadth-first traversal without a data-queue accumulator and in direct style [12] ), but it is very difficult to reason about them and they are not necessarily more efficient.. • From the point of view of expressiveness, for example, in Lisp, one can simulate the static scope of Scheme by making each lambda-abstraction a "funarg" and in Scheme, one can simulate the dynamic scope of Lisp by threading an environment of fluid variables in a state-monad fashion. Similarly, static delimited continuations can be simulated using dynamic ones by delimiting the extent of each captured continuation [10] , and dynamic delimited continuations can be simulated using static ones by threading a trail of contexts in a state-monad fashion [11, 39, 58, 77] . As to which should be used by default, the question then reduces to which behavior is the norm and which should be simulated if it is needed.. In summary, the calculi, the abstract machines, and the evaluators all differ. In one approach, continuations are dynamically composed by concatenating their representations [45] and in the other, continuations are statically composed through a metacontinuation. These differences result from distinct designs: Felleisen and his colleagues started from a calculus and wanted to go "beyond continuations" [44] , and therefore beyond CPS, whereas Danvy and Filinski were aiming at a CPS account of delimited control, one that has turned out to be not without practical, semantical, and logical content.. We have presented three corresponding calculi of closures and machines for stack inspection, showing first how the storeless fg machine reflects the λ ρ sec -calculus, second, how the λ ρ cm sec -calculus reflects the storeless cm machine, and third, how the λ ρ ucm sec -calculus reflects the unzipped storeless cm machine. In doing so, we have provided a calculus account of machine design and optimization for stack inspection.. We have presented a series of calculi and abstract machines accounting for a variety of computational effects, making it possible to directly reason about a computation in the calculus and in the corresponding abstract machine (horizontally in the diagram below) and to directly account for actual and explicit substitutions both in the world of calculi and in the world of abstract machines (vertically in the diagram below, where σ maps a closure into the corresponding λ-term and an environment-machine configuration into a configuration in the corresponding machine with actual substitutions):

O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O B B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Formalizing the structural semantics of domain-specific modeling languages Abstract Model-based approaches to system design are now widespread and successful. These approaches make extensive use of model structure to describe systems using domain-specific abstractions, to specify and implement model transformations, and to analyze structural properties of models. In spite of its general importance the structural semantics of modeling languages are not well-understood. In this paper we develop the formal foundations for the structural semantics of domain-specific modeling languages (DSML), including the mechanisms by which metamodels specify the structural semantics of DSMLs. Additionally, we show how our formalization can complement existing tools, and how it yields algorithms for the analysis of DSMLs and model transformations. In this paper we explored the structural foundations of domain-specific modeling languages. We developed a generic structural semantics that addresses structural domain constraints, model transformations, and metamodeling in a consistent fashion. We also applied our approach to a triedand-tested DSML-based modeling framework called MIC, and this resulted in the MiniMeta framework. We showed that our structural semantics can capture the essential functionality of these tools, but do so in a mathematically precise manner. This opens the door for formal analysis; several examples of which where shown in the paper. Beyond this, we implemented MiniMeta using MIC, and in doing so combine the advantages of each.. Our work has some interesting implications on current model-based tool suites. It is well-known that the basic concepts (classes, associations, etc...) in metamodeling languages are not sufficient to encode more complex structural constraints. The typical solution used by metamodeling tools is to annotate metamodels with a constraint language like OCL (Object Constraint Language). However, this is often done without a precise notion of composition between metamodeling and constraints. With our approach, metamodels are translated into constraints, so additional constraints can be injected directly into the resulting interpretation of the metamodel. This provides a consistent and compositional view of metamodels and constraint annotations: They are just two different ways of describing domain constraints. Additionally, Horn logic extended with negation seems suitable for this purpose in that it is both expressive and there exists a large body of work in constructive theorem proving for this style of logic.. Existing approaches to metamodeling have taken an "instance semantics" perspective, wherein the elements of a DSML are "instances" of objects in the metamodel. This view binds all DSMLs to the particular presentation of the metamodeling language, making it difficult to achieve tool interoperability and evolution. Our approach eliminates this binding by building metamodeling from domains and transformations. A domain is a stand-alone mathematical entity that characterizes all the well-formed and malformed model realizations belonging to that domain. A metamodeling language generates domains, but after this generation process the domains are self-sufficient. Our tools also reflect this generality-the definitions of the MiniMeta domain and the transformation process are lists of axioms. These axioms can be changed at anytime without affecting the implementation of MiniMeta within MIC, and without affecting any legacy domains. This approach can be used to implement DSMLbased modeling tools that do not rely on hard-coded metamodeling languages. (x, i path(h, y) ), map 3 (cancontain, var(x) , var(y))) ← containment (x, y), i path(h, y). (x, i path(h, y) ), map 4 (x, var(x) , var(z), var(w))) ← containment (x, y), assocClass(x), i path(h, y). (x, i path(h, y) ), map 2 (h, var(y))) ← containment (x, y), class(h), i path(h, y) . Our view of metamodeling differs from existing approaches based on an instance semantics [53, 87] . These approaches view metamodels as class-like constructs that can be instantiated. A model conforms to a metamodel if each modeling element is an instance of a metamodeling concept. A metametamodel is a metamodel whose conforming instances are metamodels. This top-down approach uses the metametamodel to drive the set of possible metamodels that drives the sets of possible models. While this approach is certainly reasonable, it makes it difficult to disassociate models from the tools and standards used to construct them. The bottomup approach is meta-metamodel agnostic, i.e., domains and transformations exist independently from any particular metamodeling lanugage.. Formalizations and applications of expressive syntax have appeared in many different forms. Within the domain-specific language community, graph-theoretic formalisms [8, 23, 81] have received the most research attention. However, the majority of work focuses on graph rewriting systems as a foundation for model transformations. See [60, 70] for a taxonomy of existing graph-theoretic model transformation approaches. The problems of calculating properties of rich syntax, composing syntax with known properties, and constructing design space representations have not received the same attention from graph-theoretic methods. For example, the model transformation tool VIATRA [18] supports executable Horn logic (i.e., Prolog) to specify transformations, but does not focus on restricting expressiveness for the purpose of analysis.. The visibility of UML has driven researchers to formalize it semantics. This is a non-trivial task because UML includes many capabilities (diagrams) including metamodeling, state machines, activities, sequence charts (interactions), and usecase diagrams [80] . Approaches for formalizing UML must tackle the temporal nature of its various behavioral semantics, necessitating more expressive formal methods. Well-known tools/methods such as Alloy [45] , B [69] , and Z [27] have been used to varying degrees of success. These approaches make trade-offs between expressiveness and the degree of automated analysis. For example, Z and B proofs typically require interactive theorem provers [6, 10] and model generation may not be supported. Z or B formalizations of UML could be a vehicle for studying rich syntax, but automated analysis is less likely to be found.. Alloy, like our tool formula, is less expressive than other methods, thereby supporting automated analysis [46] ; it also has a recently improved model generation (model finding) procedure [86] . However, the mathematical underpinnings of Alloy are quite different from our approach: Alloy supports algebraic specifications through first-order logic with relations over atoms plus transitive closure. Contrarily, our framework is based on a non-monotonic extension of Horn logic [50] . One key difference is that formula specifications can be executed like standard logic programs [84] . Complexitytheory also offers a coarse-grained way of comparing logic programs with other methods [20] .. The BNF grammars of traditional programming languages can be extended to capture richer syntaxes. Attribute grammars (AGs) [82] , proposed by Knuth [59] , could be the earliest example of such a mechanism. AGs allow the productions of a BNF grammar to trigger actions capable of examining tokens and attaching new data to tokens. These actions can be specified programmatically, thereby significantly increasing the power of the grammar. However, calculating properties of languages specified through AGs depends on the expressiveness of the actions. Additionally, composing AGs has proved to be a difficult task [28] . More recently, pluggable type systems have been studied as a mechanism to compose the type systems of traditional programming languages [4] .

