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Formulae-as-Types for an Involutive Negation 14

Formulae-as-Types for an Involutive Negation

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Joint Meeting of the 23rd EACSL annual Conference on computer science logic (CSL) / 29th annual acm/ieee symposium on logic in computer science (LICS)

作者： Munch-Maccagnoni, Guillaume Univ Paris 13 Sorbonne Paris Cite LIPN F-93430 Villetaneuse France

ISBN: (纸本)9781450328869

Negation is not involutive in the lambda C calculus because it does not distinguish captured stacks from continuations. We show that there is a formulae-as-types correspondence between the involutive negation in proof theory, and a notion of high-level access to the stacks studied by Felleisen and Clements. We introduce polarised, untyped, calculi compatible with extensionality, for both of classical sequent calculus and classical natural deduction, with connectives for an involutive negation. the involution is due to the l delimited control operator that we introduce, which allows us to implement the idea that captured stacks, unlike continuations, can be inspected. Delimiting control also gives a constructive interpretation to falsity. We describe the isomorphism there is between A and inverted left perpendicular inverted left perpendicularA, and thus between inverted left perpendicular boolean OR and there exists inverted left perpendicular.

关键词： Classical logic Formulae-as-types Delimited control operators Continuations Polarization Focalization

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Functional Reactive Types 14

Functional Reactive Types

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Joint Meeting of the 23rd EACSL annual Conference on computer science logic (CSL) / 29th annual acm/ieee symposium on logic in computer science (LICS)

作者： Jeffrey, Alan Alcatel Lucent Bell Labs Murray Hill NJ 07974 USA

ISBN: (纸本)9781450328869

Functional Reactive Programming (FRP) is an approach to streaming data with a pure functional semantics as time-indexed values. In previous work, we showed that Linear-time Temporal logic (LTL) can be used as a type system for discrete-time FRP, and that functional reactive primitives perform two roles: as combinators for building streams of data, and as proof rules for constructive LTL. In this paper, we add a third role, by showing that FRP combinators can be used to define streams of types, and that these functional reactive types can be viewed both as a constructive temporal logic, and as the types for functional reactive programs. As an application of functional reactive types, we show that past-time LTL (pLTL) can be extended with FRP to get a logic pLTL+FRP. this logic is expressed as streams of boolean expressions, and so bounded satisfiability of pLTL can be translated to Satisfiability Modulo theory (SMT). thus, pLTL+FRP can be used as a constraint language for problems which mix properties of data with temporal properties.

关键词： Functional Reactive Programming Dependent Types Temporal logic

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logic for Communicating Automata with Parameterized Topology 14

Logic for Communicating Automata with Parameterized Topology

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Joint Meeting of the 23rd EACSL annual Conference on computer science logic (CSL) / 29th annual acm/ieee symposium on logic in computer science (LICS)

作者： Bollig, Benedikt CNRS ENS Cachan LSV Paris France INRIA Le Chesnay France

ISBN: (纸本)9781450328869

We introduce parameterized communicating automata (PCA) as a model of systems where finite-state processes communicate through FIFO channels. Unlike classical communicating automata, a given PCA can be run on any network topology of bounded degree. the topology is thus a parameter of the system. We provide various Buchi-Elgot-Trakhtenbrot theorems for PCA, which roughly read as follows: Given a logical specification ' and a class of topologies T, there is a PCA that is equivalent to ' on all topologies from T. We give uniform constructions which allow us to instantiate T with concrete classes such as pipelines, ranked trees, grids, rings, etc. the proofs build on a locality theorem for first-order logic due to Schwentick and Barthelmann, and they exploit concepts from the non-parameterized case, notably a result by Genest, Kuske, and Muscholl.

关键词： communicating automata parameterized topology message sequence charts monadic second-order logic realizability

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A new correctness criterion for MLL proof nets 14

A new correctness criterion for MLL proof nets

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Joint Meeting of the 23rd EACSL annual Conference on computer science logic (CSL) / 29th annual acm/ieee symposium on logic in computer science (LICS)

作者： Ehrhard, thomas Univ Paris Diderot Sorbonne Paris Cite CNRS PPSUMR 7126 F-75205 Paris France

ISBN: (纸本)9781450328869

In Girard's original presentation, proof structures of Linear logic are hypergraphs whose hyperedges are labeled by logical rules and vertices represent the connections between these logical rules. Presentations of proof structures based on interaction nets have the same kind of graphical flavor. Other presentations of proof structures use terms instead of graphs or hypergraphs. the atomic ingredient of these terms are variables related by axiom links. However, the correctness criteria developed so far are adapted to the graphical presentations of proof structures and not to their term-based presentations. We propose a new correctness criterion for constant-free Multiplicative Linear logic with Mix which applies to a coherence space structure that a term-based proof structure induces on the set of its variables in a straightforward way.

