Pub Date : 1998-06-21DOI: 10.1109/LICS.1998.705675
Dusko Pavlovic, M. Escardó
Coinduction is often seen as a way of implementing infinite objects. Since real numbers are typical infinite objects, it may not come as a surprise that calculus, when presented in a suitable way, is permeated by coinductive reasoning. What is surprising is that mathematical techniques, recently developed in the context of computer science, seem to be shedding a new light on some basic methods of calculus. We introduce a coinductive formalization of elementary calculus that can be used as a tool for symbolic computation, and geared towards computer algebra and theorem proving. So far, we have covered parts of ordinary differential and difference equations, Taylor series, Laplace transform and the basics of the operator calculus.
{"title":"Calculus in coinductive form","authors":"Dusko Pavlovic, M. Escardó","doi":"10.1109/LICS.1998.705675","DOIUrl":"https://doi.org/10.1109/LICS.1998.705675","url":null,"abstract":"Coinduction is often seen as a way of implementing infinite objects. Since real numbers are typical infinite objects, it may not come as a surprise that calculus, when presented in a suitable way, is permeated by coinductive reasoning. What is surprising is that mathematical techniques, recently developed in the context of computer science, seem to be shedding a new light on some basic methods of calculus. We introduce a coinductive formalization of elementary calculus that can be used as a tool for symbolic computation, and geared towards computer algebra and theorem proving. So far, we have covered parts of ordinary differential and difference equations, Taylor series, Laplace transform and the basics of the operator calculus.","PeriodicalId":173462,"journal":{"name":"Proceedings. Thirteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.98CB36226)","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115213033","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 : 1998-06-21DOI: 10.1109/LICS.1998.705673
R. Viswanathan
We present a new interpretation of typed object-oriented concepts in terms of well-understood, purely procedural concepts, that preserves observational equivalence. More precisely, we give compositional translations of (a) Ob/sub 1/spl mu//, an object calculus supporting method invocation and functional method update with first-order object types and recursive types, and (b) Ob/sub 1<:/spl mu//, an extension of Ob/sub 1/spl mu// with subtyping, that are fully abstract on closed terms. The target of the translations are a first-order /spl lambda/-calculus with records and recursive types, with and without subtyping. The translation of the calculus with subtyping is subtype-preserving as well.
{"title":"Full abstraction for first-order objects with recursive types and subtyping","authors":"R. Viswanathan","doi":"10.1109/LICS.1998.705673","DOIUrl":"https://doi.org/10.1109/LICS.1998.705673","url":null,"abstract":"We present a new interpretation of typed object-oriented concepts in terms of well-understood, purely procedural concepts, that preserves observational equivalence. More precisely, we give compositional translations of (a) Ob/sub 1/spl mu//, an object calculus supporting method invocation and functional method update with first-order object types and recursive types, and (b) Ob/sub 1<:/spl mu//, an extension of Ob/sub 1/spl mu// with subtyping, that are fully abstract on closed terms. The target of the translations are a first-order /spl lambda/-calculus with records and recursive types, with and without subtyping. The translation of the calculus with subtyping is subtype-preserving as well.","PeriodicalId":173462,"journal":{"name":"Proceedings. Thirteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.98CB36226)","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117142134","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 : 1998-06-21DOI: 10.1109/LICS.1998.705674
Moshe Y. Vardi
The discussion of the relative merits of linear versus branching time frameworks goes back to early 1980s. One of the beliefs dominating this discussion has been that "while specifying is easier in LTL (linear-temporal logic), verification is easier for CTL (branching-temporal logic)". Indeed, the restricted syntax of CTL limits its expressive power and many important behaviours (e.g., strong fairness) can not be specified in CTL. On the other hand, while model checking for CTL can be done in time that is linear in the size of the specification, it takes time that is exponential in the specification for LTL. A closer examination of the the issue reveals, however, that the computational superiority of the branching time framework is perhaps illusory. In this talk we will compare the complexity of branching-time verification vs. Linear-time verification in many scenarios, and show that linear-time verification is not harder and often is even easier than branching-time verification. This suggests that the tradeoff between branching and linear time is not a simple tradeoff between complexity and expressiveness.
