pinecone/core-2020-05-10-deduplication huggingface dataset:
Uniform Closures: Order-Theoretically Reconstructing Logic Program Semantics and Abstract Domain Refinements

AbstractThe notion of uniform closure operator is introduced, and it is shown how this concept surfaces in two different areas of application of abstract interpretation, notably in semantics design for logic programs and in the theory of abstract domain refinements. In logic programming, uniform closures permit generalization, from an order-theoretic perspective, of the standard hierarchy of declarative semantics. In particular, we show how to reconstruct the model-theoretic characterization of the well-known s-semantics using pure order-theoretic concepts only. As far as the systematic refinement operators on abstract domains are concerned, we show that uniform closures capture precisely the property of a refinement of being invertible, namely of admitting a related operator that simplifies as much as possible a given abstract domain of input for that refinement. Exploiting the same argument used to reconstruct the s-semantics of logic programming, we yield a precise relationship between refinements and their inverse operators: we demonstrate that they form an adjunction with respect to a conveniently modified complete order among abstract domains
Structural Induction and Coinduction in a Fibrational Setting

AbstractWe present a categorical logic formulation of induction and coinduction principles for reasoning about inductively and coinductively defined types. Our main results provide sufficient criteria for the validity of such principles: in the presence of comprehension, the induction principle for initial algebras is admissible, and dually, in the presence of quotient types, the coinduction principle for terminal coalgebras is admissible. After giving an alternative formulation of induction in terms of binary relations, we combine both principles and obtain a mixed induction/coinduction principle which allows us to reason about minimal solutionsX≅σ(X) whereXmay occur both positively and negatively in the type constructor σ. We further strengthen these logical principles to deal with contexts and prove that such strengthening is valid when the (abstract) logic we consider is contextually/functionally complete. All the main results follow from a basic result about adjunctions between “categories of algebras” (inserters)
On Performance Congruences for Process Algebras

AbstractBased on the hypothesis of durational actions and process synchronization with “busy waiting” mechanism,performance equivalencehas been proposed to introduce a simple form of performance evaluation in process algebras. This equivalence enjoys many of the pleasant properties of those in the untimed setting but it is not a congruence for parallel composition with synchronization. In this paper we give a bisimulation-based characterization of the coarsest congruence contained within performance equivalence (and discuss alternative formulations). This problem was left open in several papers. We study how the new equivalence, calledperformance congruence, relates with other closed equivalences in the literature and show that, unlike other proposals, it is a natural extension of those standard in the untimed setting. The weak version of performance congruence, which abstracts from internal details, is also studied. A number of examples of processes related or taken apart by performance congruence, and its weak version, are provided. A nontrivial one is also presented to illustrate the utility of the new congruences. The paper concludes with further observations concerning performance congruence and with a discussion on related and further interesting work
A Conservative Look at Operational Semantics with Variable Binding

AbstractWe set up a formal framework to describe transition system specifications in the style of Plotkin. This framework has the power to express many-sortedness, general binding mechanisms, and substitutions, among other notions such as negative hypotheses and unary predicates on terms. The framework is used to present a conservativity format in operational semantics, which states sufficient criteria to ensure that the extension of a transition system specification with new transition rules does not affect the semantics of the original terms
Decidability and Complexity Analysis by Basic Paramodulation

AbstractIt is shown that for sets of Horn clauses saturated underbasic paramodulationthe word and unifiability problems are in NP, and the number of minimal unifiers is simply exponential (i). For Horn sets saturated w.r.t. a special ordering under the more restrictive inference rule ofbasic superposition, the word and unifiability problems are still decidable and unification is finitary (ii). These two results are applied to the following languages. Forshallowpresentations (equations with variables at depth at most one) we show that the closure under paramodulation can be computed in polynomial time. Applying result (i), it follows that shallow unifiability is in NP, which is optimal since unifiability in ground theories is already NP-hard. The shallow word problem is even shown to be polynomial. Generalizing shallow theories to the Horn case, we obtain (two versions of) a language we callCatalog, a natural extension of Datalog to include functions and equality. The closure under paramodulation is finite for Catalog sets, hence (i) still applies. For Catalog sets S the decidability of the full first-order theory of T(F)=Sis shown as well. Finally we definestandard theories, which include and significantly extendshallowtheories. Standard presentations can be finitely closed under superposition and result (ii) applies, thus obtaining a new fundamental class with decidable word and unifiability problems and where unification is finitary
Verifiable Properties of Database Transactions