O O B I O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O B I O B I I O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O B I O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Symbolic analysis of bounded Petri nets AbstractÐThis work presents a symbolic approach for the analysis of bounded Petri nets. The structure and behavior of the Petri net is symbolically modeled by using Boolean functions, thus reducing reasoning about Petri nets to Boolean calculation. The set of reachable markings is calculated by symbolically firing the transitions in the Petri net. Highly concurrent systems suffer from the state explosion problem produced by an exponential increase of the number of reachable states. This state explosion is handled by using Binary Decision Diagrams (BDDs) which are capable of representing large sets of markings with small data structures. Petri nets have the ability to model a large variety of systems and the flexibility to describe causality, concurrency, and conditional relations. The manipulation of vast state spaces generated by Petri nets enables the efficient analysis of a wide range of problems, e.g., deadlock freeness, liveness, and concurrency. A number of examples are presented in order to show how large reachability sets can be generated, represented, and analyzed with moderate BDD sizes. By using this symbolic framework, properties requiring an exhaustive analysis of the reachability graph can be efficiently verified. P ETRI nets are a graph-based mathematical formalism suitable to describe, model, and analyze the behavior of discrete event concurrent systems. More precisely, Petri nets can describe asynchronous sequential and nonsequential behaviors, including concurrency and nondeterministic choice, where sets of processes can interact, cooperate, and compete. Since their introduction by C.A. Petri in 1962 [11] , Petri nets (PNs) have been extensively used in a wide range of areas such as communication protocols and networks, computer architecture, distributed systems, manufacturing planning, digital circuit synthesis and verification, and high-level synthesis.. The existing methods for the analysis of PNs can be mainly classified into four categories [9] : reachability tree methods, enumerative methods, matrix-equation methods, and reduction or decomposition methods. Traditionally, the first and second methods are only applicable to small PNs due to the explosion of the number of markings in concurrent systems, while the third and fourth methods are restricted to particular subclasses of PNs.. Enumerative methods permit verifying properties of finite systems. They can also be successfully combined with analysis methods based on the structure of the PN. However, the potentially huge number of reachable markings in highly concurrent systems becomes the main bottleneck for any enumerative approach. This limitation encourages the study and application of new efficient techniques to overcome this problem.. In this work, we present a symbolic approach that implicitly enumerates the reachable markings. This method is applicable to the analysis of any type of bounded PNs [10] . The proposed technique is based on the modeling of the PN by means of Boolean algebras [1] . Problems like deadlock detection, liveness, boundedness, and persistence can be checked by properly manipulating the functions that model the PN.. Methods based on the explicit enumeration of the reachable markings suffer from the state explosion problem due to the arbitrary interleaving of concurrent transitions. The inherent complexity involved in the enumeration of the exponential number of markings in a PN is alleviated by using Binary Decision Diagrams (BDD) [2] . BDDs have the capability of representing large sets of encoded data with small data structures and enable the efficient manipulation of those sets. The utilization of BDDs not only provides algorithms which are computationally capable of manipulating large systems (due to its efficient data representation), but also provide an extremely flexible mechanism to manipulate PNs.. Symbolic model checking techniques have already been proposed in [7] , [14] , [18] for the verification of digital circuits. More recently, [18] introduced special Boolean operators to perform efficient symbolic analysis based on Zero-Suppressed BDDs (ZBDDs). The theory presented in this paper is not restricted to any particular class of Decision Diagrams and can be applied to any framework based on Boolean manipulation of Petri nets.. The remainder of this work is organized as follows: In Section 2, we introduce basic definitions on Boolean algebras, Petri nets, and Binary Decision Diagrams. The modeling of PNs is discussed in Section 3. The Boolean functions that define the dynamic behavior of the PN are described in Section 4, while the symbolic reachability analysis algorithm required to efficiently generate the markings in the PN is outlined in Section 5. In order to manipulate bounded PNs, an extension of the basic model, as well as the required reachability techniques, is proposed in Section 6. Section 7 presents a set of PN reductions that can improve the efficiency in the calculation of the state space. Algorithms for the verification of properties, such as concurrency, liveness, and persistence, are presented in Section 8. Several experimental results are presented in Section 9, including a detailed analysis on the efficiency of the method. This paper presents the combination of Boolean reasoning and BDD algorithms to manage the state explosion produced in Petri net analysis. It has been shown that BDDs can efficiently represent and manipulate large sets of reachable markings with a small number of BDD nodes. Once the reachable markings have been generated, several properties, such as safeness, boundedness, liveness, persistence, and concurrency, can be verified since they are reduced to the computation of well-known Boolean formulas. Therefore, BDDs are proposed as an alternative to the reachability tree or other enumerative techniques, providing a compact representation of the markings of any bounded PN.. Many issues are still under research to increase the applicability of the approach. The ordering of variables is a topic of major interest that must be studied in order to reduce even more the size of the BDDs, thus speeding-up BDD operations. As mentioned in Section 6, the encoding methods for k-bounded nets must be further explored. The combination of symbolic methods with structural and linear programming techniques as described in [11] , more powerful reduction methodologies, improved chaining traversal, and more compact BDD variable encoding are clear areas for future development.