{"title":"Linear vs. branching time: a complexity-theoretic perspective","authors":"Moshe Y. Vardi","doi":"10.1109/LICS.1998.705674","DOIUrl":"https://doi.org/10.1109/LICS.1998.705674","url":null,"abstract":"The discussion of the relative merits of linear versus branching time frameworks goes back to early 1980s. One of the beliefs dominating this discussion has been that \"while specifying is easier in LTL (linear-temporal logic), verification is easier for CTL (branching-temporal logic)\". Indeed, the restricted syntax of CTL limits its expressive power and many important behaviours (e.g., strong fairness) can not be specified in CTL. On the other hand, while model checking for CTL can be done in time that is linear in the size of the specification, it takes time that is exponential in the specification for LTL. A closer examination of the the issue reveals, however, that the computational superiority of the branching time framework is perhaps illusory. In this talk we will compare the complexity of branching-time verification vs. Linear-time verification in many scenarios, and show that linear-time verification is not harder and often is even easier than branching-time verification. This suggests that the tradeoff between branching and linear time is not a simple tradeoff between complexity and expressiveness.","PeriodicalId":173462,"journal":{"name":"Proceedings. Thirteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.98CB36226)","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124800143","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 : 1998-06-21DOI: 10.1109/LICS.1998.705663
Margus Veanes
Simultaneous rigid E-unification, or SREU for short, is a fundamental problem that arises in global methods of automated theorem proving in classical logic with equality. In order to do proof search in intuitionistic logic with equality one has to handle SREU as well. Furthermore, restricted forms of SREU are strongly related to word equations and finite tree automata. It was recently shown that second-order unification has a very natural reduction to simultaneous rigid E-unification, which constituted probably the most transparent undecidability proof of SREU. Here we show that there is also a natural encoding of SREU in second-order unification. It follows that the problems are logspace equivalent. So second-order unification plays the same fundamental role as SREU in automated reasoning in logic with equality. We exploit this connection and use finite tree automata techniques to present a very elementary undecidability proof of second-order unification, by reduction from the halting problem for Turing machines. It follows from that proof that second-order unification is undecidable for all nonmonadic second-order term languages having at least two second-order variables with sufficiently high arities.
{"title":"The relation between second-order unification and simultaneous rigid E-unification","authors":"Margus Veanes","doi":"10.1109/LICS.1998.705663","DOIUrl":"https://doi.org/10.1109/LICS.1998.705663","url":null,"abstract":"Simultaneous rigid E-unification, or SREU for short, is a fundamental problem that arises in global methods of automated theorem proving in classical logic with equality. In order to do proof search in intuitionistic logic with equality one has to handle SREU as well. Furthermore, restricted forms of SREU are strongly related to word equations and finite tree automata. It was recently shown that second-order unification has a very natural reduction to simultaneous rigid E-unification, which constituted probably the most transparent undecidability proof of SREU. Here we show that there is also a natural encoding of SREU in second-order unification. It follows that the problems are logspace equivalent. So second-order unification plays the same fundamental role as SREU in automated reasoning in logic with equality. We exploit this connection and use finite tree automata techniques to present a very elementary undecidability proof of second-order unification, by reduction from the halting problem for Turing machines. It follows from that proof that second-order unification is undecidable for all nonmonadic second-order term languages having at least two second-order variables with sufficiently high arities.","PeriodicalId":173462,"journal":{"name":"Proceedings. Thirteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.98CB36226)","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114378410","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 : 1998-06-21DOI: 10.1109/LICS.1998.705656
C. Hermida, M. Makkai, J. Power
We introduce the notion of higher dimensional multigraph. This notion extends that of multigraph, which underlies multicategories and is essentially equivalent to the notion of context-free grammar. We develop the definition and explain how it gives a semantically coherent category theoretic approach to the notion of higher order context-free grammar. It also gives a conceptual framework in which one can study rewrites, and rewrites of rewrites, etcetera, for proofs of sequent calculus. The definition involves a subtle interaction between geometry and linearly defined syntax; we explore the latter here, outlining the geometric intuition.
