pinecone/core-2020-05-10-deduplication huggingface dataset:
Inductive Synthesis of Recursive Processes from Logical Properties

AbstractThis paper proposes an inductive synthesis algorithm for a recursive process. To synthesize a process, facts, which must be satisfied by the target process, are given to the algorithm one by one since such facts are infinitely many in general. When n facts are input to the algorithm, it outputs a process which satisfies the given n facts. And this generating process is repeated infinitely many times. To represent facts of a process, we adopt a subcalculus of μ-calculus. First, we introduce a new preorder ⩽d on recursive processes based on the subcalculus to discuss its properties. p⩽dq means that p⊨f implies q⊨f, for all formulae f in the subcalculus. Then, its discriminative power and relationship with other preorders are also discussed. Finally, we present the synthesis algorithm. The correctness of the algorithm can be stated that the output sequence of processes by the algorithm converges to a process, which cannot be distinguished from the intended one (if we could know it) by a given enumeration of facts, in the limit. A prototype system based on the algorithm is stated as well
Bounded Queries, Approximations, and the Boolean Hierarchy

AbstractThis paper investigates nondeterministic bounded query classes in relation to the complexity of NP-hard approximation problems and the Boolean Hierarchy. Nondeterministic bounded query classes turn out be rather suitable for describing the complexity of NP-hard approximation problems. The results in this paper take advantage of this machine-based model to prove that in many cases, NP-approximation problems have the upward collapse property. That is, a reduction between NP-approximation problems of apparently different complexity at a lower level results in a similar reduction at a higher level. For example, if MAXCLIQUE reduces to (log n)-approximating MAXCLIQUE using many–one reductions, then the Traveling Salesman Problem (TSP) is equivalent to MAXCLIQUE under many–one reductions. Several upward collapse theorems are presented in this paper. The proofs of these theorems rely heavily on the machinery provided by the nondeterministic bounded query classes. In fact, these results depend on a surprising connection between the Boolean hierarchy and nondeterministic bounded query classes
Uniform Generation of NP-Witnesses Using an NP-Oracle

AbstractA uniform generation procedure for NP is an algorithm that, given any input in a fixed NP-language, outputs a uniformly distributed NP-witness for membership of the input in the language. We present a uniform generation procedure for NP that runs in probabilistic polynomial time with an NP-oracle. This improves upon results of M. Jerrum et al. (1986, Theoret. Comput. Sci.43, 169–188), which either require a ΣP2 oracle or obtain only almost uniform generation. Our procedure utilizes ideas originating in the works of M. Sipser, and L. Stockmeyer (respectively, 1983, in Proceedings of the 15th Annual Symposium on the Theory of Computing, ACM, New York), and Jerrum et al. (1986)
Strong Fairness and Full Abstraction for Communicating Processes

AbstractWe construct several denotational semantics for communicating processes that incorporate assumptions of strong (process) fairness. Strong fairness is the guarantee that every process enabled infinitely often will make progress infinitely often. Modeling fairness compositionally requires care: generally speaking, the fair computations of a command cannot be defined only in terms of the fair computations of its component commands. For this reason, we introduce the notion of parameterized fairness, which generalizes fairness sufficiently to admit a compositional characterization. In each of these semantics, a command's meaning is simply the set of fair traces representing its fair computations; each fair trace records the steps made along a computation as well as additional information made explicit by the definition of parameterized fairness. Each semantics obtains full abstraction with respect to a natural notion of strongly fair program behavior: two terms are given identical meanings precisely when they exhibit the same behaviors in all program contexts
Higher-Order Substitutions

AbstractThe λσ-calculus is a concrete λ-calculus of explicit substitutions, designed for reasoning about implementations of λ-calculi. Higher-order abstract syntax is an approach to metaprogramming that explicitly captures the variable-binding aspects of programming language constructs. A new calculus of explicit substitutions for higher-order abstract syntax is introduced, allowing a high-level description of variable binding in object languages while also providing substitutions as explicit programmer-manipulable data objects. The new calculus is termed the λσβ0-calculus, since it makes essential use of an extension of β0-unification (described in another paper). Termination and confluence are verified for the λσβ0-calculus similarly to that for the λσ-calculus, and an efficient implementation is given in terms of first-order renaming substitutions. The verification of confluence makes use of a verified adaptation of Nipkow's higher-order critical pairs lemma to the forms of rewrite rules required for the statement of the λσβ0-calculus
Perpetuality and Uniform Normalization in Orthogonal Rewrite Systems