O O O O B I O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


An Application of Quantum Finite Automata to Interactive Proof Systems Abstract: Quantum finite automata have been studied intensively since their introduction in late 1990s as a natural model of a quantum computer with finite-dimensional quantum memory space. This paper seeks their direct application to interactive proof systems in which a mighty quantum prover communicates with a quantum-automaton verifier through a common communication cell. Our quantum interactive proof systems are juxtaposed to Dwork-Stockmeyer's classical interactive proof systems whose verifiers are two-way probabilistic automata. We demonstrate strengths and weaknesses of our systems and further study how various restrictions on the behaviors of quantum-automaton verifiers affect the power of quantum interactive proof systems.Keywords: quantum finite automaton, quantum interactive proof system, quantum measurement, quantum circuitA quantum computer-quantum-mechanical computing device-has drawn wide attention as a future computing paradigm since the pioneering work of Feynman [20] , Deutsch [16], and Benioff [9] in the 1980s. Over the decades, such a device has been mathematically modeled in numerous ways to deliver a coherent theory of quantum computation. Of all computational models, Moore and Crutchfield [34] as well as Kondacs and Watrous [32] proposed a (one-head) quantum finite automaton (qfa, in short) as a simple but natural model of a quantum computer that is equipped with finite-dimensional quantum memory space † . Parallel to classical automata theory, the theory of quantum finite automata has been well established to study the nature of quantum computation. Performing a series of unitary operations as its tape head scans input symbols, a qfa may eventually enter accepting or rejecting inner states to halt. Any entry of such a unitary operation is a complex number, called a (transition) amplitude. A quantum computation is seen as an evolution of a quantum superposition of the machine's configurations, where a configuration is a pair of an inner state and a head position of the machine. As quantum physics dictates, a quantum evolution is reversible in nature. A special operation called a (quantum) measurement is performed to "observe" whether the qfa enters an accepting inner state, a rejecting inner state, or a non-halting inner state. Of all the variations of qfa's discussed in the past literature, we shall focus our study only on the early models of Moore and Crutchfield and of Kondacs and Watrous for our application to interactive proof systems.In 1997, Kondacs and Watrous [32] introduced two types of qfa's: a 1-way quantum finite automaton (1qfa, in short) whose head always moves rightward and a 2-way quantum finite automaton (2qfa, in short) whose head moves in all directions. Both qfa's perform a so-called projection measurement (or von Neumann measurement) after every move of them. Because of a finite memory constraint, no 1qfa recognizes even the regular language Zero = {x0 | x ∈ {0, 1} * } with small error probability [32] . In the model of Moore and Crutchfield, on the contrary, a 1qfa performs a measurement only once after the tape head scans the right endmarker. Their model is often referred to as a measure-once 1-way quantum finite automaton (mo-1qfa, in short). The qfa model of Kondacs and Watrous is by contrast called a measure-many 1-way quantum finite automaton. As Brodsky and Pippenger [11] showed, mo-1qfa's are so restrictive that they are fundamentally equivalent in power to "permutation" automata, which recognize exactly group languages. Unlike the 1qfa's, 2qfa's can simulate deterministic finite automata with probability 1. Moreover, Kondacs and Watrous [32] constructed a 2qfa that recognizes with small error probability the non-regular language U pal = {0 n 1 n | n ≥ 0} (unique palindromes) in worst-case linear time by exploiting its quantum superposition. The power of a qfa may vary in

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I B I I I B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


The cutoff method for the numerical computation of nonnegative solutions of parabolic PDEs with application to anisotropic diffusion and lubrication-type equations The cutoff method, which cuts off the values of a function less than a given number, is studied for the numerical computation of nonnegative solutions of parabolic partial differential equations. A convergence analysis is given for a broad class of finite difference methods combined with cutoff for linear parabolic equations. Two applications are investigated, linear anisotropic diffusion problems satisfying the setting of the convergence analysis and nonlinear lubrication-type equations for which it is unclear if the convergence analysis applies. The numerical results are shown to be consistent with the theory and in good agreement with existing results in the literature. The convergence analysis and applications demonstrate that the cutoff method is an effective tool for use in the computation of nonnegative solutions. Cutoff can also be used with other discretization methods such as collocation, finite volume, finite element, and spectral methods and for the computation of positive solutions. Many physical phenomena involve variables such as the density and concentration of a material that take only nonnegative values. The mathematical reflection of this property is that the partial differential equations (PDEs) modeling the phenomena admit nonnegative solutions. For the numerical solution of those PDEs, it is crucial that numerical schemes preserve the solution nonnegativity and produce physically meaningful numerical solutions.. A closely related concept is the maximum principle. Preserving the maximum principle is equivalent to preserving the solution nonnegativity for linear problems [50] but generally the former is more difficult than the latter. It is known (e.g., see [11] ) that a conventional numerical method, such as a finite difference (FD), finite volume (FV), or finite element (FE) method, generally does not preserve the maximum principle and can produce negative undershoot in the solution for diffusion problems, especially those with heterogeneous anisotropic diffusion coefficients. Considerable effort has been made on developing numerical schemes satisfying the maximum principle; e.g., see [6, 7, 10, 11, 28, 29, 31, 34, 46, 47, 51, 52] for steady-state isotropic diffusion problems and [15, 22, 23, 27, 30, 36, 38, 39, 40, 41, 42, 45] for steady-state anisotropic diffusion problems. Particularly, Ciarlet and Raviart [11] show that the linear FE approximation of an elliptic isotropic diffusion problem satisfies the maximum principle when the mesh is simplicial and nonobtuse. The result is generalized to anisotropic diffusion problems by Huang and his coworkers in [27, 36, 41] . On the other hand, less progress has been made for time dependent problems. For example, Fujii [21] shows that the linear FE approximation of the heat equation satisfies the maximum principle when the mesh is simplicial and acute and the time step size is bounded above by a bound proportional to the squared maximal element size and below by a bound proportional to the squared minimal element in-diameter. He also shows that when the lumped mass matrix is used, the maximum principle holds without requiring the time step size to be bounded from below. Fujii's results are extended to more general isotropic diffusion problems by Faragó et al. [17, 19, 20] and to anisotropic diffusion problems by Li and Huang [37] . Faragó and Horváth [18] study the relations between the maximum principle, nonnegativity preservation, and maximum norm contractivity for linear parabolic equations and their finite difference and Galerkin finite element discretizations. Thomée and Wahlbin [50] consider more general parabolic PDEs and show that the maximum principle cannot hold for the conventional semidiscrete FE problem and Fujii's conditions on the mesh are essentially sharp for the lumped mass matrix. Le Potier [32, 33] (also see Lipnikov et al. [39] ) proposes two nonlinear FV schemes for linear anisotropic diffusion problems and shows that they are second order in space and satisfy monotonicity [32] or the maximum principle [33] .. We consider initial-boundary value problems of parabolic PDEs which are well posed and have a unique, nonnegative solution. Instead of employing a maximum-principle preserving scheme, we propose to use the cutoff method that cuts off the negative values in the computed solution at each time step and then continues the time integration with the corrected solution; see Fig. 1 for a sketch of the solution procedure. The cutoff method shares a similar idea with many projection and correction methods. For example, projection methods [9, 49] are an effective means of enforcing the incompressibility condition in the numerical solution of time dependent incompressible fluid flow problems. Projection is also used by some researchers in the numerical solution of Hamiltonian systems to preserve the energy; e.g., see [26] . A FE/implicit Euler discretization of a Cahn-Hilliard equation with logarithmic nonlinearity is considered in [13] and iterative methods to solve the resulting nonlinear systems of equations are developed to keep the solution within its physically relevant range. Solution compression is used in the design of maximum-principle-satisfying high order schemes for scalar conservation laws by Zhang and Shu [53] . It should be emphasized that the cutoff method provides several advantages over many positivity-preserving or maximum-principle-preserving schemes. Its implementation is simple and requires no significant changes in the existing code. Moreover, the cutoff procedure does not impose any constraint on the mesh and time step which maximum-principle-preserving schemes often impose. However, unlike projection methods, there do not seem to exist published theoretical or numerical studies on the cutoff method.. The objective of this paper is to provide a theoretical and numerical study of the cutoff method for use in the computation of nonnegative solutions of parabolic PDEs. We shall first prove that a broad class of finite difference methods are convergent when they are incorporated with the cutoff method for linear parabolic PDEs. Two applications are then investigated. The first is a linear anisotropic diffusion problems which satisfies the setting of the convergence analysis. It is known that a conventional finite difference or finite element method with a uniform or quasi-uniform mesh does not preserve the maximum principle (nor the solution nonnegativity) and typically produces negative undershoot in the computed solution. The cutoff method removes the unphysical negative values in the solution while keeping the same convergence order of the underlying scheme. The second application is nonlinear lubrication-type equations. It is unclear if the convergence analysis (which can be extended to some nonlinear equations; see Remark 2.1) applies to those equations. A distinct feature of lubrication-type equations is that a positive solution can develop a finite time singularity of the form u → 0 and become identically zero on some spatial interval for a period of time. A conventional finite difference or finite element method can produce negative values in the computed solution during this development of singularity. Negative solution values are not only unphysical but also cease the computation for typical situations where the nonlinear diffusion coefficients are undefined for negative solution values. The application of the cutoff method avoids this difficulty. Moreover, it is shown that no regularization is needed when cutoff is used. Numerical results are shown to be in good agreement with existing ones in the literature.. The outline of the paper is as follows. The cutoff method is described and some of its properties are given in Section 2. The convergence of a broad class of finite difference methods is proved also in Section 2 when they are incorporated with the cutoff method for the computation of nonnegative solutions of linear parabolic PDEs. Application of finite difference methods with cutoff to a linear anisotropic diffusion problem and a lubrication-type PDE is studied in Sections 3 and 4, respectively. Finally, Section 5 contains conclusions and further comments.

