Pub Date : 2001-06-16DOI: 10.1109/LICS.2001.932495
S. Cook, A. Kolokolova
We introduce a second-order system V/sub 1/-Horn of bounded arithmetic formalizing polynomial-time reasoning, based on Gradel's (1992) second-order Horn characterization of P. Our system has comprehension over P predicates (defined by Gradel's second-order Horn formulas), and only finitely, many function symbols. Other systems of polynomial-time reasoning either allow induction on NP predicates (such as Buss's (1986) S/sub 2//sup 1/ or the second-order V/sub 1//sup 1/), and hence are more powerful than our system (assuming the polynomial hierarchy does not collapse), or use Cobham's theorem to introduce function symbols for all polynomial-time functions (such as Cook's PV and Zambella's P-def). We prove that our system is equivalent to QPV and Zambella's (1996) P-def. Using our techniques, we also show that V/sub 1/-Horn is finitely, axiomatizable, and, as a corollary, that the class of /spl forall//spl Sigma//sub 1//sup b/ consequences of S/sub 2//sup 1/ is finitely axiomatizable as well, thus answering an open question.
{"title":"A second-order system for polytime reasoning using Gradel's theorem","authors":"S. Cook, A. Kolokolova","doi":"10.1109/LICS.2001.932495","DOIUrl":"https://doi.org/10.1109/LICS.2001.932495","url":null,"abstract":"We introduce a second-order system V/sub 1/-Horn of bounded arithmetic formalizing polynomial-time reasoning, based on Gradel's (1992) second-order Horn characterization of P. Our system has comprehension over P predicates (defined by Gradel's second-order Horn formulas), and only finitely, many function symbols. Other systems of polynomial-time reasoning either allow induction on NP predicates (such as Buss's (1986) S/sub 2//sup 1/ or the second-order V/sub 1//sup 1/), and hence are more powerful than our system (assuming the polynomial hierarchy does not collapse), or use Cobham's theorem to introduce function symbols for all polynomial-time functions (such as Cook's PV and Zambella's P-def). We prove that our system is equivalent to QPV and Zambella's (1996) P-def. Using our techniques, we also show that V/sub 1/-Horn is finitely, axiomatizable, and, as a corollary, that the class of /spl forall//spl Sigma//sub 1//sup b/ consequences of S/sub 2//sup 1/ is finitely axiomatizable as well, thus answering an open question.","PeriodicalId":366313,"journal":{"name":"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115314748","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}
Pub Date : 2001-06-16DOI: 10.1109/LICS.2001.932518
Michael Benedikt, L. Libkin, T. Schwentick, L. Segoufin
We study algebras of definable string relations, classes of regular n-ary relations that arise as the definable sets within a model whose carrier is the set of all strings. We show that the largest such algebra-the collection of regular relations-has some quite undesirable computational and model-theoretic properties. In contrast, we exhibit several definable relation algebras that have much tamer behavior: for example, they admit quantifier elimination, and have finite VC dimension. We show that the properties of a definable relation algebra are not at all determined by the one-dimensional definable sets. We give models whose definable sets are all star-free, but whose binary relations are quite complex, as well as models whose definable sets include all regular sets, but which are much more restricted and tractable than the full algebra of regular relations.
{"title":"A model-theoretic approach to regular string relations","authors":"Michael Benedikt, L. Libkin, T. Schwentick, L. Segoufin","doi":"10.1109/LICS.2001.932518","DOIUrl":"https://doi.org/10.1109/LICS.2001.932518","url":null,"abstract":"We study algebras of definable string relations, classes of regular n-ary relations that arise as the definable sets within a model whose carrier is the set of all strings. We show that the largest such algebra-the collection of regular relations-has some quite undesirable computational and model-theoretic properties. In contrast, we exhibit several definable relation algebras that have much tamer behavior: for example, they admit quantifier elimination, and have finite VC dimension. We show that the properties of a definable relation algebra are not at all determined by the one-dimensional definable sets. We give models whose definable sets are all star-free, but whose binary relations are quite complex, as well as models whose definable sets include all regular sets, but which are much more restricted and tractable than the full algebra of regular relations.","PeriodicalId":366313,"journal":{"name":"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114481014","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}
Pub Date : 2001-06-16DOI: 10.1109/LICS.2001.932480
Aaron Stump, Clark W. Barrett, D. Dill, J. Levitt
A decision procedure for a theory of arrays is of interest for applications in formal verification, program analysis and automated theorem proving. This paper presents a decision procedure for an extensional theory of arrays and proves it correct.