关键词： Linear logic proof nets correctness criteria

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Asymptotic behaviour in temporal logic 14

Asymptotic behaviour in temporal logic

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Joint Meeting of the 23rd EACSL annual Conference on computer science logic (CSL) / 29th annual acm/ieee symposium on logic in computer science (LICS)

作者： Asarin, Eugene Blockelet, Michel Degorre, Aldric Dima, Catalin Mu, Chunyan Univ Paris Diderot LIAFA Paris France CNRS Paris France Univ Paris Est Creteil LACL Creteil France Univ Birmingham Sch Comp Sci Birmingham W Midlands England

ISBN: (纸本)9781450328869

We study the "approximability" of unbounded temporal operators with time-bounded operators, as soon as some time bounds tend to infinity. More specifically, for formulas in the fragments PLTL lozenge and PLTL square of the Parametric Linear Temporal logic of Alur et al., we provide algorithms for computing the limit entropy as all parameters tend to 1. As a consequence, we can decide the problem whether the limit entropy of a formula in one of the two fragments coincides with that of its time-unbounded transformation, obtained by replacing each occurrence of a time-bounded operator into its time-unbounded version. the algorithms proceed by translation of the two fragments of PLTL into two classes of discrete-time timed automata and analysis of their strongly-connected components.

关键词： entropy temporal logic

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Anchored LTL Separation 14

Anchored LTL Separation

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Joint Meeting of the 23rd EACSL annual Conference on computer science logic (CSL) / 29th annual acm/ieee symposium on logic in computer science (LICS)

作者： Maretic, Grgur Petric Dashti, Mohammad Torabi Basin, David Swiss Fed Inst Technol Dept Comp Sci Zurich Switzerland

ISBN: (纸本)9781450328869

Gabbay's separation theorem is a fundamental result for linear temporal logic (LTL). We show that separating a restricted class of LTL formulas, called anchored LTL, is elementary if and only if the translation from LTL to the linear temporal logic with only future temporal connectives is elementary. To prove this result, we define a canonical separation for LTL, and establish a correspondence between a canonical separation of anchored LTL formulas and the omega-automata that recognize these formulas. the canonical separation of anchored LTL formulas has two further applications. First, we constructively prove that the safety closure of any LTL property is an LTL property, thus proving the decomposition theorem for LTL: every LTL formula is equivalent to the conjunction of a safety LTL formula and a liveness LTL formula. Second, we characterize safety, liveness, absolute liveness, stable, and fairness properties in LTL. Our characterization is effective: We reduce the problem of deciding whether an LTL formula defines any of these properties to the validity problem for LTL.

关键词： Linear Temporal logic omega-automata Safety Liveness

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On the Hoare theory of Monadic Recursion Schemes 14

On the Hoare Theory of Monadic Recursion Schemes

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Joint Meeting of the 23rd EACSL annual Conference on computer science logic (CSL) / 29th annual acm/ieee symposium on logic in computer science (LICS)

作者： Mamouras, Konstantinos Cornell Univ Ithaca NY 14853 USA

ISBN: (纸本)9781450328869

the equational theory of monadic recursion schemes is known to be decidable by the result of Senizergues on the decidability of the problem of DPDA equivalence. In order to capture some properties of the domain of computation, we augment equations with certain hypotheses. this preserves the decidability of the theory, which we call simple implicational theory. the asymptotically fastest algorithm known for deciding the equational theory, and also for deciding the simple implicational theory, has running time that is non-elementary. We therefore consider a restriction of the properties about schemes to check: instead of arbitrary equations f equivalent to g between schemes, we focus on propositional Hoare assertions {p}f{q}, where f is a scheme and p, q are tests. Such Hoare assertions have a straightforward encoding as equations. We investigate the Hoare theory of monadic recursion schemes, that is, the set of valid implications whose conclusions are Hoare assertions and whose premises are of a certain simple form. We present a sound and complete Hoare-style calculus for this theory. We also show that the Hoare theory can be decided in exponential time, and that it is complete for this class.