O B O O O O O O O O O O O O O O B I O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O B O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O B O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O B O O O O O O O O O O O O O B I O O B O O O B I O O O O O O O O O O O O O O O O O O O O O


LinMap: Visualizing Complexity Gradients in Evolutionary Landscapes Abstract This article describes an interactive visualization tool, LinMap, for exploring the structure of complexity gradients in evolutionary landscapes. LinMap is a computationally efficient and intuitive tool for visualizing and exploring multidimensional parameter spaces. An artificial cell lineage model is presented that allows complexity to be quantified according to several different developmental and phenotypic metrics. LinMap is applied to the evolutionary landscapes generated by this model to demonstrate that different definitions of complexity produce different gradients across the same landscape; that landscapes are characterized by a phase transition between proliferating and quiescent cell lineages where both complexity and diversity are maximized; and that landscapes defined by adaptive fitness and complexity can display different topographical features. In order to understand the evolution of complexity, we need to understand how complexity is distributed across the multidimensional landscape in which evolution occurs. The evolution of a species is often viewed as a trajectory through a landscape of possibilities. Each point in such a landscape corresponds to a particular genotype (or phenotype), while the height of a point reflects the adaptive fitness of that genotype or phenotype [2] . Over time, natural selection will draw populations toward the fitness peaks. An alternative view of an evolutionary landscape is to associate height with complexity. The contours of the landscape will then represent complexity gradients; and questions about how complexity changes during evolution can be phrased in terms of the alignment between gradients of complexity and adaptive fitness.. There is a pervasive belief that complexity has increased over evolutionary time [6, 45, 34, 8, 50] . Major transitions in evolution have increased the dimensionality of evolutionary landscapes so that more complex organisms (with a greater number of parts, or types of parts) become possible [27] . In particular, the advent of multicellularity and development has resulted in an explosion of new vectors of possible variation [8] . Nonetheless, the view that complexity has increased during evolution is difficult to prove definitively: Several instances have been found in which species appear to have evolved toward simpler configurations [34] .. Existing studies of biological complexity provide a picture of how certain aspects of complexity (e.g., number of cell types or body parts) can vary across localized regions of evolutionary landscapes [6, 45, 34] . These studies, by drawing on empirical data, focus on regions that have been realized throughout evolutionary history. However, the set of possible organisms is likely to be far larger than the subset so far encountered by evolution, and it has been observed that regions of interest (i.e., successful species) are distributed in a nonuniform fashion [15, 39] . Modeling is one approach to obtaining a broader understanding of the evolution of complexity.. Several models have been proposed for exploring evolutionary trends in complexity using stochastic processes [45, 33, 37] . These abstract models omit the genetic and developmental mechanisms that underlie the production of complex organisms and focus on the macroscopic evolutionary mechanisms that may affect complexity. Such models have been used to distinguish between two possible evolutionary trends: passive, in which there is no bias toward increasing complexity, but probabilistic changes to complexity (possibly limited by a lower boundary) result in diffusion toward high complexity; and driven, in which changes to complexity are biased toward increases rather than decreases [34] . An alternative approach is to consider how microscopic evolutionary mechanisms affect complexity. Models simulating the evolution of cell lineages have demonstrated how the developmental processes of some organisms may have become simpler over time [3] and that there may be an overall trend toward average complexity [30] .. At a lower level of description, a variety of models have been constructed to explore how genetic and developmental mechanisms interact to generate phenotypic complexity (see [42] for a comprehensive review). Some of these models enable complexity to be quantitatively measured (e.g., [5, 29, 26] ). Other models have bridged the divide between the genetic and developmental mechanisms that build complex forms and the evolutionary mechanisms with which they interact [23, 40] . In general, the complexity of these models limits their application to a relatively small number of possible parameter combinations and experimental replications, illustrating only limited regions of evolutionary landscapes that they define.. There are several challenges for the design of a modeling framework that can achieve a synthesis between the short-term developmental processes that build complex phenotypes and the longterm evolutionary processes that result in observable trends. Most importantly, it is necessary to understand how genetics, development, and environment interact to generate an evolutionary landscape. We currently lack a general framework that allows evolutionary landscapes to be simulated and visualized. General models of adaptive landscapes have previously been proposed (such as Kauffman's NK landscapes [24] ); however, these omit a developmental component, which limits the ways in which complexity gradients can be defined.. The aim of this article is to introduce a modeling framework and an associated visualization tool that allows the complexity gradients in evolutionary landscapes to be explored in an intuitive fashion. The following section describes the network-lineage model that was used to define the evolutionary landscape. Several theoretical notions of complexity are then reviewed and interpreted so that they can be applied to the network-lineage model. The visualization tool, LinMap, and its application to the network-lineage model are described. Finally, we discuss several insights into the distribution of complexity across evolutionary landscapes that were obtained using LinMap. This article has presented an interactive visualization tool, LinMap, for exploring the complexity gradients in evolutionary landscapes. This tool has been applied to exploring the landscapes generated by a stylized model of biological development. The network-lineage model, to which LinMap was applied, is a useful framework for modeling the interaction of evolutionary and developmental dynamics. It combines a rich variety of dynamic behaviors with a high level of computational efficiency, enabling large and detailed evolutionary landscapes to be explored rapidly and efficiently. Several uses of LinMap have been demonstrated: the rapid exploration of a multidimensional parameter space; the comparison of different complexity measures; the identification of a complexity phase transition in evolutionary space; and the comparison between complexity gradients and adaptive gradients.. Complexity and adaptive fitness constitute parallel views of an evolutionary landscape. While a complexity gradient may be constant, adaptive gradients will change depending on the adaptive context of a population: Visualization allows us to assess the degree of correlation between these gradients in different adaptive contexts, and to begin to understand the conditions governing increases and decreases in complexity during evolution.