{"title":"A decision procedure for an extensional theory of arrays","authors":"Aaron Stump, Clark W. Barrett, D. Dill, J. Levitt","doi":"10.1109/LICS.2001.932480","DOIUrl":"https://doi.org/10.1109/LICS.2001.932480","url":null,"abstract":"A decision procedure for a theory of arrays is of interest for applications in formal verification, program analysis and automated theorem proving. This paper presents a decision procedure for an extensional theory of arrays and proves it correct.","PeriodicalId":366313,"journal":{"name":"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127748285","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}
Pub Date : 2001-06-16DOI: 10.1109/LICS.2001.932501
A. Appel
Proof-carrying code is a framework for the mechanical verification of safety properties of machine-language programs, but the problem arises of "quis custodiat ipsos custodes" - i.e. who verifies the verifier itself? Foundational proof-carrying code is verification from the smallest possible set of axioms, using the simplest possible verifier and the smallest possible runtime system. I describe many of the mathematical and engineering problems to be solved in the construction of a foundational proof-carrying code system.
{"title":"Foundational proof-carrying code","authors":"A. Appel","doi":"10.1109/LICS.2001.932501","DOIUrl":"https://doi.org/10.1109/LICS.2001.932501","url":null,"abstract":"Proof-carrying code is a framework for the mechanical verification of safety properties of machine-language programs, but the problem arises of \"quis custodiat ipsos custodes\" - i.e. who verifies the verifier itself? Foundational proof-carrying code is verification from the smallest possible set of axioms, using the simplest possible verifier and the smallest possible runtime system. I describe many of the mathematical and engineering problems to be solved in the construction of a foundational proof-carrying code system.","PeriodicalId":366313,"journal":{"name":"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science","volume":"106 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132598737","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}
Pub Date : 2001-06-16DOI: 10.1109/LICS.2001.932487
J. Laird
A fully abstract game semantics for an extension of Idealized Algol with locally declared exceptions is presented. It is based on "Hyland-Ong games" (J.M.E. Hyland & C.-H.L. Ong, 1995), but as well as relaxing the constraints which impose functional behavior (as in games models of other computational effects, such as continuations and references), new structure is added to plays in the form of additional pointers which track the flow of control. The semantics is proved to be fully abstract by a factorization of strategies into a "new-exception generator" and a strategy with local control flow. It is shown, using examples, that there is no model of exceptions which is a conservative extension of the semantics of Idealized Algol without the new pointers.
提出了一种具有局部声明异常的理想Algol扩展的完全抽象博弈语义。它基于“Hyland-Ong游戏”(J.M.E. Hyland & c - h.l. Ong, 1995)，但同时也放松了强加于功能行为的约束(游戏邦注:就像在其他计算效果的游戏模型中一样，如延续和引用)，新结构以跟踪控制流的额外指针的形式添加到游戏中。通过将策略分解为“新异常生成器”和具有局部控制流的策略，证明了该语义是完全抽象的。通过实例表明，在没有新指针的情况下，不存在异常模型，异常模型是理想化Algol语义的保守扩展。
{"title":"A fully abstract game semantics of local exceptions","authors":"J. Laird","doi":"10.1109/LICS.2001.932487","DOIUrl":"https://doi.org/10.1109/LICS.2001.932487","url":null,"abstract":"A fully abstract game semantics for an extension of Idealized Algol with locally declared exceptions is presented. It is based on \"Hyland-Ong games\" (J.M.E. Hyland & C.-H.L. Ong, 1995), but as well as relaxing the constraints which impose functional behavior (as in games models of other computational effects, such as continuations and references), new structure is added to plays in the form of additional pointers which track the flow of control. The semantics is proved to be fully abstract by a factorization of strategies into a \"new-exception generator\" and a strategy with local control flow. It is shown, using examples, that there is no model of exceptions which is a conservative extension of the semantics of Idealized Algol without the new pointers.","PeriodicalId":366313,"journal":{"name":"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125010007","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}
Pub Date : 2001-06-16DOI: 10.1109/LICS.2001.932517
N. Alon, T. Milo, F. Neven, Dan Suciu, V. Vianu
Motivated by the need to export relational databases as XML data in the context of the World Wide Web, we investigate the type-checking problem for transformations of relational data into tree data (i.e. XML). The problem consists of statically verifying that the output of every transformation belongs to a given output tree language (specified for XML by a document type definition), for input databases satisfying given integrity constraints. The type-checking problem is parameterized by the class of formulas defining the transformation, the class of output tree languages and the class of integrity constraints. While undecidable in its most general formulation, the type-checking problem has many special cases of practical interest that turn out to be decidable. The main contribution of this paper is to trace a fairly tight boundary of decidability for type-checking in this framework. In the decidable cases, we examine the complexity and show lower and upper bounds. We also exhibit a practically appealing restriction for which type-checking is in PTIME.
