Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)最新文献
Event structures form a canonical model of concurrent behaviour which has a natural game-theoretic interpretation. This game-based interpretation was initially given for zero-sum concurrent games. This paper studies an extension of such games on event structures to include a much wider class of game types and solution concepts. The extension permits modelling scenarios where, for instance, cooperation or independent goal-driven behaviour of computer agents is desired. Specifically, we will define non-zero-sum games on event structures, and give full characterisations---existence and completeness results---of the kinds of games, payoff sets, and strategies for which Nash equilibria and subgame perfect Nash equilibria always exist. The game semantics of various logics and systems are outlined to illustrate the power of this framework.
{"title":"Equilibria of concurrent games on event structures","authors":"J. Gutierrez, M. Wooldridge","doi":"10.1145/2603088.2603145","DOIUrl":"https://doi.org/10.1145/2603088.2603145","url":null,"abstract":"Event structures form a canonical model of concurrent behaviour which has a natural game-theoretic interpretation. This game-based interpretation was initially given for zero-sum concurrent games. This paper studies an extension of such games on event structures to include a much wider class of game types and solution concepts. The extension permits modelling scenarios where, for instance, cooperation or independent goal-driven behaviour of computer agents is desired. Specifically, we will define non-zero-sum games on event structures, and give full characterisations---existence and completeness results---of the kinds of games, payoff sets, and strategies for which Nash equilibria and subgame perfect Nash equilibria always exist. The game semantics of various logics and systems are outlined to illustrate the power of this framework.","PeriodicalId":20649,"journal":{"name":"Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81734283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract interpretation is a theory of abstraction and constructive approximation of the mathematical structures used in the formal description of complex or infinite systems and the inference or verification of their combinatorial or undecidable properties. Developed in the late seventies, it has been since then used, implicitly or explicitly, to many aspects of computer science (such as static analysis and verification, contract inference, type inference, termination inference, model-checking, abstraction/refinement, program transformation (including watermarking, obfuscation, etc), combination of decision procedures, security, malware detection, database queries, etc) and more recently, to system biology and SAT/SMT solvers. Production-quality verification tools based on abstract interpretation are available and used in the advanced software, hardware, transportation, communication, and medical industries. The talk will consist in an introduction to the basic notions of abstract interpretation and the induced methodology for the systematic development of sound abstract interpretation-based tools. Examples of abstractions will be provided, from semantics to typing, grammars to safety, reachability to potential/definite termination, numerical to protein-protein abstractions, as well as applications (including those in industrial use) to software, hardware and system biology. This paper is a general discussion of abstract interpretation, with selected publications, which unfortunately are far from exhaustive both in the considered themes and the corresponding references.
{"title":"Abstract interpretation: past, present and future","authors":"P. Cousot, R. Cousot","doi":"10.1145/2603088.2603165","DOIUrl":"https://doi.org/10.1145/2603088.2603165","url":null,"abstract":"Abstract interpretation is a theory of abstraction and constructive approximation of the mathematical structures used in the formal description of complex or infinite systems and the inference or verification of their combinatorial or undecidable properties. Developed in the late seventies, it has been since then used, implicitly or explicitly, to many aspects of computer science (such as static analysis and verification, contract inference, type inference, termination inference, model-checking, abstraction/refinement, program transformation (including watermarking, obfuscation, etc), combination of decision procedures, security, malware detection, database queries, etc) and more recently, to system biology and SAT/SMT solvers. Production-quality verification tools based on abstract interpretation are available and used in the advanced software, hardware, transportation, communication, and medical industries. The talk will consist in an introduction to the basic notions of abstract interpretation and the induced methodology for the systematic development of sound abstract interpretation-based tools. Examples of abstractions will be provided, from semantics to typing, grammars to safety, reachability to potential/definite termination, numerical to protein-protein abstractions, as well as applications (including those in industrial use) to software, hardware and system biology. This paper is a general discussion of abstract interpretation, with selected publications, which unfortunately are far from exhaustive both in the considered themes and the corresponding references.","PeriodicalId":20649,"journal":{"name":"Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88864683","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Two graphs are Hanf-equivalent with respect to radius r if there is a bijection between their vertex sets which preserves the isomorphism types of the vertices' neighbourhoods of radius r. For r = 1 this means that the graphs have the same degree sequence. In this paper we relate Hanf-equivalence to the graph-theoretical concept of subgraph equivalence. To make this concept applicable to graphs that are not necessarily connected, we first generalise the notion of the radius of a connected graph to general graphs in a suitable way, which we call the generalised radius. We say that two graphs G and H are subgraph-equivalent up to generalised radius r if for all graphs S of generalised radius r, the number of induced subgraphs isomorphic to S is the same in G and H. We prove that Hanf-equivalence with respect to radius r is equivalent to subgraph-equivalence up to generalised radius r, thereby relating the purely logical and the graph-theoretical concepts in a very strong way. The notion of subgraph-equivalence up to order s is defined accordingly, where all graphs S of order at most s are taken into account. As a corollary we obtain that Hanf-equivalence with respect to radius r implies subgraph-equivalence up to order s, provided that r ≥ 3s/4. In particular, this implies that two graphs which are Hanf-equivalent with respect to radius 3s/4 satisfy exactly the same unions of conjunctive queries of quantifier rank at most s.