{"title":"Higher dimensional multigraphs","authors":"C. Hermida, M. Makkai, J. Power","doi":"10.1109/LICS.1998.705656","DOIUrl":"https://doi.org/10.1109/LICS.1998.705656","url":null,"abstract":"We introduce the notion of higher dimensional multigraph. This notion extends that of multigraph, which underlies multicategories and is essentially equivalent to the notion of context-free grammar. We develop the definition and explain how it gives a semantically coherent category theoretic approach to the notion of higher order context-free grammar. It also gives a conceptual framework in which one can study rewrites, and rewrites of rewrites, etcetera, for proofs of sequent calculus. The definition involves a subtle interaction between geometry and linearly defined syntax; we explore the latter here, outlining the geometric intuition.","PeriodicalId":173462,"journal":{"name":"Proceedings. Thirteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.98CB36226)","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124446924","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 : 1998-06-21DOI: 10.1109/LICS.1998.705669
S. Abramsky, Kohei Honda, G. McCusker
A games model of a programming language with higher-order store in the style of ML-references is introduced. The category used for the model is obtained by relaxing certain behavioural conditions on a category of games previously used to provide fully abstract models of pure functional languages. The model is shown to be fully abstract by means of factorization arguments which reduce the question of definability for the language with higher-order store to that for its purely functional fragment.
{"title":"A fully abstract game semantics for general references","authors":"S. Abramsky, Kohei Honda, G. McCusker","doi":"10.1109/LICS.1998.705669","DOIUrl":"https://doi.org/10.1109/LICS.1998.705669","url":null,"abstract":"A games model of a programming language with higher-order store in the style of ML-references is introduced. The category used for the model is obtained by relaxing certain behavioural conditions on a category of games previously used to provide fully abstract models of pure functional languages. The model is shown to be fully abstract by means of factorization arguments which reduce the question of definability for the language with higher-order store to that for its purely functional fragment.","PeriodicalId":173462,"journal":{"name":"Proceedings. Thirteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.98CB36226)","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131137675","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 : 1998-06-21DOI: 10.1109/LICS.1998.705639
Martin Grohe
We study the expressive power of inflationary fixed-point logic IFP and inflationary fixed-point logic with counting IFP+C on planar graphs. We prove the following results: (1) IFP captures polynomial time on 3-connected planar graphs, and IFP+C captures polynomial time on arbitrary planar graphs. (2) Planar graphs can be characterized up to isomorphism in a logic with finitely many variables and counting. This answers a question of Immerman (1987). (3) The class of planar graphs is definable in IFP. This answers a question of Dawar and Gradel.
{"title":"Fixed-point logics on planar graphs","authors":"Martin Grohe","doi":"10.1109/LICS.1998.705639","DOIUrl":"https://doi.org/10.1109/LICS.1998.705639","url":null,"abstract":"We study the expressive power of inflationary fixed-point logic IFP and inflationary fixed-point logic with counting IFP+C on planar graphs. We prove the following results: (1) IFP captures polynomial time on 3-connected planar graphs, and IFP+C captures polynomial time on arbitrary planar graphs. (2) Planar graphs can be characterized up to isomorphism in a logic with finitely many variables and counting. This answers a question of Immerman (1987). (3) The class of planar graphs is definable in IFP. This answers a question of Dawar and Gradel.","PeriodicalId":173462,"journal":{"name":"Proceedings. Thirteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.98CB36226)","volume":"114 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123640174","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 : 1998-06-21DOI: 10.1109/LICS.1998.705672
H. Yokouchi
This paper develops type assignment systems for intersection and union types, and type quantifiers. The known system for these types is not semantically complete. We introduce a certain class of typing statements, called stable statements, which include all statements without type quantifiers, and we show that the known system is complete for stable statements if we add two axiom schemas expressing the distributive laws of intersection over union and existential quantifier, respectively. All the results are obtained in a systematic way with sequent calculi for type assignment and the cut-elimination for them.