{"title":"Typechecking XML views of relational databases","authors":"N. Alon, T. Milo, F. Neven, Dan Suciu, V. Vianu","doi":"10.1109/LICS.2001.932517","DOIUrl":"https://doi.org/10.1109/LICS.2001.932517","url":null,"abstract":"Motivated by the need to export relational databases as XML data in the context of the World Wide Web, we investigate the type-checking problem for transformations of relational data into tree data (i.e. XML). The problem consists of statically verifying that the output of every transformation belongs to a given output tree language (specified for XML by a document type definition), for input databases satisfying given integrity constraints. The type-checking problem is parameterized by the class of formulas defining the transformation, the class of output tree languages and the class of integrity constraints. While undecidable in its most general formulation, the type-checking problem has many special cases of practical interest that turn out to be decidable. The main contribution of this paper is to trace a fairly tight boundary of decidability for type-checking in this framework. In the decidable cases, we examine the complexity and show lower and upper bounds. We also exhibit a practically appealing restriction for which type-checking is in PTIME.","PeriodicalId":366313,"journal":{"name":"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123707969","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}
Pub Date : 2001-06-16DOI: 10.1109/LICS.2001.932509
A. Salibra
In this paper, we give a topological proof of the following result: there exist 2¿(/spl aleph//sub 0/) lambda theories of the untyped lambda calculus without a model in any semantics based on D.S. Scott's (1972, 1981) view of models as partially ordered sets and of functions as monotonic functions. As a consequence of this result, we positively solve the conjecture, stated by O. Bastonero and X. Gouy (1999) and by C. Berline (2000), that the strongly stable semantics is incomplete.
{"title":"A continuum of theories of lambda calculus without semantics","authors":"A. Salibra","doi":"10.1109/LICS.2001.932509","DOIUrl":"https://doi.org/10.1109/LICS.2001.932509","url":null,"abstract":"In this paper, we give a topological proof of the following result: there exist 2¿(/spl aleph//sub 0/) lambda theories of the untyped lambda calculus without a model in any semantics based on D.S. Scott's (1972, 1981) view of models as partially ordered sets and of functions as monotonic functions. As a consequence of this result, we positively solve the conjecture, stated by O. Bastonero and X. Gouy (1999) and by C. Berline (2000), that the strongly stable semantics is incomplete.","PeriodicalId":366313,"journal":{"name":"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science","volume":"279 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133233849","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}
Pub Date : 2001-06-16DOI: 10.1109/LICS.2001.932498
K. Terui
Light linear logic (LLL) and its variant, intuitionistic light affine logic (ILAL), are logics of polytime computation. All polynomial-time functions are representable by proofs of these logics (via the proofs-as-programs correspondence), and, conversely, that there is a specific reduction (cut-elimination) strategy which normalizes a given proof in polynomial time (the latter may well be called the polytime "weak" normalization theorem). In this paper, we introduce an untyped term calculus, called the light affine lambda calculus (/spl lambda//sub LA/), generalizing the essential ideas of light logics into an untyped framework. It is a simple modification of the /spl lambda/-calculus, and has ILAL as a type assignment system. Then, in this generalized setting, we prove the polytime "strong" normalization theorem: any reduction strategy normalizes a given /spl lambda//sub LA/ term (of fixed depth) in a polynomial number of reduction steps, and indeed in polynomial time.