{"title":"On Hanf-equivalence and the number of embeddings of small induced subgraphs","authors":"S. Kreutzer, Nicole Schweikardt","doi":"10.1145/2603088.2603148","DOIUrl":"https://doi.org/10.1145/2603088.2603148","url":null,"abstract":"Two graphs are Hanf-equivalent with respect to radius r if there is a bijection between their vertex sets which preserves the isomorphism types of the vertices' neighbourhoods of radius r. For r = 1 this means that the graphs have the same degree sequence. In this paper we relate Hanf-equivalence to the graph-theoretical concept of subgraph equivalence. To make this concept applicable to graphs that are not necessarily connected, we first generalise the notion of the radius of a connected graph to general graphs in a suitable way, which we call the generalised radius. We say that two graphs G and H are subgraph-equivalent up to generalised radius r if for all graphs S of generalised radius r, the number of induced subgraphs isomorphic to S is the same in G and H. We prove that Hanf-equivalence with respect to radius r is equivalent to subgraph-equivalence up to generalised radius r, thereby relating the purely logical and the graph-theoretical concepts in a very strong way. The notion of subgraph-equivalence up to order s is defined accordingly, where all graphs S of order at most s are taken into account. As a corollary we obtain that Hanf-equivalence with respect to radius r implies subgraph-equivalence up to order s, provided that r ≥ 3s/4. In particular, this implies that two graphs which are Hanf-equivalent with respect to radius 3s/4 satisfy exactly the same unions of conjunctive queries of quantifier rank at most s.","PeriodicalId":20649,"journal":{"name":"Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78764991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Context semantics is a tool inspired by Girard' s geometry of interaction. It has had many applications from study of optimal reduction to proofs of complexity bounds. Yet, context semantics have been defined only on λ-calculus and linear logic. In order to study other languages, in particular languages with more primitives (built-in arithmetic, pattern matching,...) we define a context semantics for a broader framework: interaction nets. These are a well-behaved class of graph rewriting systems. Here, two applications are explored. First, we define a notion of weight, based on context semantics paths, which bounds the length of reduction of nets. Then, we define a denotational semantics for a large class of interaction net systems.
{"title":"On context semantics and interaction nets","authors":"Matthieu Perrinel","doi":"10.1145/2603088.2603155","DOIUrl":"https://doi.org/10.1145/2603088.2603155","url":null,"abstract":"Context semantics is a tool inspired by Girard' s geometry of interaction. It has had many applications from study of optimal reduction to proofs of complexity bounds. Yet, context semantics have been defined only on λ-calculus and linear logic. In order to study other languages, in particular languages with more primitives (built-in arithmetic, pattern matching,...) we define a context semantics for a broader framework: interaction nets. These are a well-behaved class of graph rewriting systems. Here, two applications are explored. First, we define a notion of weight, based on context semantics paths, which bounds the length of reduction of nets. Then, we define a denotational semantics for a large class of interaction net systems.","PeriodicalId":20649,"journal":{"name":"Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79527405","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Homotopy type theory is an extension of Martin-Löf type theory with principles inspired by category theory and homotopy theory. With these extensions, type theory can be used to construct proofs of homotopy-theoretic theorems, in a way that is very amenable to computer-checked proofs in proof assistants such as Coq and Agda. In this paper, we give a computer-checked construction of Eilenberg-MacLane spaces. For an abelian group G, an Eilenberg-MacLane space K(G,n) is a space (type) whose nth homotopy group is G, and whose homotopy groups are trivial otherwise. These spaces are a basic tool in algebraic topology; for example, they can be used to build spaces with specified homotopy groups, and to define the notion of cohomology with coefficients in G. Their construction in type theory is an illustrative example, which ties together many of the constructions and methods that have been used in homotopy type theory so far.