关键词： Hoare logic propositional Hoare logic monadic recursion schemes monadic program schemes sound and complete Hoare calculus

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Preservation and decomposition theorems for bounded degree structures 14

Preservation and decomposition theorems for bounded degree s...

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Joint Meeting of the 23rd EACSL annual Conference on computer science logic (CSL) / 29th annual acm/ieee symposium on logic in computer science (LICS)

作者： Harwath, Frederik Heimberg, Lucas Schweikardt, Nicole Goethe Univ Frankfurt Main Inst Informat Frankfurt Germany

ISBN: (纸本)9781450328869

We provide elementary algorithms for two preservation theorems for first-order sentences with modulo m counting quantifiers (FO+MODm) on the class C-d of all finite structures of degree at most d: For each FO+MODm-sentence that is preserved under extensions (homomorphisms) on C-d, a C-d-equivalent existential (existential-positive) FO-sentence can be constructed in 6-fold (4-fold) exponential time. For FO-sentences, the algorithm has 5-fold (4-fold) exponential time complexity. this is complemented by lower bounds showing that for FO-sentences a 3-fold exponential blow-up of the computed existential (existential-positive) sentence is unavoidable. Furthermore, we show that for an input FO-formula, a C-d-equivalent Feferman-Vaught decomposition can be computed in 3-fold exponential time. We also provide a matching lower bound.

关键词： computational logic first-order logic modulo counting quantifiers structures of bounded degree Hanf locality elementary algorithms preservation theorems existential preservation homomorphism preservation Los-Tarski Feferman-Vaught

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Pattern logics and Auxiliary Relations 14

Pattern Logics and Auxiliary Relations

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Joint Meeting of the 23rd EACSL annual Conference on computer science logic (CSL) / 29th annual acm/ieee symposium on logic in computer science (LICS)

作者： Figueira, Diego Libkin, Leonid Univ Edinburgh Edinburgh Midlothian Scotland

ISBN: (纸本)9781450328869

A common theme in the study of logics over finite structures is adding auxiliary predicates to enhance expressiveness and convey additional information. Examples include adding an order or arithmetic for capturing complexity classes, or the power of real-life declarative languages. A recent trend is to add a data-value comparison relation to words, trees, and graphs, for capturing modern data models such as XML and graph databases. Such additions often result in the loss of good properties of the underlying logic. Our goal is to show that such a loss can be avoided if we use pattern-based logics, standard in XML and graph data querying. the essence of such logics is that auxiliary relations are tested locally with respect to other relations in the structure. these logics are shown to admit strong versions of Hanf and Gaifman locality theorems, which are used to prove a homomorphism preservation theorem, and a decidability result for the satisfiability problem. We discuss applications of these results to pattern logics over data forests, and consequently to querying XML data.

关键词： First-order logic pattern finite model theory locality homomorphism preservation theorem data trees XML decidability

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Faster decision of first-order graph properties 14

Faster decision of first-order graph properties

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Joint Meeting of the 23rd EACSL annual Conference on computer science logic (CSL) / 29th annual acm/ieee symposium on logic in computer science (LICS)

作者： Williams, Ryan Stanford Univ Stanford CA 94305 USA

ISBN: (纸本)9781450328869

First-order logic captures a vast number of computational problems on graphs. We study the time complexity of deciding graph properties definable by first-order sentences in prenex normal form with k variables. the trivial algorithm for this problem runs in O(n(k)) time on n-node graphs (the big-O hides the dependence on k). Answering a question of Miklos Ajtai, we give the first algorithms running faster than the trivial algorithm, in the general case of arbitrary first-order sentences and arbitrary graphs. One algorithm runs in O(n(k-3+omega)) <= O(n(k-0.627)) time for all k >= 3, where omega < 2.373 is the n x n matrix multiplication exponent. By applying fast rectangular matrix multiplication, the algorithm can be improved further to run in n(k-1+o(1)) time, for all k >= 9. Finally, we observe that the exponent of k - 1 is optimal, under the popular hypothesis that CNF satisfiability with n variables and m clauses cannot be solved in (2 - epsilon)(n) . poly(m) time for some epsilon > 0.

关键词： first-order logic graph algorithms matrix multiplication satisfiability

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