pinecone/core-2020-05-10-deduplication huggingface dataset:
Quiescence, Fairness, Testing, and the Notion of Implementation

AbstractTwo formalisms for concurrency, the Input/Output automaton model and the theory of testing, are compared and are shown to have common foundations. The relationship between the fair and quiescent preorders of I/O automata is investigated and the two preorders are shown to coincide subject to some restrictions. I/O automata are encoded into the theory of testing and the reversedmustpreorder is shown to be equivalent to the quiescent preorder for strongly convergent, finitely branching I/O automata up to encoding. Conversely, a theory of testing is defined directly on I/O automata, and the new reversedmustpreorder is shown to coincide with the quiescent preorder on strongly convergent, finitely branching I/O automata
Efficient Execution of Nondeterministic Parallel Programs on Asynchronous Systems

AbstractWe consider the problem of asynchronous execution of parallel programs. We assume that the original program is designed for a synchronous system, whereas the actual system may be asynchronous. We seek an automaticexecution scheme, which allows the asynchronous system to execute the synchronous program. Previous execution schemes provide solutions only for the case where the original program is deterministic. Here, we provide the first solution for the more general case where the original program can be nondeterministic (e.g., randomized). Our scheme is based on a novel agreement protocol for the asynchronous parallel setting. Our protocol allowsnasynchronous processors to agree onnword-sizedvalues inO(nlognloglogn)total work, assuming an oblivious adversary scheduler. Total work is defined to be the summation of the number of steps performed by all processors (including steps from busy waiting)
The Complexity of Parallel Prefix Problems on Small Domains

AbstractWe establish non-trivial lower bounds for several prefix problems in the CRCW PRAM model. The chaining problem is, given a binary input, for each 1 in the input, to find the index of the nearest 1 to its left. Our main result is that for an input ofnbits, solving the chaining problem usingO(n) processors requires inverse-Ackerman time. This matches the previously known upper bound. We also give a reduction to show that the same lower bound applies to a parenthesis matching problem, again matching the previously known upper bound. We also give reductions to show that similar lower bounds hold for the prefix maxima and the range maxima problem
On the Jacopini Technique

AbstractThe general concern of the Jacopini technique is the question: “Is it consistent to extend a given lambda calculus with certain equations?” The technique was introduced by Jacopini in 1975 in his proof that in the untyped lambda calculusΩis easy, i.e.,Ωcan be assumed equal to any other (closed) term without violating the consistency of the lambda calculus. The presentations of the Jacopini technique that are known from the literature are difficult to understand and hard to generalise. In this paper we generalise the Jacopini technique for arbitrary lambda calculi. We introduce the concept ofproof-replaceabilityby which the structure of the technique is simplified considerably. We illustrate the simplicity and generality of our formulation of the technique with some examples. We apply the Jacopini technique to theλμ-calculus, and we prove a general theorem concerning the consistency of extensions of theλμ-calculus of a certain form. Many well known examples (e.g., the easiness ofΩ) are immediate consequences of this general theorem
On the Complexity of Learning from Drifting Distributions

AbstractWe consider two models of on-line learning of binary-valued functions from drifting distributions due to Bartlett. We show that if each example is drawn from a joint distribution which changes in total variation distance by at mostO(ε3/(dlog(1/ε))) between trials, then an algorithm can achieve a probability of a mistake at mostεworse than the best function in a class of VC-dimensiond. We prove a corresponding necessary condition ofO(ε3/d). Finally, in the case that a fixed function is to be learned from noise-free examples, we show that if the distributions on the domain generating the examples change by at mostO(ε2/(dlog(1/ε))), then any consistent algorithm learns to within accuracyε
A Complete Axiomatization of Finite-state ACSR Processes