AbstractWe study perpetuality of reduction steps, as well as perpetuality of redexes, in orthogonal rewrite systems. A perpetual step is a reduction step which retains the possibility of infinite reductions. A perpetual redex is a redex which, when put into an arbitrary context, yields a perpetual step. We generalize and refine existing criteria for the perpetuality of reduction steps and redexes in orthogonal term rewriting systems and the λ-calculus due to Bergstra and Klop and others. We first introduce context-sensitive conditional expression reduction systems (CCERSs) and define a concept of orthogonality (which implies confluence) for them. In particular, several important λ-calculi and their extensions and restrictions can naturally be embedded into orthogonal CCERSs. We then define a perpetual reduction strategy which enables one to construct minimal (w.r.t. Lévy's permutation ordering on reductions) infinite reductions in orthogonal fully-extended CCERSs. Using the properties of the minimal perpetual strategy, we prove 1.perpetuality of any reduction step that does not erase potentially infinite arguments, which are arguments that may become, via substitution, infinite after a number of outside steps, and 2.perpetuality (in every context) of any safe redex, which is a redex whose substitution instances may discard infinite arguments only when the corresponding contracta remain infinite. We prove both these perpetuality criteria for orthogonal fully-extended CCERSs and then specialize and apply them to restricted λ-calculi, demonstrating their usefulness. In particular, we prove the equivalence of weak and strong normalization (whose equivalence is here called uniform normalization) for various restricted λ-calculi, most of which cannot be derived from previously known perpetuality criteria
On Equations for Union-Free Regular Languages

AbstractIn this paper we consider the variety UF generated by all algebras of binary relations equipped with the operations of composition, reflexive-transitive closure, and the empty set and the identity relation as constants. This variety coincides with the variety generated by the union-free reducts of Kleene algebras of languages and its free objects are formed by union-free regular languages, that is, regular languages represented by regular expressions having no occurrence of +. We show that the variety UF is not finitely based. The situation does not change if we consider the variety UF∨ generated by the above algebras of binary relations equipped with the conversion operation
Semantics of Temporal Classes

AbstractA model theory of a typed, declarative, temporal object-oriented language system is presented. The declarative nature of the language makes it very different from the dominating procedural, strongly typed object-oriented programming languages. In this declarative system, methods are specified in a high-level, temporal constraint language. Two fundamental properties of these constraints are that they have an execution model and algebraic semantics. The model theory is based on temporal order-sorted algebras with predicates. A variety of orderings are explored in order to represent various types of inheritance, as well as the subtyping discipline. Temporal classes are viewed as temporal theories and some inheritance relationships as morphisms of temporal theories. A model of a temporal class is a temporal order-sorted structure with predicates which satisfies a set of temporal constraints specified in that class. Morphisms of those models are naturally required to preserve type coercions. A distinguished model of a temporal theory is constructed as a colimit of a suitably defined functor. This colimit construction reflects the temporal nature of the paradigm and generalizes the classical initial algebra semantics. In contradistinction to major difficulties in developing a model theory for full-fledged, typed procedural object-oriented languages, this paper shows that such a task becomes possible for a suitably defined declarative object-oriented language. This, in particular, leads to model-theoretic results on the preservation of the behavioral properties in the inheritance hierarchies
Pushdown Processes: Games and Model-Checking

AbstractA pushdown game is a two player perfect information infinite game on a transition graph of a pushdown automaton. A winning condition in such a game is defined in terms of states appearing infinitely often in the play. It is shown that if there is a winning strategy in a pushdown game then there is a winning strategy realized by a pushdown automaton. An EXPTIME procedure for finding a winner in a pushdown game is presented. The procedure is then used to solve the model-checking problem for the pushdown processes and the propositional μ-calculus. The problem is shown to be DEXPTIME-complete
A Partition Refinement Algorithm for the π-Calculus

AbstractThe partition refinement algorithm is the basis for most of the tools for checking bisimulation equivalences and for computing minimal realisations of CCS-like finite state processes. In this paper, we present a partition refinement algorithm for the π-calculus, a development of CCS where channel names can be communicated. It can be used to check bisimilarity and to compute minimal realisations of finite control processes—the π-calculus counterpart of CCS finite state processes. The algorithm is developed for strong open bisimulation and can be adapted to late and early bisimulations, as well as to weak bisimulations. To arrive at the algorithm, a few laws, proof techniques, and four characterizations of open bisimulation are proved
On the Formalization of the Modal μ-Calculus in the Calculus of Inductive Constructions

AbstractWe present a natural deduction proof system for the propositional modal μ-calculus and its formalization in the calculus of inductive constructions. We address several problematic issues, such as the use of higher-order abstract syntax in inductive sets in the presence of recursive constructors, and the formalization of modal (sequent-style) rules and of context sensitive grammars. The formalization can be used in the system Coq, providing an experimental computer-aided proof environment for the interactive development of error-free proofs in the modal μ-calculus. The techniques we adopt can be readily ported to other languages and proof systems featuring similar problematic issues
Rollback-Dependency Trackability: A Minimal Characterization and Its Protocol