AbstractIt is often necessary to ensure that database transactions preserve integrity constraints that specify valid database states. While it is possible to monitor for violations of constraints at run-time, rolling back transactions when violations are detected, it is preferable to verify correctness statically,beforetransactions are executed. This can be accomplished if we can verify transaction safety with respect to a set of constraints by means of calculatingweakest preconditions. We study properties of weakest preconditions for a number of transaction and specification languages. We show that some simple transactions do not admit weakest preconditions over first-order logic and some of its extensions such as first-order logic with counting and monadicΣ11. We also show that the class of transactions that admit weakest preconditions over first-order logic cannot be captured by any transaction language. We consider a strong local form of verifiability, and show that it is different from the general form. We define robustly verifiable transactions as those that can be statically analyzed regardless of extensions to the signature of the specification language, and we show that the class of robustly verifiable transactions over first-order logic is exactly the class of transactions that admit the local form of verifiability. We discuss the implications of these results for the design of verifiable transaction languages
Threshold Circuits of Small Majority-Depth

AbstractConstant-depth polynomial-size threshold circuits are usually classified according to their total depth. For example, the best known threshold circuits for iterated multiplication and division have depths four and three, respectively. In this paper, the complexity of threshold circuits is investigated from a different point of view: explicit AND, OR gates are allowed in the circuits, and a threshold circuit is said to have majority-depthdif no path traverses more thandthreshold gates. It is then shown that iterated multiplication can be computed by polynomial-size threshold circuits of total depth five but of majority-depth three. Circuits of depth four and majority-depth two are obtained for division and powering. These results rely on a careful implementation of iterated addition and Chinese remaindering. In addition, a simple symbolic calculus for composing circuit classes is developed: this notation allows for a concise and elegant presentation of the results
Dynamic Dictionary Matching in External Memory

AbstractIn thedynamic dictionary matchingproblem, a dictionaryDcontains a set of patterns that can change over time under insertion and deletion of individual patterns. Given an arbitrary textT, we must efficiently list all the dictionary patterns that occur at each text position. We investigate the I/O complexity of this problem for a large dictionary that must be stored in external storage devices. By following a completely new approach, we devise an efficient solution which is based upon the SB-tree data structure (P. Ferragina and R. Grossi, 1995,in“Proc. ACM Symposium on Theory of Computing,” pp. 693–702), and a novel notion of certificate for the dictionary matching problem. Our data structure can be adapted to efficiently work in main memory and to solve other problems, thus providing a new insight into the nature of the dictionary matching problem
The Expressive Power of Stratified Logic Programs with Value Invention

AbstractThe expressive power of the family wILOG(⌝)of relational query languages is investigated. The languages are rule based, with value invention and stratified negation. The semantics for value invention is based on Skolem functor terms. We study a hierarchy of languages based on the number of strata allowed in programs. We first show that, in presence of value invention, the class of stratified programs made of two strata has the expressive power of the whole family, thus expressing the computable queries. We then show that the language wILOG≠of programs with nonequality and without negation expresses the mono- tone computable queries, and that the language wILOG1/2, ⌝of semipositive programs expresses the semimonotone computable queries
Usage Counting Analysis for Lazy Functional Languages

AbstractIf it can be determined at compile-time how many times values will be used within lazy functional programs, a number of useful optimisations can be performed. For example, call-by-need parameter passing can be converted to call-by-name, and in-place updating and compile-time garbage collection can be performed. In this paper, it is shown how this usage counting information can be obtained by static analysis. This analysis is not itself a major contribution of this paper; similar analyses have been defined before. The major contributions of this paper are that it provides a framework against which this analysis can be proved correct for a lazy functional language, and the analysis is proved to be correct with respect to this framework. The framework for proving the correctness of the analysis is provided by defining a store semantics which counts the number of times values are used
The Generating Power of Total Deterministic Tree Transducers

AbstractAttributed tree transducers are abstract models used to study properties of attribute grammars. One abstraction which occurs when modeling attribute grammars by attributed tree transducers is that arbitrary trees over a ranked alphabet are taken as input, instead of derivation trees of a context-free grammar. In this paper we show that with respect to the generating power this isnotan abstraction; i.e., we show that attributed tree transducers and attribute grammars generate the same class of term (or tree) languages. To prove this, a number of results concerning the generating power of top-down tree transducers are established, which are interesting in their own. We also show that the classes of output languages of attributed tree transducers form a hierarchy with respect to the number of attributes. The latter result is achieved by proving a hierarchy of classes of tree languages generated by context-free hypergraph grammars with respect to their rank
Noise-Tolerant Parallel Learning of Geometric Concepts

