Pub Date : 2000-06-26DOI: 10.1109/LICS.2000.855769
J. Chroboczek
While game semantics has been remarkably successful at modelling, often in a fully abstract manner a wide range of features of programming languages, there has to date been no attempt at applying it to subtyping. We show how the simple device of explicitly introducing error values in the syntax of the calculus leads to a notion of subtyping for game semantics. We construct an interpretation of a simple /spl lambda/-calculus with subtyping and show how the range of the interpretation of types is a complete lattice, thus yielding an interpretation of bounded quantification.
{"title":"Game semantics and subtyping","authors":"J. Chroboczek","doi":"10.1109/LICS.2000.855769","DOIUrl":"https://doi.org/10.1109/LICS.2000.855769","url":null,"abstract":"While game semantics has been remarkably successful at modelling, often in a fully abstract manner a wide range of features of programming languages, there has to date been no attempt at applying it to subtyping. We show how the simple device of explicitly introducing error values in the syntax of the calculus leads to a notion of subtyping for game semantics. We construct an interpretation of a simple /spl lambda/-calculus with subtyping and show how the range of the interpretation of types is a complete lattice, thus yielding an interpretation of bounded quantification.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"146 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122910504","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 : 2000-06-26DOI: 10.1109/LICS.2000.855778
K. McMillan
Model checking techniques make it possible to verify properties of finite state programs of significant complexity in an automatic way. However, they are limited in scale for complexity reasons, and, of course, limited to finite state models. It is natural, then, to consider using a model checker as a decision procedure within a general-purpose theorem prover. In this way, the general-purpose prover could be used to reduce proof goals to finite-state subgoals of sufficiently small scale to be discharged by the model checker. Thus, in principle we can exploit the advantages of model checking to reduce the manual effort required constructing proofs of complex, infinite state systems.
{"title":"Some strategies for proving theorems with a model checker abstract of invited talk","authors":"K. McMillan","doi":"10.1109/LICS.2000.855778","DOIUrl":"https://doi.org/10.1109/LICS.2000.855778","url":null,"abstract":"Model checking techniques make it possible to verify properties of finite state programs of significant complexity in an automatic way. However, they are limited in scale for complexity reasons, and, of course, limited to finite state models. It is natural, then, to consider using a model checker as a decision procedure within a general-purpose theorem prover. In this way, the general-purpose prover could be used to reduce proof goals to finite-state subgoals of sufficiently small scale to be discharged by the model checker. Thus, in principle we can exploit the advantages of model checking to reduce the manual effort required constructing proofs of complex, infinite state systems.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128642168","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 : 2000-06-26DOI: 10.1109/LICS.2000.855754
S. Lindell, S. Weinstein
We establish that the decidability of the first order theory of a class of finite structures C is a simple and useful condition for guaranteeing that the expressive power of FO+LFP properly extends that of FO on C, unifying separation results for various classes of structures that have been studied. We then apply this result to show that it encompasses certain constructive pebble game techniques which are widely used to establish separations between FO and FO+LFP, and demonstrate that these same techniques cannot succeed in performing separations from any complexity class that contains DLOGTIME.
{"title":"The role of decidability in first order separations over classes of finite structures","authors":"S. Lindell, S. Weinstein","doi":"10.1109/LICS.2000.855754","DOIUrl":"https://doi.org/10.1109/LICS.2000.855754","url":null,"abstract":"We establish that the decidability of the first order theory of a class of finite structures C is a simple and useful condition for guaranteeing that the expressive power of FO+LFP properly extends that of FO on C, unifying separation results for various classes of structures that have been studied. We then apply this result to show that it encompasses certain constructive pebble game techniques which are widely used to establish separations between FO and FO+LFP, and demonstrate that these same techniques cannot succeed in performing separations from any complexity class that contains DLOGTIME.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127639980","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 : 2000-06-26DOI: 10.1109/LICS.2000.855771
E. Grädel, C. Hirsch, M. Otto
Guarded fixed point logic /spl mu/GF extends the guarded fragment by means of least and greatest fixed points, and thus plays the same role within the domain of guarded logics as the modal /spl mu/-calculus plays within the modal domain. We provide a semantic characterisation of /spl mu/GF within an appropriate fragment of second-order logic, in terms of invariance under guarded bisimulation. The corresponding characterisation of the modal /spl mu/-calculus, due to D. Janin and I. Walukiewicz (1999), is lifted from the modal to the guarded domain by means of model theoretic translations. At the methodological level, these translations make the intuitive analogy between modal and guarded logics available as a tool in the analysis of the guarded domain.