AbstractA real-time process algebra, called ACSR, has been developed to facilitate the specification and analysis of real-time systems. ACSR supports synchronous timed actions and asynchronous instantaneous events. Timed actions are used to represent the usage of resources and to model the passage of time. Events are used to capture synchronization between processes. To be able to specify real-time systems accurately, ACSR supports a notion of priority that can be used to arbitrate among timed actions competing for the use of resources and among events that are ready for synchronization. In addition to operators common to process algebra, ACSR includes the scope operator, which can be used to model timeouts and interrupts. Equivalence between ACSR terms is based on the notion of strong bisimulation. This paper briefly describes the syntax and semantics of ACSR and then presents a set of algebraic laws that can be used to prove equivalence of ACSR processes. The contribution of this paper is the soundness and completeness proofs of this set of laws. The completeness proof is for finite-state ACSR processes, which are defined to be processes without free variables under parallel operator or scope operator
Complexity of Equivalence Problems for Concurrent Systems of Finite Agents

AbstractA concurrent system of synchronous communicating agents is assembled from simpler sequential agents by parallel composition and hiding. For example,hide a1,…alin (p1‖p2…‖pn) describes the system of communicating agentsp1,…pnin which the communication eventsa1,…alare hidden. Consider descriptions of two systemspandqof synchronously communicating finite state agents. Assume that one wants to check whetherp∼qfor one of the commonly used equivalence ∼. We show that this question is PSPACE hard for all equivalences that lie between strong bisimulation and trace equivalences. For some equivalences exponential lower and upper bounds are proven. We also show that this problem is NP hard and co-NP hard even for a class of very simple finite agents
Termination of SystemF-bounded: A Complete Proof

AbstractSystemF-bounded is a second-order typedλ-calculus with subtyping which has been defined to carry out foundational studies about the type systems of object-oriented languages. The almost recursive nature of the essential feature of this system makes one wonder whether it retains the strong normalization property, with respect to first- and second-orderβϵreduction of systemF⩽. We prove that this is the case. The proof is carried out to the last detail to allow the reader to be convinced of its correctness
Axiomatizing Shuffle and Concatenation in Languages

AbstractWe consider the varietyLanggenerated by all language structures (PΣ,·,⊗+,0,1), and the varietyLg⩽of ordered algebras generated by the structures (PΣ,·,⊗0,1,⊆), wherePΣis the powerset ofΣ*, and whereB·Cis the complex concatenation of the languagesB,C⊆Σ*,B⊗Cis their shuffle product, andB+Cis their union. We prove that for each finite setEof equations valid inLangthere is a (finite) modelSEofEin which some inequation valid inLg⩽fails. It follows that neither variety is finitely axiomatizable
Time Bounded Frequency Computations

Abstract(1) We obtain two new results concerning the inclusion problem of polynomial time frequency classes with equal numbers of errors. 1.(m,m+d)P⊉(m+1,m+d+1)Pform<2d. 2.(m,m+d)P=(m+1,m+d+1)Pform⩾c(d) wherec(d) is large enough. This disproves a conjecture of Kinber. (2) We give a transparent proof of a generalization of Kinber's result that there exist arbitrarily complex problems admitting a polynomial time frequency computation. Several corollaries provide more insight into the structure of the hierarchy of polynomial time frequency classes. (3) The relationships between polynomial time frequency classes and selectivity classes are studied
A Worst-Case Analysis of the LZ2 Compression Algorithm

AbstractSheinwald, Lempel, and Ziv (1995,Inform. and Comput.116, 128–133) proved that the power of off-line coding is not useful if we want on-line decodable files, as far as asymptotical results are concerned. In this paper, we are concerned with the finite case and consider the notion of on-line decodable optimal parsing based on the parsing defined by the Ziv–Lempel (LZ2) compression algorithm. De Agostino and Storer (1996,Inform. Process. Lett.59, 169–174) proved the NP-completeness of computing the optimal parsing and that a sublogarithmic factor approximation algorithm cannot be realized on-line. We show that the Ziv–Lempel algorithm and two widely used practical implementations produce an O(n1/4) approximation of the optimal parsing, wherenis the length of the string. By working with de Bruijn sequences, we show also infinite families of binary strings on which the approximation factor isΘ(n1/4)
On Interval Routing Schemes and Treewidth