{"title":"Eilenberg-MacLane spaces in homotopy type theory","authors":"Daniel R. Licata, Eric Finster","doi":"10.1145/2603088.2603153","DOIUrl":"https://doi.org/10.1145/2603088.2603153","url":null,"abstract":"Homotopy type theory is an extension of Martin-Löf type theory with principles inspired by category theory and homotopy theory. With these extensions, type theory can be used to construct proofs of homotopy-theoretic theorems, in a way that is very amenable to computer-checked proofs in proof assistants such as Coq and Agda. In this paper, we give a computer-checked construction of Eilenberg-MacLane spaces. For an abelian group G, an Eilenberg-MacLane space K(G,n) is a space (type) whose nth homotopy group is G, and whose homotopy groups are trivial otherwise. These spaces are a basic tool in algebraic topology; for example, they can be used to build spaces with specified homotopy groups, and to define the notion of cohomology with coefficients in G. Their construction in type theory is an illustrative example, which ties together many of the constructions and methods that have been used in homotopy type theory so far.","PeriodicalId":20649,"journal":{"name":"Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75386581","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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.
{"title":"Functional reactive types","authors":"A. Jeffrey","doi":"10.1145/2603088.2603106","DOIUrl":"https://doi.org/10.1145/2603088.2603106","url":null,"abstract":"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.","PeriodicalId":20649,"journal":{"name":"Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78854820","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Slot and van Emde Boas' weak invariance thesis states that reasonable machines can simulate each other within a polynomially overhead in time. Is λ-calculus a reasonable machine? Is there a way to measure the computational complexity of a λ-term? This paper presents the first complete positive answer to this long-standing problem. Moreover, our answer is completely machine-independent and based over a standard notion in the theory of λ-calculus: the length of a leftmost-outermost derivation to normal form is an invariant cost model. Such a theorem cannot be proved by directly relating λ-calculus with Turing machines or random access machines, because of the size explosion problem: there are terms that in a linear number of steps produce an exponentially long output. The first step towards the solution is to shift to a notion of evaluation for which the length and the size of the output are linearly related. This is done by adopting the linear substitution calculus (LSC), a calculus of explicit substitutions modelled after linear logic proof nets and admitting a decomposition of leftmost-outermost derivations with the desired property. Thus, the LSC is invariant with respect to, say, random access machines. The second step is to show that LSC is invariant with respect to the λ-calculus. The size explosion problem seems to imply that this is not possible: having the same notions of normal form, evaluation in the LSC is exponentially longer than in the λ-calculus. We solve such an impasse by introducing a new form of shared normal form and shared reduction, deemed useful. Useful evaluation avoids those steps that only unshare the output without contributing to β-redexes, i.e. the steps that cause the blow-up in size. The main technical contribution of the paper is indeed the definition of useful reductions and the thorough analysis of their properties.
{"title":"Beta reduction is invariant, indeed","authors":"Beniamino Accattoli, Ugo Dal Lago","doi":"10.1145/2603088.2603105","DOIUrl":"https://doi.org/10.1145/2603088.2603105","url":null,"abstract":"Slot and van Emde Boas' weak invariance thesis states that reasonable machines can simulate each other within a polynomially overhead in time. Is λ-calculus a reasonable machine? Is there a way to measure the computational complexity of a λ-term? This paper presents the first complete positive answer to this long-standing problem. Moreover, our answer is completely machine-independent and based over a standard notion in the theory of λ-calculus: the length of a leftmost-outermost derivation to normal form is an invariant cost model. Such a theorem cannot be proved by directly relating λ-calculus with Turing machines or random access machines, because of the size explosion problem: there are terms that in a linear number of steps produce an exponentially long output. The first step towards the solution is to shift to a notion of evaluation for which the length and the size of the output are linearly related. This is done by adopting the linear substitution calculus (LSC), a calculus of explicit substitutions modelled after linear logic proof nets and admitting a decomposition of leftmost-outermost derivations with the desired property. Thus, the LSC is invariant with respect to, say, random access machines. The second step is to show that LSC is invariant with respect to the λ-calculus. The size explosion problem seems to imply that this is not possible: having the same notions of normal form, evaluation in the LSC is exponentially longer than in the λ-calculus. We solve such an impasse by introducing a new form of shared normal form and shared reduction, deemed useful. Useful evaluation avoids those steps that only unshare the output without contributing to β-redexes, i.e. the steps that cause the blow-up in size. The main technical contribution of the paper is indeed the definition of useful reductions and the thorough analysis of their properties.","PeriodicalId":20649,"journal":{"name":"Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77260882","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Achim Blumensath, Thomas Colcombet, Denis Kuperberg, P. Parys, M. V. Boom
Regular cost functions provide a quantitative extension of regular languages that retains most of their important properties, such as expressive power and decidability, at least over finite and infinite words and over finite trees. Much less is known over infinite trees. We consider cost functions over infinite trees defined by an extension of weak monadic second-order logic with a new fixed-point-like operator. We show this logic to be decidable, improving previously known decidability results for cost logics over infinite trees. The proof relies on an equivalence with a form of automata with counters called quasi-weak cost automata, as well as results about converting two-way alternating cost automata to one-way alternating cost automata.