{"title":"Light affine lambda calculus and polytime strong normalization","authors":"K. Terui","doi":"10.1109/LICS.2001.932498","DOIUrl":"https://doi.org/10.1109/LICS.2001.932498","url":null,"abstract":"Light linear logic (LLL) and its variant, intuitionistic light affine logic (ILAL), are logics of polytime computation. All polynomial-time functions are representable by proofs of these logics (via the proofs-as-programs correspondence), and, conversely, that there is a specific reduction (cut-elimination) strategy which normalizes a given proof in polynomial time (the latter may well be called the polytime \"weak\" normalization theorem). In this paper, we introduce an untyped term calculus, called the light affine lambda calculus (/spl lambda//sub LA/), generalizing the essential ideas of light logics into an untyped framework. It is a simple modification of the /spl lambda/-calculus, and has ILAL as a type assignment system. Then, in this generalized setting, we prove the polytime \"strong\" normalization theorem: any reduction strategy normalizes a given /spl lambda//sub LA/ term (of fixed depth) in a polynomial number of reduction steps, and indeed in polynomial time.","PeriodicalId":366313,"journal":{"name":"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science","volume":"371 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134130301","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}
Pub Date : 2001-06-16DOI: 10.1109/LICS.2001.932489
Y. Gurevich
Analysis of foundational problems like "What is computation" leads to a sketch of the paradigm of abstract state machines (ASMs). This is followed by a brief discussion on ASMs applications. Then we present some theoretical problems that bridge between the traditional LICS themes and abstract state machines.
{"title":"Logician in the land of OS: abstract state machines in Microsoft","authors":"Y. Gurevich","doi":"10.1109/LICS.2001.932489","DOIUrl":"https://doi.org/10.1109/LICS.2001.932489","url":null,"abstract":"Analysis of foundational problems like \"What is computation\" leads to a sketch of the paradigm of abstract state machines (ASMs). This is followed by a brief discussion on ASMs applications. Then we present some theoretical problems that bridge between the traditional LICS themes and abstract state machines.","PeriodicalId":366313,"journal":{"name":"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science","volume":"165 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133790274","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}
Pub Date : 2001-06-16DOI: 10.1109/LICS.2001.932515
A. Bouajjani, A. Muscholl, Tayssir Touili
Proposes a natural subclass of regular languages, called alphabetic pattern constraints (APC), which is effectively closed under permutation rewriting, i.e. under iterative application of rules of the form ab/spl rarr/ba. It is well-known that regular languages do not have this closure property in general. Our result can be applied for example to regular model checking, for verifying properties of parametrized linear networks of regular processes and for modeling and verifying properties of asynchronous distributed systems. We also consider the complexity of testing membership in APC, and show that the question is complete for PSPACE when the input is an NFA (nondeterministic finite automaton) and complete for NLOGSPACE when it is a DFA (deterministic finite automaton). Moreover, we show that both the inclusion problem and the question of closure under permutation rewriting are PSPACE-complete when we restrict ourselves to the APC class.
{"title":"Permutation rewriting and algorithmic verification","authors":"A. Bouajjani, A. Muscholl, Tayssir Touili","doi":"10.1109/LICS.2001.932515","DOIUrl":"https://doi.org/10.1109/LICS.2001.932515","url":null,"abstract":"Proposes a natural subclass of regular languages, called alphabetic pattern constraints (APC), which is effectively closed under permutation rewriting, i.e. under iterative application of rules of the form ab/spl rarr/ba. It is well-known that regular languages do not have this closure property in general. Our result can be applied for example to regular model checking, for verifying properties of parametrized linear networks of regular processes and for modeling and verifying properties of asynchronous distributed systems. We also consider the complexity of testing membership in APC, and show that the question is complete for PSPACE when the input is an NFA (nondeterministic finite automaton) and complete for NLOGSPACE when it is a DFA (deterministic finite automaton). Moreover, we show that both the inclusion problem and the question of closure under permutation rewriting are PSPACE-complete when we restrict ourselves to the APC class.","PeriodicalId":366313,"journal":{"name":"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132750206","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}
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