O O B O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O B O O O O O O O O O O B O B O O O O O B O O O O O O O O B O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O B O O B O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B O O O O B O O O O O O O O O O O B O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O B O O O O O O O O O B O O O O B O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B


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of

end-to-end

traffic

streams

without

requiring

specialized

hardware

for

the

network

components.

The

hard

latency

constraints

are

met

by

carefully

designing

the

NoC

topology

and

selecting

the

appropriate

routes

for

flow

using

lean

best-effort

network

components.

We

perform

experiments

on

several

System

on

Chip

(SoC)

benchmarks.

We

compared

against

a

topology

synthesis

method

with

no

support

for

real-time

constraints

and

we

show

that

the

proposed

method

can

produce

topologies

that

can

meet

significantly

tighter

worst

case

latency

constraints

(on

average

We

also

show

that

the

tightest

worst

case

latency

can

be

provided

with

little

overhead

on

power

consumption

(on

average

Networks

on

Chips

(NoCs)

use

scalable

networking

principles

on

a

chip

scale.

They

provide

better

performance,

modularity

and

faster

design

closure

when

compared

to

bus

based

interconnects.

Today,

building

NoCs

that

meet

hard

latency

constraints

imposed

by

real-time

streams

is

a

major

challenge

for

designers.

Several

applications

have

strict

requirements

on

latency

for

one

or

more

traffic

streams.

For

example,

in.

The

authors

would

like

to

acknowledge

the

financial

contribution

of

European

Research

Council

under

project

and

project

Authors'

addresses:

C.

Seiculescu

and

G.

De

Micheli,

LSI

EPFL

Switzerland;

email:

{ciprian.seiculescu,

giovanni.demichli}@epfl.ch;

D.

Rahmati

and

H.

Sarbazi-Azad,

HPCAN,

Sharif

University

of

Technology,

Tehran,

Iran;

email:

drahmati@ce.sharif.edu,

azad@sharif.edu;

S.

Murali,

iNoCs

Sarl

Lausanne

Switzerland;

email:

murali@inocs.com;

L.

Benini,

DEIS,

University

of

Bologna,

Bologna,

Italy;

email:

luca.benini@unibo.it.

Permission

to

make

digital

or

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of

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or

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work

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or

classroom

use

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fee

provided

that

copies

are

not

made

or

distributed

for

profit

or

commercial

advantage

and

that

copies

show

this

notice

on

the

first

page

or

initial

screen

of

a

display

along

with

the

full

citation.

Copyrights

for

components

of

this

work

owned

by

others

than

ACM

must

be

honored.

Abstracting

with

credit

is

permitted.

To

copy

otherwise,

to

republish,

to

post

on

servers,

to

redistribute

to

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or

to

use

any

component

of

this

work

in

other

works

requires

prior

specific

permission

and/or

a

fee.

Permissions

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requested

from

Publications

Dept.,

ACM,

Inc.,

Penn

Plaza,

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York,

NY

USA,

fax

or

permissions@acm.org.

c

ACM

DOI:

-We

provide

an

algorithm

to

automatically

design

the

NoC

topology

to

meet

the

required

worse-case

delay

bounds..

We

perform

experiments

on

several

System

on

Chip

(SoC)

benchmarks.

When

compared

to

a

topology

synthesis

methods

with

no

support

for

real-time

constraints,

our

proposed

method

can

produce

topologies

that

can

meet

significantly

tighter

worst-case

latency

constraints

(on

average

The

results

also

show

that

the

power

consumption

and

average

zero-load

latency

values

of

the

topologies

designed

using

the

proposed

scheme

are

only

marginally

higher

than

a

synthesis

method

that

does

not

support

real

time

constraints

(on

average

Indeed,

when

only

certain

traffic

streams

require

hard

QoS

guarantees,

the

topologies

synthesized

by

our

proposed

method

has

negligible

power

consumption

or

area

overhead.

We

have

shown

that

guaranteeing

worst-case

latencies

for

communication

flows

in

a

best-effort

NoC

fabric

can

be

done

without

specific

hardware

support,

by

judiciously

synthesizing

a

QoS-aware

topology.

The

proposed

method

gives

worst

case

latency

guarantees

by

carefully

designing

the

application

specific

topologies

for

the

NoC

and

can

be

used

with

switches

that

do

not

have

any

specialized

hardware

for

QoS.

The

only

assumption

is

that

the

switches

use

a

fair

arbitration

policy,

such

as

round

robin..

In

our

experiments

we

show

that

our

proposed

algorithm

can

guarantee

meeting

real

time

latency

constraints

with

little

resource

and

power

consumption

overhead

(average

An

introduction

to

the

NoC

principles

can

be

found

in

De

Micheli

and

Benini

More

aspects

for

the

design

of

NoCs

are

summarized

Flich

and

Bertozzi

and

Cristina

Silvano

and

Palermo

Several

works

have

addressed

the

synthesis

of

NoC

topologies

to

meet

application

performance

constraints

[Pinto

et

al.

Ho

and

Pinkston

Ahonen

et

al.

Srinivasan

et

al.

Hansson

et

al.

Zhu

and

Malik

Xu

et

al.

Murali

et

al.

However,

all

of

these

works

produce

topologies

that

meet

the

average

latency

constraints

and

not

the

worst-case

ones.

Mapping

of

core

to

regular

topologies

is

addressed

in

Hu

and

Marculescu

Micheli

and

Murali

et

al.

However,

except

for

[Murali

et

al.

QoS

is

not

considered.

In

[Murali

et

al.

the

authors

consider

critical

streams

and

map

them

more

efficiently

than

normal

streams.

However,

they

do

not

provide

any

bounds

on

the

latencies.