AbstractIn this paper, we investigate which processor networks allowk-label Interval Routing Schemes, under the assumption that costs of edges may vary. We show that for each fixedk⩾1, the class of graphs allowing such routing schemes is closed under minor-taking in the domain of connected graphs, and hence has a linear time recognition algorithm. This result connects the theory of compact routing with the theory of graph minors and treewidth. We show that every graph that does not containK2,:ras a minor has treewidth at most 2r−2. As a consequence, graphs that allowk-label Interval Routing Schemes under dynamic cost edges have treewidth at most 4k. Similar results are shown for other types of Interval Routing Schemes
Liveness in Timed and Untimed Systems

AbstractWhen proving the correctness of algorithms in distributed systems, one generally considerssafetyconditions andlivenessconditions. The Input/Output (I/O) automaton model and its timed version have been used successfully, but have focused on safety conditions and on a restricted form of liveness called fairness. In this paper we develop a new I/O automaton model, and a new timed I/O automaton model, that permit the verification of general liveness properties on the basis of existing verification techniques. Our models include a notion ofreceptivenesswhich extends the idea ofreceptivenessof other existing formalisms, and enables the use of compositional verification techniques. The presentation includes anembeddingof the untimed model into the timed model which preserves all the interesting attributes of the untimed model. Thus, our models constitute acoordinated frameworkfor the description of concurrent and distributed systems satisfying general liveness properties
Some Consequences of Cryptographical Conjectures forS12and EF

AbstractWe show that there is a pair of disjoint NP-sets, whose disjointness is provable inS12and which cannot be separated by a set in P/poly, if the cryptosystem RSA is secure. Further we show that factoring and the discrete logarithm are implicitly definable in any extension ofS12admitting an NP-definition of primes about which it can prove that no number satisfying the definition is composite. As a corollary we obtain that the Extended Frege (EF) proof system does not admit a feasible interpolation theorem unless the RSA cryptosystem is not secure and that an extension of EF by tautologiesτp(pprimes), formalizing thatpis not composite, as additional axioms do not admit a feasible interpolation theorem unless factoring and the discrete logarithm are in P/poly
Metafinite Model Theory

AbstractMotivated by computer science challenges, we suggest to extend the approach and methods of finite model theory beyond finite structures. We study definability issues and their relation to complexity onmetafinite structureswhich typically consist of (i) a primary part, which is a finite structure, (ii) a secondary part, which is a (usually infinite) structure that can be viewed as a structured domain of numerical objects, and (iii) a set of “weight” functions from the first part into the second. We discuss model-theoretic properties of metafinite structures, present results on descriptive complexity, and sketch some potential applications
Complexity and Categoricity

AbstractWe define a notion of a feasible Scott family of formulas for a feasible model and give various conditions on a Scott family which imply that two models with the same family are feasibly isomorphic. For example, ifAandBpossess a common strongly p-time Scott family and both have universe {1}*, then they are p-time isomorphic. These results are applied to the study of permutation structures, linear orderings, equivalence relations, and Abelian groups. For example, conditions on two permutation structures (A,f) and (B,g) are given which imply that (A,f) and (B,g) are p-time isomorphic
On Chromatic Sums and Distributed Resource Allocation

AbstractThis paper studies an optimization problem that arises in the context of distributed resource allocation: Given a conflict graph that represents the competition of processors over resources, we seek an allocation under which no two jobs with conflicting requirements are executed simultaneously. Our objective is to minimize theaverage response timeof the system. In alternative formulation this is known as theMinimum Color Sum (MCS)problem (E. Kubicka and A. J. Schwenk, 1989. An introduction to chromatic sums,in“Proceedings of the ACM Computer Science Conference,” pp. 39–45.). We show that the algorithm based on finding iteratively a maximum independent set (MaxIS) is a 4-approximation to the MCS. This bound is tight to within a factor of 2. We give improved ratios for the classes of bipartite, bounded-degree, and line graphs. The bound generalizes to a 4ρ-approximation of MCS for classes of graphs for which the maximum independent set problem can be approximated within a factor ofρ. On the other hand, we show that ann1−ε-approximation is NP-hard, for someε>0. For some instances of the resource allocation problem, such as theDining Philosophers, an efficient solution requiresedgecoloring of the conflict graph. We introduce theMinimum Edge Color Sum (MECS)problem which is shown to be NP-hard. We show that a 2-approximation to MECS(G) can be obtained distributively usingcompactcoloring withinO(log2n) communication round
A Collusion Problem and Its Solution