AbstractWe present several efficient parallel algorithms for PAC-learning geometric concepts in a constant-dimensional space. The algorithms are robust even against malicious classification noise of any rate less than 1/2. We first give an efficient noise-tolerant parallel algorithm to PAC-learn the class of geometric concepts defined by a polynomial number of (d−1)-dimensional hyperplanes against an arbitrary distribution where each hyperplane has a slope from a set of known slopes. We then describe how boosting techniques can be used so that our algorithms' dependence onεandδdoes not depend ond. Next, we give an efficient noise-tolerant parallel algorithm to PAC-learn the class of geometric concepts defined by a polynomial number of (d−1)-dimensional hyperplanes (of unrestricted slopes) against a uniform distribution. We then show how to extend our algorithm to learn this class against any (unknown) product distribution. Next we define a complexity measure of any setSof (d−1)-dimensional surfaces that we call thevariantofSand prove that the class of geometric concepts defined by surfaces of polynomial variant can be efficiently learned in parallel under a product distribution (even under malicious classification noise). Furthermore, we show that the VC-dimension of the class of geometric concepts defined by a single surface of variant one is ∞. Finally, we give an efficient, parallel, noise-tolerant algorithm to PAC-learn any 2-dimensional geometric concept defined by a setSof 1-dimensional surfaces of polynomial length under a uniform distribution
A Fully Abstract Semantics for Concurrent Constraint Programming

AbstractA compositional and fully abstract semantics for concurrent constraint programming is developed. It is the first fully abstract semantics which takes into account both non-determinism, infinite computations, and fairness. We present a simple concurrent constraint programming language, whose semantics is given by a set of reduction rules augmented with fairness requirements. In the fully abstract semantics we consider two aspects of a trace, viz. the function computed by the trace (the functionality) and the set of input and output data (the limit of the trace). We then derive the fully abstract semantics from the set of traces using a closure operation. We give two proofs of full abstraction; the first relies on the use of a syntactically infinite context. The second proof requires only a finite context, but assumes as input a representation of the function to be computed by the context. Finally, we examine the algebraic properties of the programming language with respect to the fully abstract semantics. It turns out that the non-deterministic selection operation can be defined using operations derived from parallel composition and the usual set-theoretic operations on sets of traces
On the Modelling of Search in Theorem Proving— Towards a Theory of Strategy Analysis

AbstractWe present a model for representing search in theorem proving. This model captures the notion ofcontraction, which has been central in some of the recent developments in theorem proving. We outline an approach to measuring the complexity of search which can be applied to analyze and evaluate the behaviour of theorem-proving strategies. Using our framework, we compare contraction-based strategies of different contraction power and show how they affect the evolution of the respective search spaces during the derivation
A Calculus for Cryptographic Protocols: The Spi Calculus

AbstractWe introduce the spi calculus, an extension of the pi calculus designed for describing and analyzing cryptographic protocols. We show how to use the spi calculus, particularly for studying authentication protocols. The pi calculus (without extension) suffices for some abstract protocols; the spi calculus enables us to consider cryptographic issues in more detail. We represent protocols as processes in the spi calculus and state their security properties in terms of coarse-grained notions of protocol equivalence
Computations on Nondeterministic Cellular Automata

AbstractThis work concerns the trade-offs between the dimension and the time and space complexity of computations on nondeterministic cellular automata. We assume that the space complexity is the diameter of area in space involved in computation. It is proved that (1) every nondeterministic cellular automata (NCA) A of dimensionr, computing a predicatePwith time complexityT(n) and space complexityS(n) can be simulated byr-dimensional NCA with time and space complexityO(T1/(r+1)Sr/(r+1)) and byr+1 dimensional NCA with time and space complexityO(T1/2+S), whereTandSare functions constructible in time, (2) for any predicatePand integerr>1 if A is a fastestr-dimensional NCA computingPwith time complexityT(n) and space complexityS(n), thenT=O(S), and (3) ifTr,Pis the time complexity of a fastestr-dimensional NCA computing predicatePthenTr+1,P=O((Tr, P)1−r/(r+1)2),Tr+1,P=O((Tr, P)1+2/r).Similar problems for deterministic cellular automata (CA) are discussed
Positive Versions of Polynomial Time

AbstractWe show that restricting a number of characterizations of the complexity classPto be positive (in natural ways) results in the same class of (monotone) problems, which we denote byposP. By a well-known result of Razborov,posPis a proper subclass of the class of monotone problems inP. We exhibit complete problems forposPvia weak logical reductions, as we do for other logically defined classes of problems. Our work is a continuation of research undertaken by Grigni and Sipser, and subsequently Stewart; indeed, we introduce the notion of a positive deterministic Turing machine and consequently solve a problem posed by Grigni and Sipser
On Computation with Pulses