{"title":"Two-way cost automata and cost logics over infinite trees","authors":"Achim Blumensath, Thomas Colcombet, Denis Kuperberg, P. Parys, M. V. Boom","doi":"10.1145/2603088.2603104","DOIUrl":"https://doi.org/10.1145/2603088.2603104","url":null,"abstract":"Regular cost functions provide a quantitative extension of regular languages that retains most of their important properties, such as expressive power and decidability, at least over finite and infinite words and over finite trees. Much less is known over infinite trees. We consider cost functions over infinite trees defined by an extension of weak monadic second-order logic with a new fixed-point-like operator. We show this logic to be decidable, improving previously known decidability results for cost logics over infinite trees. The proof relies on an equivalence with a form of automata with counters called quasi-weak cost automata, as well as results about converting two-way alternating cost automata to one-way alternating cost automata.","PeriodicalId":20649,"journal":{"name":"Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80523511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
J. Brotherston, Carsten Fuhs, J. A. Pérez, Nikos Gorogiannis
We show that the satisfiability problem for the "symbolic heap" fragment of separation logic with general inductively defined predicates --- which includes most fragments employed in program verification --- is decidable. Our decision procedure is based on the computation of a certain fixed point from the definition of an inductive predicate, called its "base", that exactly characterises its satisfiability. A complexity analysis of our decision procedure shows that it runs, in the worst case, in exponential time. In fact, we show that the satisfiability problem for our inductive predicates is EXPTIME-complete, and becomes NP-complete when the maximum arity over all predicates is bounded by a constant. Finally, we provide an implementation of our decision procedure, and analyse its performance both on a synthetically generated set of test formulas, and on a second test set harvested from the separation logic literature. For the large majority of these test cases, our tool reports times in the low milliseconds.
{"title":"A decision procedure for satisfiability in separation logic with inductive predicates","authors":"J. Brotherston, Carsten Fuhs, J. A. Pérez, Nikos Gorogiannis","doi":"10.1145/2603088.2603091","DOIUrl":"https://doi.org/10.1145/2603088.2603091","url":null,"abstract":"We show that the satisfiability problem for the \"symbolic heap\" fragment of separation logic with general inductively defined predicates --- which includes most fragments employed in program verification --- is decidable. Our decision procedure is based on the computation of a certain fixed point from the definition of an inductive predicate, called its \"base\", that exactly characterises its satisfiability. A complexity analysis of our decision procedure shows that it runs, in the worst case, in exponential time. In fact, we show that the satisfiability problem for our inductive predicates is EXPTIME-complete, and becomes NP-complete when the maximum arity over all predicates is bounded by a constant. Finally, we provide an implementation of our decision procedure, and analyse its performance both on a synthetically generated set of test formulas, and on a second test set harvested from the separation logic literature. For the large majority of these test cases, our tool reports times in the low milliseconds.","PeriodicalId":20649,"journal":{"name":"Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90487311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider the two-variable fragment of first-order logic with counting, subject to the stipulation that a single distinguished binary predicate be interpreted as an equivalence. We show that the satisfiability and finite satisfiability problems for this logic are both NExpTime-complete. We further show that the corresponding problems for two-variable first-order logic with counting and two equivalences are both undecidable.
{"title":"Logics with counting and equivalence","authors":"Ian Pratt-Hartmann","doi":"10.1145/2603088.2603117","DOIUrl":"https://doi.org/10.1145/2603088.2603117","url":null,"abstract":"We consider the two-variable fragment of first-order logic with counting, subject to the stipulation that a single distinguished binary predicate be interpreted as an equivalence. We show that the satisfiability and finite satisfiability problems for this logic are both NExpTime-complete. We further show that the corresponding problems for two-variable first-order logic with counting and two equivalences are both undecidable.","PeriodicalId":20649,"journal":{"name":"Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91220571","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
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