{"title":"Completeness of type assignment systems with intersection, union, and type quantifiers","authors":"H. Yokouchi","doi":"10.1109/LICS.1998.705672","DOIUrl":"https://doi.org/10.1109/LICS.1998.705672","url":null,"abstract":"This paper develops type assignment systems for intersection and union types, and type quantifiers. The known system for these types is not semantically complete. We introduce a certain class of typing statements, called stable statements, which include all statements without type quantifiers, and we show that the known system is complete for stable statements if we add two axiom schemas expressing the distributive laws of intersection over union and existential quantifier, respectively. All the results are obtained in a systematic way with sequent calculi for type assignment and the cut-elimination for them.","PeriodicalId":173462,"journal":{"name":"Proceedings. Thirteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.98CB36226)","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121901765","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 : 1998-06-21DOI: 10.1109/LICS.1998.705645
O. Kupferman, Moshe Y. Vardi
Model checking is a method for the verification of systems with respect to their specifications. Symbolic model-checking, which enables the verification of large systems, proceeds by calculating fixed-point expressions over the system's set of states. The /spl mu/-calculus is a branching-time temporal logic with fixed-point operators. As such, it is a convenient logic for symbolic model-checking tools. In particular, the alternation-free fragment of /spl mu/-calculus has a restricted syntax, making the symbolic evaluation of its formulas computationally easy. Formally, it takes time that is linear in the size of the system. On the other hand, specifiers find the /spl mu/-calculus inconvenient. In addition, specifiers often prefer to use Linear-time formalisms. Such formalisms, however, cannot in general be translated to the alternation-free CL-calculus, and their symbolic evaluation involves nesting of fixed-points, resulting in time complexity that is quadratic in the size of the system. In this paper we characterize linear-time properties that can be specified in the alternation-free /spl mu/-calculus. We show that a linear-time property can be specified in the alternation-free /spl mu/-calculus if it can be recognized by a deterministic Buchi automation. We study the problem of deciding whether a linear-time property, specified by either an automaton or an LTL formula, can be translated to an alternation-free /spl mu/-calculus formula, and describe the translation, when exists.
{"title":"Freedom, weakness, and determinism: from linear-time to branching-time","authors":"O. Kupferman, Moshe Y. Vardi","doi":"10.1109/LICS.1998.705645","DOIUrl":"https://doi.org/10.1109/LICS.1998.705645","url":null,"abstract":"Model checking is a method for the verification of systems with respect to their specifications. Symbolic model-checking, which enables the verification of large systems, proceeds by calculating fixed-point expressions over the system's set of states. The /spl mu/-calculus is a branching-time temporal logic with fixed-point operators. As such, it is a convenient logic for symbolic model-checking tools. In particular, the alternation-free fragment of /spl mu/-calculus has a restricted syntax, making the symbolic evaluation of its formulas computationally easy. Formally, it takes time that is linear in the size of the system. On the other hand, specifiers find the /spl mu/-calculus inconvenient. In addition, specifiers often prefer to use Linear-time formalisms. Such formalisms, however, cannot in general be translated to the alternation-free CL-calculus, and their symbolic evaluation involves nesting of fixed-points, resulting in time complexity that is quadratic in the size of the system. In this paper we characterize linear-time properties that can be specified in the alternation-free /spl mu/-calculus. We show that a linear-time property can be specified in the alternation-free /spl mu/-calculus if it can be recognized by a deterministic Buchi automation. We study the problem of deciding whether a linear-time property, specified by either an automaton or an LTL formula, can be translated to an alternation-free /spl mu/-calculus formula, and describe the translation, when exists.","PeriodicalId":173462,"journal":{"name":"Proceedings. Thirteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.98CB36226)","volume":"812 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122025414","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 : 1998-06-21DOI: 10.1109/LICS.1998.705683