Hansson

et

al.

present

a

method

to

synthesize

NoCs

for

a

TDMA

based

architecture.

They

also

consider

the

design

of

TDMA

slot

tables

to

meet

hard

QoS

constraints.

However,

the

method

only

applies

to

NoCs

where

the

underlying

architecture

uses

additional

hardware

to

support

QoS.

Moreover,

with

a

TDMA

scheme,

the

average

performance

of

the

system

could

be

poorer

than

with

a

scheme

where

packet

injection

times

are

not

so

tightly

constrained..

There

have

been

many

works

that

provide

QoS

guarantees

by

adding

specialized

hardware

to

the

NoC

architecture.

The

AEthereal

NoC,

presented

in

Goossens

et

al.

adds

guaranteed

services

on

top

of

best

effort

services

to

provide

QoS

support.

Kopetz

et

al.

describe

the

MARS

architecture

where

TDMA

is

used

to

provide

QoS

guarantees.

In

Shi

and

Burns

a

priority

based

scheme

is

used

to

provide

QoS,

and

Paukovits

and

Kopetz

present

the

concept

of

a

predictable

TimeTriggered

NoC,

where

QoS

is

ensured

through

communication

services.

Marescaux

and

Corporaal

present

a

QoS

NoC

architecture

that

uses

both

best

effort

and

guaranteed

traffic,

but

requires

specialized

hardware

and

virtual

channels.

Many

works

present

improvements

and

variations

[Bolotin

et

al.

Bjerregaard

and

Sparso

Bouhraoua

and

Elrabaa

Feliciian

and

Furber

Kavaldjiev

et

al.

Leroy

et

al.

Mello

et

al.

Millberg

et

al.

Mondinelli

et

al.

Mullins

et

al.

Radulescu

et

al.

Rijpkema

et

al.

but

all

use

specialized

hardware

to

provide

QoS.

A

recent

survey

of

NoCs

[Salminen

shows

that

most

NoC

architectures

do

not

have

specialized

hardware

for

QoS

and

therefore

a

method

to

design

NoCs

that

provides

guarantees

on

the

delay

of

communication

flows

is

necessary.

Lee

presents

a

method

to

characterize

the

real

time

behaviour

of

communication

flows

in

best

effort

wormhole

general

networks

for

parallel

computing.

However

this

method

requires

traffic

regulation,

which

is

not

desirable

in

a

majority

of

applications.

In

Rahmati

et

al.

we

presented

models

to

analyze

and

compute

worst

C.

Seiculescu

et

al.

case

latency

bounds,

even

the

input

traffic

is

not

regulated.

In

this

work,

we

use

the

methods

for

calculating

the

worst-case

latencies

during

the

topology

synthesis

process

itself,

and

we

use

the

computed

values

to

tune

the

instantiation

of

network

components

to

produce

topologies

that

meet

the

real

time-constraints.

O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B B O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B O O O O B I I O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O