AbstractWe explore the computational power of formal models for computation with pulses. Such models are motivated by realistic models for biological neurons and by related new types of VLSI (“pulse stream VLSI”). In preceding work it was shown that the computational power of formal models for computation with pulses is quite high if the pulses arriving at a computational unit have an approximately linearly rising or linearly decreasing initial segment. This property is satisfied by common models for biological neurons. On the other hand, several implementations of pulse stream VLSI employ pulses that are approximately piecewise constant (i.e., step functions). In this article we investigate the relevance of the shape of pulses in formal models for computation with pulses. The results show that the computational power drops significantly if one replaces pulses with linearly rising or decreasing initial segments by piecewise constant pulses. We provide an exact characterization of the latter model in terms of a weak version of a random access machine (RAM). We also compare the language recognition capability of a recurrent version of this model with that of deterministic finite automata and Turing machines
Unfair Problems and Randomized Algorithms for Metrical Task Systems

AbstractBorodin, Linial, and Saks introduced a general model for online systems calledmetrical task systems(1992,J. Assoc. Comput. Mach.39(4), 745–763). In this paper, the unfair two state problem, a natural generalization of the two state metrical task system problem, is studied. A randomized algorithm for this problem is presented, and it is shown that this algorithm is optimal. Using the analysis of the unfair two state problem, a proof of a decomposition theorem similar to that of Blum, Karloff, Rabani, and Saks (1992, “Proc. 33rd Symposium on Foundations of Computer Science,” pp. 197–207) is presented. This theorem allows one to design divide and conquer algorithms for specific metrical task systems. Our theorem gives the same bounds asymptotically, but it has less restrictive boundary conditions
A Finite Equational Axiomatization of the Functional Algebras for the Lambda Calculus

AbstractA lambda theory satisfies an equation between contexts, where a context is aλ-term with some “holes” in it, if all the instances of the equation fall within the lambda theory. In the main result of this paper it is shown that the equations (between contexts) valid in every lambda theory have an explicit finite equational axiomatization. The variety of algebras determined by the above equational theory is characterized as the class of isomorphic images of functional lambda abstraction algebras. These are algebras of functions and naturally arise as the “coordinatizations” of environment models or lambda models, the natural combinatory models of the lambda calculus. The main result of this paper is also applied to obtain a completeness theorem for the infinitary lambda calculus recently introduced by Berarducci
Group Axioms for Iteration

AbstractIteration theories provide a sound and complete axiomatization of the equational properties of the iteration (or fixed point) operation in many models of theoretical computer science including ordered and metric structures, trees and synchronization trees. All known equational axiomatizations of iteration theories consist of a small set of equational axioms for Conway theories and a complicated equation scheme, the commutative identity. Here we associate an identity with each finite semigroup. We prove that the set consisting of the Conway identities and the group identities associated with the finite (simple) groups is complete. Moreover, we prove that the Conway identities and a subcollection of the semigroup identities associated with a subclass of the finite semigroups is complete iff each finite (simple) group divides one of the semigroups in the subclass. We also formulate a conjecture and study its consequences. The results are a generalization of Krob's axiomatization of the equational theory of the regular sets
Set Constraints and Automata

AbstractWe define a new class of automata which is an acceptor model for mappings from the set of termsTΣover a ranked alphabetΣinto a setEof labels. WhenE={0,1}nan automaton can be viewed as an acceptor model forn-tuples of tree languages. We prove decidability of emptiness and closure properties for this class of automata. As a consequence of these results, we prove decidability of satisfiability of systems of positive and negative set constraints without projection symbols. We prove the decidability of the satisfiability problem for systems of positive and negative set constraints without projection symbols. Moreover we prove that a nonempty set of solutions always contain a regular solution (i.e., an-tuple of regular tree languages). We also deduce decidability results for properties of sets of solutions of systems of set constraints
Perpetual Reductions inλ-Calculus

AbstractThis paper surveys a part of the theory ofβ-reduction inλ-calculus which might aptly be calledperpetual reductions. The theory is concerned withperpetual reduction strategies, i.e., reduction strategies that compute infinite reduction paths fromλ-terms (when possible), and withperpetual redexes, i.e., redexes whose contraction inλ-terms preserves the possibility (when present) of infinite reduction paths. The survey not only recasts classical theorems in a unified setting, but also offers new results, proofs, and techniques, as well as a number of applications to problems inλ-calculus and type theory
Order-Sorted Inductive Types

AbstractSystemFω⩽is an extension of systemFωwith subtyping and bounded quantification. Order-sorted algebra is an extension of many-sorted algebra with overloading and subtyping. We combine both formalisms to obtainIFω⩽, a higher-order typedλ-calculus with subtyping, bounded quantification, and order-sorted inductive types, i.e., data types with built-in subtyping and overloading. Moreover we show thatIFω⩽enjoys important meta-theoretic properties, including confluence, strong normalization, subject reduction, and decidability of type checking