AbstractConsider a group of colluders, each with certain knowledge such as the identity of some other colluders, some cryptographic keys, and some data, possibly multiply encrypted. Two colluders can combine their knowledge if their current knowledge satisfies certain conditions. Their cryptographic keys can help decrypt each other's encrypted data, expanding their knowledge and revealing more collusion opportunities, and the process of collusion continues. The question we address is whether it is possible for the colluders to uncover a target set of unencrypted data. In this paper we formulate the collusion problem and provide an algorithm that determines whether a collusion problem has a solution and, if so, computes one. A solution is a specific way by which the colluders can uncover the hidden information. The solution generated by our algorithm is generally not one that involves the minimum number of colluders. We show, however, that to find such a solution is NP-complete. Complex communications protocols employing cryptographic building blocks are being developed to transfer information among some users and hide from others. The algorithm presented here can be applied to determine whether and how a subset of protocol users can discover during or after the protocol's execution the information that is to be hidden from them
Common Knowledge and Update in Finite Environments

AbstractLogics of knowledge have been shown to provide a useful approach to the high level specification and analysis of distributed systems. It has been proposed that such systems can be developed using knowledge- based protocols, in which agents' actions have preconditions that test their state of knowledge. Both computer-assisted analysis of the knowledge properties of systems and automated compilation of knowledge-based protocols require the development of algorithms for the computation of states of knowledge. This paper studies one of the computational problems of interest, the model checking problem for knowledge formulae in the S5nKripke structures generated by finite state environments in which states determine an observation for each agent. Agents are assumed to have perfect recall and may operate synchronously or asynchronously. It is shown that, in this setting, model checking of common knowledge formulae is intractable, but efficient incremental algorithms are developed for formulae containing only knowledge operators. Connections to knowledge updates and compilation of knowledge-based protocols are discussed
Growing Context-Sensitive Languages and Church–Rosser Languages

AbstractThe growing context-sensitive languages are characterized by a non-deterministic machine model, the so-calledshrinking two-pushdown automaton. Then the deterministic version of this automaton is considered, and it is shown that it characterizes the class ofgeneralized Church–Rosser languages. As a consequence we obtain the result that the class of (generalized) Church–Rosser languages and the class of context-free languages are incomparable under set inclusion, thus verifying a conjecture of McNaughtonet al.(1988,J. Assoc. Comput. Math.35, 324–344). Finally, we prove that each growing context-sensitive language is accepted in polynomial time by some one-way auxiliary pushdown automaton with a logarithmic space bound, which improves upon a result of Dahlhaus and Warmuth (1986,J. Comput. System Sci.33, 456–472)
Bridging across the log(n) Space Frontier

AbstractThis paper establishes the importance of even the lowest possible level of space bounded computations. We show that DLOG does not coincide with NLOG if and only if there exists a tally set in NSPACE(loglogn)\DSPACE(loglogn). This result stands in perfect analogy to the related results concerning linear space or exponential time. Moreover, the above problem is equivalent to the existence of a functions(n), with arbitrarily slow or rapid growth rate, that is nondeterministically fully space constructible but cannot be constructed deterministically. We also present a “hardest” fully space constructibles(n)∈O(loglogn), a functional counterpart of log-space complete languages. These nonrelativized results are obtained by the use of oracle machines consuming much larger amount of space, in range betweennand 2d·n
Conjunctions of Unate DNF Formulas: Learning and Structure