Learning sequences of actions in collectives of autonomous agents In this paper we focus on the problem of designing a collective of autonomous agents that individually learn sequences of actions such that the resultant sequence of joint actions achieves a predetermined global objective. Directly applying Reinforcement Learning (RL) concepts to multi-agent systems often proves problematic, as agents may work at crosspurposes, or have difficulty in evaluating their contribution to achievement of the global objective, or both. Accordingly, the crucial design step in designing multi-agent systems focuses on how to set the rewards for the RL algorithm of each agent so that as the agents attempt to maximize those rewards, the system reaches a globally "desirable" solution. In this work we consider a version of this problem involving multiple autonomous agents in a grid world. We use concepts from collective intelligence [15, 23] to design rewards for the agents that are "aligned" with the global reward, and are "learnable" in that agents can readily see how their behavior affects their reward. We show that reinforcement learning agents using those rewards outperform both "natural" extensions of single agent algorithms and global reinforcement learning solutions based on "team games". Many challenging problems involve coordinating a large number of autonomous agents to collectively address a well-. • ensuring that, as far as the provided "world utility function" is concerned, the agents do not work at crosspurposes (i.e., making sure that the private goals of the agents and the global goal are "aligned").. For single agent systems, the first of these issues has been dealt with extensively, and there are many learning systems, (e.g., Q-learners [17] ) that have successfully been applied to real world problems [2] . The second problem has received less attention, and generally the solution consists of either each agent receiving the world utility as their payoff utility (e.g., "team" games [4] ), or of imposing external mechanisms (e.g., contracts, auctions) that encourage the agents to work together [8, 11] .. Addressing these two issues simultaneously is one of the main problems in designing multi-agent systems [9, 12] . If the agents are not designed to work well with each other, they may not learn their task properly, may interfere with each other's ability to contribute to the world utility, or simply perform useless repetitive work. Hand tailoring the agents' payoff functions may offer an alternative, but such systems: (i) have to be laboriously modeled; (ii) provide "brittle" global performance; (iii) are not "adaptive" to changing environments; and (iv) generally do not scale well.. To sidestep these problems, yet address the design requirements listed above (i.e., "alignedness" and "learnability") one can use the "COllective INtelligence" (COIN) framework [15, 21] . A COIN is a large multi-agent system where there is a well-defined "world utility" function which rates the possible dynamic histories of the collection and where there is little to no centralized control. We are particularly interested in the case where each agent is "selfish" and runs a Reinforcement Learning (RL) algorithm [14] .. Given this framework, COIN theory addresses a new design problem: Assuming the individual agents are able to maximize their own utility functions (e.g., through reinforcement learning), what set of payoff utilities for the individual agents will, when pursued by those agents, result in high world utility? In other words, how can we leverage an assumption that our learners are individually fairly good at what they do, to induce good collective behavior?. There are two quantifiable properties (discussed in detail in Section 2) that help answer this question. First, the utility functions for the individual agents need to be "aligned" with the world utility, in that an action taken by an agent that improves its payoff utility also improves the world utility. Second, the utility functions need to be "learnable" in that an agent has to be able to discern the effect of its actions on its utility and select actions that optimize that utility. As we will highlight below, COIN theory provides utilities for individual agents that maximize the second property while satisfying the first one.. A canonical example of a naturally occurring system that can be viewed as a COIN is a human economy. One can take the agents to be the individuals trying to maximize their payoff utilities (e.g., maximize bank account, advance career). One might then take the time average of the gross domestic product as the world utility ("world utility" is not a construction internal to a human economy, but rather something defined from the outside). To achieve high world utility it is necessary to avoid having the agents work at crosspurposes lest frustrational phenomena like the tragedy of the commons occur, in which individual avarice works to lower world utility [7] . One way to avoid such phenomena is by modifying the agents' utility functions via punitive legislation, in essence making sure the agents' utility functions are aligned with the world utility. Securities and Exchange Commission (SEC) regulations designed to prevent insider trading can be viewed as a real world example of an attempt to make such a modification to the agents' utilities. For example, a trade that once may have added to your wealth while hurting the economy, may now lead to your prosecution. You are therefore unlikely to make such a trade. Your utility and the world utility have become more aligned.. In designing a COIN we have more freedom than the SEC though, in that there is no base-line "organic" payoff utility function over which we must superimpose legislation-like incentives. Rather, the entire "psychology" of the individual agents is at our disposal when designing a COIN. This freedom is a major strength of the COIN approach, in that it obviates the need for honesty-elicitation mechanisms, like auctions, which form a central component of conventional economics.. The COIN design problem is related to work in many fields beyond multiagent systems and computational economics, including mechanism design, reinforcement learning for adaptive control, computational ecologies, and game theory. However none of these fields directly addresses the inverse problem of how to design the agents' utilities to reach a desirable world utility value in its full generality. This is even true for the field of mechanism design, which while addressing an inverse problem similar to that of COIN design, does so only for certain restricted domains, and does not address the "learnability" issue. (Mechanism design is mostly appropriate when there are pre-specified goals underlying agents' utilities over which "incentives" need to be provided, and when Pareto-optimality (rather than optimization of a world utility) is often the goal [21] .). The COIN framework has been successfully applied to multiple domains including packet routing over a data network [20] and the congestion game known as Arthur's El Farol Bar problem [23] . In particular, in the routing domain, the COIN approach achieved performance improvements of a factor of three over the conventional Shortest Path Algorithm (SPA) routing algorithms currently running on the internet [19] , and avoided the Braess' routing paradox which plagues the SPA-based systems [15] .. In the work described above, agents were concerned with optimizing "rewards" (i.e., utility value of a single time step). In this paper we extend these results to a problem where agents need to optimize a time-extended utility function through selecting sequences of actions. We show that in this significantly more complex domain, agents that use COIN theory-based utilities provided solutions that are significantly superior to agents that either use team games or "natural" utilities. In Section 2, we provide some background on COIN-theoretic concepts and highlight relevant theoretical developments. In Section 3, we describe the problem domain and develop the COIN solution to this problem. In Section 4, we present and discuss the simulation results. Finally in Section 5, we provide a simple example that demonstrates how and why COIN-theory based algorithms significantly outperformed more "natural" or "traditional" approaches. In this work we focus on the problem of designing a collective of autonomous agents that individually learn sequences of actions such that the resultant sequence of joint actions achieves a predetermined global objective. In particular we discuss the problem of controlling multiple agents in a grid world, a problem related to many real world problems including exploration vehicles trying to maximize aggregate scientific data collection (e.g., rovers on the surface of Mars). In this domain, we addressed the critical issue of what utility functions those agents should strive to maximize. We extended previous results on collective intelligence to agents attempting to maximize sequences of actions, and used Qlearning with rewards set by COIN theory. Our results demonstrate that RL rovers using COIN-derived goals outperform both "natural" extensions of single agent algorithms and global reinforcement learning solutions based on "team games".. Our investigations revealed an interesting situation where the theoretically "best" strategy was not necessarily the best approach in practice. Although AU is theoretically superior to WLU (higher learnability), two issues prevent us from fully exploiting its power: First, the "expected" action is impossible to compute in a time extended setting, since even a simple case where an agent has four actions and ten time steps leads to 4 10 possible actions. Even Monte Carlo sampling of such a space will yield highly inaccurate estimates of the potential actions and their rewards. Second, estimating the correct probability distributions over the possible actions causes the utility values to change, creating a selfconsistency problem. To sidestep both issues, in this article we chose to focus on the last time step (e.g., current step for the agent) and approximated the AU with the agent taking each of the four actions possible in that time step with equal likelihood. The resulting utility function provided good solutions, but the performance of such a "handicapped" AU did not exceed those of the conceptually simpler WLU.. Future work in this area includes investigating efficient AU computation for sequences of actions, and investigating the "mean field" approximation to AU by clamping the actions of an agent to the average action discussed in Figure 2 . This approach avoids both difficulties associated with the proper AU, and has been shown to lead to good world utility values in single step reward maximization problems [21] . To evaluate the effectiveness of the COIN approach in the Multi-agent Grid World, we conducted experiments where the agents used four different utility functions. The first of these was the Selfish Utility (SU), where each agent receives the weighted total of the tokens that it alone collected. It is the natural extension of the single agent problem, and represents the optimal utility in the single rover domain. The second utility was the Team Game (TG) utility where each agent received the full world utility. The third utility was the WLU, which represents the contribution an agent made to the token collection, by looking at the difference in the total token collection with and without that agent. The fourth and final utility was AU, where the agent's contribution is computed as the difference between the action it took and its expected action.. Each agent was controlled by a Q-learner. A learner's input space consisted of the location of the agent in the grid world, and the action space was the four directions that the agent could move. The Q-tables were initially set to zero, and the discounting parameter was set to 0.95. Actions were chosen stochastically based on Q-values, where the probability that an agent took action ai given state s =. In our experiments k was set to 50. Figure 4 shows the results for 10 agents on a 100 unitsquare grid where an episode consists of 10 time steps (including error bars of ± one σ). The results showed that SU produced poor results, results that were indeed worse than random actions. This is caused by all agents aiming to acquire the most valuable tokens, in effect competing rather than cooperating. The agents using TG fared better, but their learning was slow. This system was plagued by the signal-to-noise problem associated with each agent receiving the full world reward for each individual action they took. Notice both the selfish agents and those trained with TG had a drop in their performance in the early going, as they learned the "wrong" actions. Team game agents overcame this early setback whereas selfish agents never did. In contrast, agents using WLU and AU performed almost optimally, because the reinforcement signal they received more clearly showed how their actions affected the world reward. 