{"title":"Back and forth between guarded and modal logics","authors":"E. Grädel, C. Hirsch, M. Otto","doi":"10.1109/LICS.2000.855771","DOIUrl":"https://doi.org/10.1109/LICS.2000.855771","url":null,"abstract":"Guarded fixed point logic /spl mu/GF extends the guarded fragment by means of least and greatest fixed points, and thus plays the same role within the domain of guarded logics as the modal /spl mu/-calculus plays within the modal domain. We provide a semantic characterisation of /spl mu/GF within an appropriate fragment of second-order logic, in terms of invariance under guarded bisimulation. The corresponding characterisation of the modal /spl mu/-calculus, due to D. Janin and I. Walukiewicz (1999), is lifted from the modal to the guarded domain by means of model theoretic translations. At the methodological level, these translations make the intuitive analogy between modal and guarded logics available as a tool in the analysis of the guarded domain.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114852380","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 : 2000-06-26DOI: 10.1109/LICS.2000.855773
B. Moszkowski
Interval temporal logic (ITL) is a formalism for reasoning about time periods. To date no one has proved completeness of a relatively simple ITL deductive system supporting infinite time and permitting infinite sequential iteration comparable to /spl omega/-regular expressions. We give a complete axiomatization for such a version of quantified ITL over finite domains and can show completeness by representing finite-state automata in ITL and then translating ITL formulas into them. The axiom system (and completeness) is extended to infinite time.
{"title":"A complete axiomatization of interval temporal logic with infinite time","authors":"B. Moszkowski","doi":"10.1109/LICS.2000.855773","DOIUrl":"https://doi.org/10.1109/LICS.2000.855773","url":null,"abstract":"Interval temporal logic (ITL) is a formalism for reasoning about time periods. To date no one has proved completeness of a relatively simple ITL deductive system supporting infinite time and permitting infinite sequential iteration comparable to /spl omega/-regular expressions. We give a complete axiomatization for such a version of quantified ITL over finite domains and can show completeness by representing finite-state automata in ITL and then translating ITL formulas into them. The axiom system (and completeness) is extended to infinite time.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117150488","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 : 2000-06-26DOI: 10.1109/LICS.2000.855788
Guillem Godoy, R. Nieuwenhuis
A new technique is presented for superposition with first order clauses with built-in abelian groups (AG). Compared with previous approaches, it is simpler, and no inferences with the AG axioms or abstraction rules are needed. Furthermore, AG-unification is used instead of the computationally more expensive unification modulo associativity and commutativity. Due to the simplicity and restrictiveness of our inference system, its compatibility with redundancy notions and constraints, and the fact that standard term orderings like RPO can be used, we believe that our technique will become the method of choice for practice, as well as a basis for new theoretical developments like logic-based complexity and decidability analysis.
{"title":"Paramodulation with built-in abelian groups","authors":"Guillem Godoy, R. Nieuwenhuis","doi":"10.1109/LICS.2000.855788","DOIUrl":"https://doi.org/10.1109/LICS.2000.855788","url":null,"abstract":"A new technique is presented for superposition with first order clauses with built-in abelian groups (AG). Compared with previous approaches, it is simpler, and no inferences with the AG axioms or abstraction rules are needed. Furthermore, AG-unification is used instead of the computationally more expensive unification modulo associativity and commutativity. Due to the simplicity and restrictiveness of our inference system, its compatibility with redundancy notions and constraints, and the fact that standard term orderings like RPO can be used, we believe that our technique will become the method of choice for practice, as well as a basis for new theoretical developments like logic-based complexity and decidability analysis.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127152216","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 present a general notion of realizability, encompassing both standard Kleene style realizability over partial combinatory algebras and Kleene style realizability over more general structures, including all partial cartesian closed categories. We show how the general notion of realizability can be used to get models of dependent predicate logic, thus obtaining as a corollary (the known result) that the category Equ of equilogical spaces models dependent predicate logic. Moreover, we characterize when the general notion of realizability gives rise to a topos.
{"title":"A general notion of realizability","authors":"L. Birkedal","doi":"10.2178/bsl/1182353873","DOIUrl":"https://doi.org/10.2178/bsl/1182353873","url":null,"abstract":"We present a general notion of realizability, encompassing both standard Kleene style realizability over partial combinatory algebras and Kleene style realizability over more general structures, including all partial cartesian closed categories. We show how the general notion of realizability can be used to get models of dependent predicate logic, thus obtaining as a corollary (the known result) that the category Equ of equilogical spaces models dependent predicate logic. Moreover, we characterize when the general notion of realizability gives rise to a topos.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"32 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113971537","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 : 2000-06-26DOI: 10.1109/LICS.2000.855758
Klaus Aehlig, H. Schwichtenberg
A purely syntactical proof is given that all functions definable in a certain affine linear typed /spl lambda/-calculus with iteration in all types are polynomial time computable. The proof also gives explicit polynomial bounds that can easily be calculated.