AbstractA central topic in query learning is to determine which classes of Boolean formulas are efficiently learnable with membership and equivalence queries. We consider the class Rkconsisting of conjunctions ofkunate DNF formulas. This class generalizes the class ofk-clause CNF formulas and the class of unate DNF formulas, both of which are known to be learnable in polynomial time with membership and equivalence queries. We prove that R2can be properly learned with a polynomial number of polynomial-size membership and equivalence queries, but can be properly learned in polynomial time with such queries if and only if P=NP. Thus the barrier to properly learning R2with membership and equivalence queries is computational rather than informational. Few results of this type are known. In our proofs, we use recent results of Hellersteinet al.(1997,J. Assoc. Comput. Mach.43(5), 840–862), characterizing the classes that are polynomial-query learnable, together with work of Bshouty on the monotone dimension of Boolean functions. We extend some of our results to Rkand pose open questions on learning DNF formulas of small monotone dimension. We also prove structural results for Rk. We construct, for any fixedk⩾2, a class of functionsfthat cannot be represented by any formula in Rk, but which cannot be “easily” shown to have this property. More precisely, for any functionfonnvariables in the class, the value offon any polynomial-size set of points in its domain is not a witness thatfcannot be represented by a formula in Rk. Our construction is based on BCH codes
A Canonical Form of Vector Machines

AbstractWe introduce RS-vector machines (RS-VMs) as a canonical form of vector machines. They are based on vector operations calledrepeatandstretch.Repeatenlarges a vector (a1,a2, …,am) to (a1,a2, …,am,a1,a2, …,am) andstretchenlarges (a1,a2, …,am) to (a1,a1,a2,a2, …,am,am), when the expansion factord(m)=2. It is shown that we can change the power of RS-VMs depending on this single parameterd(m): (i) Polynomial-time RS-VMs ofd(m)=2 have the same power as polynomial-space TMs, and (ii) polynomial-time RS-VMs ofd(m)=mhave the same power as exponential-time, polynomial-alternation, alternating TMs. The more general results are: (iii) RS-VMs ofd(m)=k(k⩾2 is constant) have the same power as RS-VMs ofd(m)=2; (iv) a wide variety ofd(m)s such asd(m)=m,m2, …,cmk, 2m/m, …,A(2, m)/m, have at least the same power asd(m)=m, whereA(i, j) is Ackermann's function; and (v) any polynomiald(m) inmcannot surpass the power ofd(m)=m
Efficient Learning with Virtual Threshold Gates

AbstractWe reduce learning simple geometric concept classes to learning disjunctions over exponentially many variables. We then apply an online algorithm called Winnow whose number of prediction mistakes grows only logarithmically with the number of variables. The hypotheses of Winnow are linear threshold functions with one weight per variable. We find ways to keep the exponentially many weights of Winnow implicitly so that the time for the algorithm to compute a prediction and update its “virtual” weights is polynomial. Our method can be used to learnd-dimensional axis-parallel boxes whendis variable and unions ofd-dimensional axis-parallel boxes whendis constant. The worst-case number of mistakes of our algorithms for the above classes is optimal to within a constant factor, and our algorithms inherit the noise robustness of Winnow. We think that other online algorithms with multiplicative weight updates whose loss bounds grow logarithmically with the dimension are amenable to our methods
Error-Free and Best-Fit Extensions of Partially Defined Boolean Functions

AbstractIn this paper, we address a fundamental problem related to the induction of Boolean logic: Given a set of data, represented as a set of binary “truen-vectors” (or “positive examples”) and a set of “falsen-vectors” (or “negative examples”), we establish a Boolean function (or an extension)f, so thatfis true (resp., false) in every given true (resp., false) vector. We shall further require that such an extension belongs to a certain specified class of functions, e.g., class of positive functions, class of Horn functions, and so on. The class of functions represents our a priori knowledge or hypothesis about the extensionf, which may be obtained from experience or from the analysis of mechanisms that may or may not cause the phenomena under consideration. The real-world data may contain errors, e.g., measurement and classification errors might come in when obtaining data, or there may be some other influential factors not represented as variables in the vectors. In such situations, we have to give up the goal of establishing an extension that is perfectly consistent with the given data, and we are satisfied with an extensionfhaving the minimum number of misclassifications. Both problems, i.e., the problem of finding an extension within a specified class of Boolean functions and the problem of finding a minimum error extension in that class, will be extensively studied in this paper. For certain classes we shall provide polynomial algorithms, and for other cases we prove their NP-hardness