2 In the actual implementation there are some tie breaking rules if more than one agent goes into the same square at the same time. Figure 5 shows results for 100 agents on a 1024 unit-square grid where an episode consists of 32 time steps. Qualitatively, the results are similar to the 10 agent case. However, note that the team game agents have a harder time learning, because in this case the reinforcement signal is even further diluted. We explore this scaling issue in more detail in Figure 6 . With very few agents, the selfish learners did not compete with each other as much and were able to obtain acceptable results. Their performance however, deteriorated rapidly, when the number of agents in the system increased. Similarly, agents using the team game reward were not hampered as much by the noise associated with other agents when the number of agents was low. As the system scaled up however, only the WLR-trained agents were able to operate collectively. This underscores the need for a utility that has good signal-to-noise properties so that the agents have an opportunity to learn the actions that will optimize their utilities.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Statistical relationships between journal use and research output at academic institutions in South Korea Abstract In this study, we analysed the statistical association between e-journal use and research output at the institution level in South Korea by performing comparative and diachronic analyses, as well as the analysis by field. The datasets were compiled from four different sources: national reports on research output indicators in science fields, two statistics databases on higher education institutions open to the public, and e-journal usage statistics generated by 47 major publishers. Due to the different data sources utilized, a considerable number of missing values appeared in our datasets and various mapping issues required corrections prior to the analysis. Two techniques for handling missing data were applied and the impact of each technique was discussed. In order to compile the institutional data by field, journals were first mapped, and then the statistics were summarized according to subject field. We observed that e-journal use exhibited stronger correlations with the number of publications and the times cited, in contrast to the number of undergraduates, graduates, faculty members and the amount of research funds, and this was the case regardless of the NA handling method or author type. The difference between the maximum correlation for the amount of external research funding with two average indicators and that of the correlation for e-journal use were not significant. Statistically, the accountability of e-journal use for the average times cited per article and the average JIF was quite similar with external research funds. It was found that the number of e-journal articles used had a strong positive correlation (Pearson's correlation coefficients of r [ 0.9, p \ 0.05) with the (2015 ( ) 103:751-777 DOI 10.1007( /s11192-015-1563 number of articles published in SCI(E) journals and the times cited regardless of the author type, NA handling method or time period. We also observed that the top-five institutions in South Korea, with respect to the number of publications in SCI(E) journals, were generally across a balanced range of academic activities, while producing significant research output and using published material. Finally, we confirmed that the association of e-journal use with the two quantitative research indicators is strongly positive, even for the analyses by field, with the exception of the Arts and Humanities. Usage statistics data by themselves are not a new phenomenon (Matthews 2009 ). Traditionally, libraries have maintained statistics records for gate counts, circulation, interlibrary loans, and information services (NISO 2007) . Academic libraries also frequently gather statistics on reserve items and submit reports to government agencies, parent institutions and library boards. Such information can then be used to understand work flow and improve library services. Since the rapid emergence of electronic resources and the explosion of online services becoming available through the internet, many institutions have acknowledged the benefits of investing in the collecting, reporting and analysis of usage statistics (Welch 2005) . Usage statistics for online resources have also been a primary analytical data source for public and private library consortia. The Virtual Library of Virginia consortia have undertaken a project to streamline, automate and standardize statistical data collection and the reporting process (Matthews 2009 ). Joint Information Systems Committee has been developing the Journal Usage Statistics Portal providing a 'one-stop-service' for librarians to view, download and analyze their usage reports. Since 2009, the Korea Institute of Science and Technology Information (KISTI) has consolidated the usage statistics of member institutions in order to provide integrated usage data with subscription and bibliographic information to members, as well as to monitor the use of e-journal packages distributed through the Korea Electronic Site Licensing Initiative (KESLI) consortia .. Recently, a number of researchers have attempted to measure scientific or research impact from usage data available online from publishers, aggregators, electronic resource management systems and link resolvers (Bollen et al. 2009 ). Larsen and Von Ins (2010) argued that the coverage of SCI has declined with the rapid growth of scientific publications. Existing citation databases such as WoS, Scopus and Google Scholar have limitations in coverage and depth for non-English language journals. Zainab et al. (2012) and Choi et al. (2013) argue that WoS and Scopus are comprehensive databases for English journals but do not adequately cover most national journals published in developing countries.. Usage data regarding PDF downloads, HTML views and SNS saves are considered as valuable, and complement traditional citation-based assessment metrics. The PLoS Medicine Editors (2006) predicted that new measures including the number of times downloaded, coverage in mainstream media, and times referenced in policy documents might be useful inputs to measure the impact of rarely cited but influential articles. ''Altmetrics'' builds on information from social media use, and is suggested to present a nuanced and multidimensional view of multiple research impact measures over time, together with traditional citation-based metrics (Priem and Piwowar 2012) . Bollen et al. (2009) analyzed and compared citation and usage networks, as well as various social network and hybrid measures to explore the most suitable methods for expressing and interpreting scientific impact. As a result, the 'Usage Closeness Centrality' incorporating 39 measures was deemed the best candidate for determining a 'consensus' view of scientific impact. Priem and Piwowar (2012) demonstrated that PDF downloads and HTML views correlate at moderate to high levels with almost all other Altmetrics. In particular, a moderately strong relationship between citation count and PDF/HTML download count for the three journals analyzed was reported in the study. Brody and Harnad (2005) postulated that if a correlation exists between citations and downloads, a higher rate of downloads in the first year of an article could be used to predict a higher number of eventual citations later. They identified an overall correlation of 0.4 between the citation numbers and download impact of articles in physics and mathematics archived in the UK's arXiv.org. Moed (2005) determined that during the first 3 months after an article is cited, the number of downloads increased 25 % compared to what would be expected had the article not been cited. In contrast, no relation between the usage factor and two measures of citation impact including the Journal Impact Factor and Elsevier's Source Normalized Impact per Paper (SNIP) metric was reported (CIBER Research Limited 2011) . Nevertheless, this particular report concluded that the new usage-based metric opens up the possibility of developing new ways of looking at scholarly communication, with different journals occupying very different niches within a complex ecosystem. Two reasons for the importance of download impact were highlighted by Brody and Harnad (2005) : (1) The proportion of download variance correlated with citation counts provides an early estimate of probable citation impact that can be tracked from the instant an article is made Open Access, and attains its maximum predictive power after 6 months; and (2) The portion of download variance that does not correlate with citation counts provides a second, partly independent estimate of the impact of an article, sensitive to another form of research usage that is not reflected in citation counts. In the same context, efforts to develop and substantiate usage-based metrics have been undertaken by several research groups (Bollen and Van de Sompel 2008; Gorraiz and Gumpenberger 2010) as well as the Counting Online Usage of NeTworked Electronic Resources (COUNTER) group (Shepherd 2011) .. It has generally been assumed that economic factors such as Gross Domestic Product (GDP), Gross Domestic Expenditures on Research and Development (GERD), and human resources have a linear or exponential relationship with research performance at the national level (Yoon 2007; Vinkler 2010) . According to Wood (1990) , personal characteristics and differences in research style, processes and techniques for research, as well as funding availability are the most important factors influencing the research productivity of academics. Heavy teaching loads were seen as a distraction from research activity in general. In particular, for the majority of science departments in academic institutions, the extent and continuation of funding are critical for facilitating research and many serious problems arise due to funding restrictions. However, to the best of our knowledge, there have been no previous studies investigating the statistical relationship between the production of resesarch publications and the use of them at the national or institutional level. Although the use of research publications is a daily necessity for researchers, investigations into the relationship between the use and production of research output at the institutional level in comparison to studies based on journal-specific metrics have been lacking.. In this study, our objective is to explore the relationship between research performance and the usage of publications at the level of institutions by performing comparative, diachronic analyses and an analysis by field. Specifically, we address the following three research questions:. 1. Which is most highly correlated with research output at the institutional level: human resources, economic factors or the use of research publications? 2. Does the extent of correlation of e-journal use with four research output measures for long term data differ when assessed from a short term perspective? 3. What is the statistical relationship between the use of research publications and research productivity at the institutional level (by field)?. Data, methodology and limitations

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