AbstractConsidering a checkpoint and communication pattern, the rollback-dependency trackability (RDT) property stipulates that there is no hidden dependency between local checkpoints. In other words, if there is a dependency between two checkpoints due to a noncausal sequence of messages (Z-path), then there exists a causal sequence of messages (C-path) that doubles the noncausal one and that establishes the same dependency.This paper introduces the notion of RDT-compliance. A property defined on Z-paths is RDT-compliant if the causal doubling of Z-paths having this property is sufficient to ensure RDT. Based on this notion, the paper provides examples of such properties. Moreover, these properties are visible, i.e., they can be tested on the fly. One of these properties is shown to be minimal with respect to visible and RDT-compliant properties. In other words, this property defines a minimal visible set of Z-paths that have to be doubled for the RDT property to be satisfied.Then, a family of communication-induced checkpointing protocols that ensure on-the-fly RDT properties is considered. Assuming processes take local checkpoints independently (called basic checkpoints), protocols of this family direct them to take on-the-fly additional local checkpoints (called forced checkpoints) in order that the resulting checkpoint and communication pattern satisfies the RDT property. The second contribution of this paper is a new communication-induced checkpointing protocol P. This protocol, based on a condition derived from the previous characterization, tracks a minimal set of Z-paths and breaks those not perceived as being doubled. Finally, a set of communication-induced checkpointing protocols are derived from P. Each of these derivations considers a particular weakening of the general condition used by P. It is interesting to note that some of these derivations produce communication-induced checkpointing protocols that have already been proposed in the literature
Iterated Function Systems and Control Languages

AbstractValuations—morphisms from (Σ*, ·, e) to ((0, ∞), ·, 1)—are a generalization of Bernoulli morphisms introduced by Eilenberg [“Automata, Languages, and Machines”, Academic Press, New York, 1974]. Here, we show how to generalize the notion of entropy (of a language) in order to obtain new formulas to determine the Hausdorff dimension of fractal sets (also in Euclidean spaces), especially defined via regular (ω-)languages. By doing this, we can sharpen and generalize earlier results in two ways: first, we treat the case where the underlying basic iterated function system contains noncontractive mappings and, second, we obtain results valid for nonregular languages as well
How Hard Is Computing the Edit Distance?

AbstractThe notion of edit distance arises in very different fields such as self-correcting codes, parsing theory, speech recognition, and molecular biology. The edit distance between an input string and a language L is the minimum cost of a sequence of edit operations (substitution of a symbol in another incorrect symbol, insertion of an extraneous symbol, deletion of a symbol) needed to change the input string into a sentence of L. In this paper we study the complexity of computing the edit distance, discovering sharp boundaries between classes of languages for which this function can be efficiently evaluated and classes of languages for which it seems to be difficult to compute. Our main result is a parallel algorithm for computing the edit distance for the class of languages accepted by one-way nondeterministic auxiliary pushdown automata working in polynomial time, a class that strictly contains context–free languages. Moreover, we show that this algorithm can be extended in order to find a sentence of the language from which the input string has minimum distance
Working with ARMs: Complexity Results on Atomic Representations of Herbrand Models

AbstractAn atomic representation of a Herbrand model (ARM) is a finite set of (not necessarily ground) atoms over a given Herbrand universe. Each ARM represents a possibly infinite Herbrand interpretation. This concept has emerged independently in different branches of computer science as a natural and useful generalization of the concept of finite Herbrand interpretation. It was shown that several recursively decidable problems on finite Herbrand models (or interpretations) remain decidable on ARMs.The following problems are essential when working with ARMs: Deciding the equivalence of two ARMs, deciding subsumption between ARMs, and evaluating clauses over ARMs. These problems were shown to be decidable, but their computational complexity has remained obscure so far. The previously published decision algorithms require exponential space. In this paper, we prove that all mentioned problems are coNP-complete
How to Sign Digital Streams

AbstractWe present a new efficient paradigm for signing digital streams. The problem of signing digital streams to prove their authenticity is substantially different from the problem of signing regular messages. Traditional signature schemes are message oriented and require the receiver to process the entire message before being able to authenticate its signature. However, a stream is a potentially very long (or infinite) sequence of bits that the sender sends to the receiver and the receiver is required to consume the received bits at more or less the input rate and without excessive delay. Therefore it is infeasible for the receiver to obtain the entire stream before authenticating and consuming it. Examples of streams include digitized video and audio files, data feeds, and applets. We present two solutions to the problem of authenticating digital streams. The first one is for the case of a finite stream which is entirely known to the sender (say a movie). We use this constraint to devise an extremely efficient solution. The second case is for a (potentially infinite) stream which is not known in advance to the sender (for example a live broadcast). We present proofs of security of our constructions. Our techniques also have applications in other areas, for example, efficient authentication of long files when communication is at a cost and signature-based filtering at a proxy server
On Full Abstraction for PCF: I, II, and III