{"title":"A syntactical analysis of non-size-increasing polynomial time computation","authors":"Klaus Aehlig, H. Schwichtenberg","doi":"10.1109/LICS.2000.855758","DOIUrl":"https://doi.org/10.1109/LICS.2000.855758","url":null,"abstract":"A purely syntactical proof is given that all functions definable in a certain affine linear typed /spl lambda/-calculus with iteration in all types are polynomial time computable. The proof also gives explicit polynomial bounds that can easily be calculated.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"370 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116520066","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 : 2000-06-26DOI: 10.1109/LICS.2000.855755
Achim Blumensath, E. Grädel
We study definability and complexity issues for automatic and /spl omega/-automatic structures. These are, in general, infinite structures but they can be finitely presented by a collection of automata. Moreover they admit effective (in fact automatic) evaluation of all first-order queries. Therefore, automatic structures provide an interesting framework for extending many algorithmic and logical methods from finite structures to infinite ones. We explain the notion of (/spl omega/-)automatic structures, give examples, and discuss the relationship to automatic groups. We determine the complexity of model checking and query evaluation on automatic structures for fragments of first-order logic. Further we study closure properties and definability issues on automatic structures and present a technique for proving that a structure is not automatic. We give model-theoretic characterisations for automatic structures via interpretations. Finally we discuss the composition theory of automatic structures and prove that they are closed under finitary Feferman-Vaught-like products.
{"title":"Automatic structures","authors":"Achim Blumensath, E. Grädel","doi":"10.1109/LICS.2000.855755","DOIUrl":"https://doi.org/10.1109/LICS.2000.855755","url":null,"abstract":"We study definability and complexity issues for automatic and /spl omega/-automatic structures. These are, in general, infinite structures but they can be finitely presented by a collection of automata. Moreover they admit effective (in fact automatic) evaluation of all first-order queries. Therefore, automatic structures provide an interesting framework for extending many algorithmic and logical methods from finite structures to infinite ones. We explain the notion of (/spl omega/-)automatic structures, give examples, and discuss the relationship to automatic groups. We determine the complexity of model checking and query evaluation on automatic structures for fragments of first-order logic. Further we study closure properties and definability issues on automatic structures and present a technique for proving that a structure is not automatic. We give model-theoretic characterisations for automatic structures via interpretations. Finally we discuss the composition theory of automatic structures and prove that they are closed under finitary Feferman-Vaught-like products.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133719175","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 : 2000-06-26DOI: 10.1109/LICS.2000.855761
E. Emerson, John Havlicek, Richard J. Trefler
We provide a general method for ameliorating state explosion via symmetry reduction in certain asymmetric systems, such as systems with many similar, but not identical, processes. The method applies to systems whose structures (i.e., state transition graphs) have more state symmetries than arc symmetries. We introduce a new notion of "virtual symmetry" that strictly subsumes earlier notions of "rough symmetry" and "near symmetry" (Emerson and Trefler, 1999). Virtual symmetry is the most general condition under which the structure of a system is naturally bisimilar to its quotient by a group of state symmetries. We give several example systems exhibiting virtual symmetry that are not amenable to symmetry reduction by earlier techniques: a one-lane bridge system, where the direction with priority for crossing changes dynamically; an abstract system with asymmetric communication network; and a system with asymmetric resource sharing motivated from the drinking philosophers problem. These examples show that virtual symmetry reduction applies to a significantly broader class of asymmetric systems than could be handled before.
{"title":"Virtual symmetry reduction","authors":"E. Emerson, John Havlicek, Richard J. Trefler","doi":"10.1109/LICS.2000.855761","DOIUrl":"https://doi.org/10.1109/LICS.2000.855761","url":null,"abstract":"We provide a general method for ameliorating state explosion via symmetry reduction in certain asymmetric systems, such as systems with many similar, but not identical, processes. The method applies to systems whose structures (i.e., state transition graphs) have more state symmetries than arc symmetries. We introduce a new notion of \"virtual symmetry\" that strictly subsumes earlier notions of \"rough symmetry\" and \"near symmetry\" (Emerson and Trefler, 1999). Virtual symmetry is the most general condition under which the structure of a system is naturally bisimilar to its quotient by a group of state symmetries. We give several example systems exhibiting virtual symmetry that are not amenable to symmetry reduction by earlier techniques: a one-lane bridge system, where the direction with priority for crossing changes dynamically; an abstract system with asymmetric communication network; and a system with asymmetric resource sharing motivated from the drinking philosophers problem. These examples show that virtual symmetry reduction applies to a significantly broader class of asymmetric systems than could be handled before.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"193 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115345217","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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