AbstractWe present an order-extensional, order (or inequationally) fully abstract model for Scott's language pcf. The approach we have taken is very concrete and in nature goes back to S. C Kleene (1978, in “General Recursion Theory II, Proceedings of the 1977 Oslo Symposium,” North-Holland, Amsterdam) and R. O. Gandy (1993, “Dialogues, Blass Games, Sequentiality for Objects of Finite Type,” unpublished manuscript) in one tradition, and to G. Kahn and G. D. Plotkin (1993, Theoret. Comput. Sci.121, 187–278) and G. Berry and P.-L. Curien (1982, Theoret. Comput. Sci.20, 265–321) in another. Our model of computation is based on a kind of game in which each play consists of a dialogue of questions and answers between two players who observe the following principles of civil conversation: 1.Justification. A question is asked only if the dialogue at that point warrants it. An answer is proffered only if a question expecting it has already been asked. 2.Priority. Questions pending in a dialogue are answered on a last-asked-first-answered basis. This is equivalent to Gandy's no-dangling-question-mark condition. We analyze pcf-style computations directly in terms of partial strategies based on the information available to each player when he or she is about to move. Our players are required to play an innocent strategy: they play on the basis of their view which is that part of the history that interests them currently. Views are continually updated as the play unfolds. Hence our games are neither history-sensitive nor history-free. Rather they are view-dependent. These considerations give expression to what seems to us to be the nub of pcf-style higher-type sequentiality in a (dialogue) game-semantical setting
Improved Lower Bounds for Learning from Noisy Examples: An Information-Theoretic Approach

AbstractThis paper presents a general information-theoretic approach for obtaining lower bounds on the number of examples required for Probably Approximately Correct (PAC) learning in the presence of noise. This approach deals directly with the fundamental information quantities, avoiding a Bayesian analysis. The technique is applied to several different models, illustrating its generality and power. The resulting bounds add logarithmic factors to (or improve the constants in) previously known lower bounds
Languages Defined with Modular Counting Quantifiers

AbstractWe prove that a regular language defined by a boolean combination of generalized Σ1-sentences built using modular counting quantifiers can be defined by a boolean combination of Σ1-sentences in which only regular numerical predicates appear. The same statement, with “Σ1” replaced by “first-order,” is equivalent to the conjecture that the nonuniform circuit complexity class ACC is strictly contained in NC1. The argument introduces some new techniques, based on a combination of semigroup theory and Ramsey theory, which may shed some light on the general case
Privacy via Subsumption

AbstractWe describe an object calculus allowing object extension and structural subtyping. Each object has a “dictionary” to mediate the connection between names and components. This extra indirection yields the first object calculus combining both object extension and full width subtyping in a type-safe manner. If class inheritance is modeled with object extension, private fields and methods can be achieved directly by scoping restrictions: private fields or methods are those hidden by subsumption. We prove that the type system is sound, discuss a variant allowing covariant self types, and give some examples of the expressiveness of the calculus
Full Abstraction for PCF

AbstractAn intensional model for the programming language PCF is described in which the types of PCF are interpreted by games and the terms by certain history-free strategies. This model is shown to capture definability in PCF. More precisely, every compact strategy in the model is definable in a certain simple extension of PCF. We then introduce an intrinsic preorder on strategies and show that it satisfies some striking properties such that the intrinsic preorder on function types coincides with the pointwise preorder. We then obtain an order-extensional fully abstract model of PCF by quotienting the intensional model by the intrinsic preorder. This is the first syntax-independent description of the fully abstract model for PCF. (Hyland and Ong have obtained very similar results by a somewhat different route, independently and at the same time.) We then consider the effective version of our model and prove a universality theorem: every element of the effective extensional model is definable in PCF. Equivalently, every recursive strategy is definable up to observational equivalence
On Some Schützenberger Conjectures

AbstractIn this paper we consider factorizing codes C over A, i.e., codes verifying the factorization conjecture by Schützenberger. Let n be the positive integer such that anεC, we show how we can construct C starting with factorizing codes C′ with an′εC′ and n′ < n, under the hypothesis that all words aizaj in C, with zε(A\a)A*(A\a) ∪ (A\a), satisfy i, j, >n. The operation involved, already introduced by Anselmo, is also used to show that all maximal codes C=P(A−1)S+1 with P, SεZ〈A〉 and P or S in Z〈a〉 can be constructed by means of this operation starting with prefix and suffix codes. Old conjectures by Schützenberger have been revised