L. Libkin
The expressive power of first-order logic over finite structures is limited in two ways: it lacks a recursion mechanism, and it cannot count. Overcoming the first limitation has been a subject of extensive study. A number of fixpoint logics have been introduced, and shown to be subsumed by an infinitary logic L/sub /spl infin//spl omega///sup /spl omega//. This logic is easier to analyze than fixpoint logics, and it still lacks counting power, as it has a 0-1 law. On the counting side, there is no analog of L/sub /spl infin//spl omega///sup /spl omega//. There are a number of logics with counting power, usually introduced via generalized quantifiers. Most known expressivity bounds are based on the fact that counting extensions of first-order logic preserve the locality properties. This paper has three main goals. First, we introduce a new logic L/sub /spl infin//spl omega//*(C) that plays the same role for counting as L/sub /spl infin//spl omega///sup /spl omega// does for recursion-it subsumes a number of extensions of first-order logic with counting, and has nice properties that make it easy to study. Second, we give a simple direct proof that L/sub /spl infin//spl omega//*(C) expresses only local properties: those that depend on the properties of small neighborhoods, but cannot grasp a structure as a whole. This is a general way of saying that a logic lacks a recursion mechanism. Third, we consider a finer analysis of locality of counting logics. In particular, we address the question of how local a logic is, that is, how big are those neighborhoods that local properties depend on. We get a uniform answer for a variety of logics between first-order and L/sub /spl infin//spl omega//*(C). This is done by introducing a new form of locality that captures the tightest condition that the duplicator needs to maintain in order to win a game. We use this technique to give bounds on outputs of L/sub /spl infin//spl omega//*(C)-definable queries. We also specialize some of the results for structures of small degree.
{"title":"On counting logics and local properties","authors":"L. Libkin","doi":"10.1109/LICS.1998.705683","DOIUrl":"https://doi.org/10.1109/LICS.1998.705683","url":null,"abstract":"The expressive power of first-order logic over finite structures is limited in two ways: it lacks a recursion mechanism, and it cannot count. Overcoming the first limitation has been a subject of extensive study. A number of fixpoint logics have been introduced, and shown to be subsumed by an infinitary logic L/sub /spl infin//spl omega///sup /spl omega//. This logic is easier to analyze than fixpoint logics, and it still lacks counting power, as it has a 0-1 law. On the counting side, there is no analog of L/sub /spl infin//spl omega///sup /spl omega//. There are a number of logics with counting power, usually introduced via generalized quantifiers. Most known expressivity bounds are based on the fact that counting extensions of first-order logic preserve the locality properties. This paper has three main goals. First, we introduce a new logic L/sub /spl infin//spl omega//*(C) that plays the same role for counting as L/sub /spl infin//spl omega///sup /spl omega// does for recursion-it subsumes a number of extensions of first-order logic with counting, and has nice properties that make it easy to study. Second, we give a simple direct proof that L/sub /spl infin//spl omega//*(C) expresses only local properties: those that depend on the properties of small neighborhoods, but cannot grasp a structure as a whole. This is a general way of saying that a logic lacks a recursion mechanism. Third, we consider a finer analysis of locality of counting logics. In particular, we address the question of how local a logic is, that is, how big are those neighborhoods that local properties depend on. We get a uniform answer for a variety of logics between first-order and L/sub /spl infin//spl omega//*(C). This is done by introducing a new form of locality that captures the tightest condition that the duplicator needs to maintain in order to win a game. We use this technique to give bounds on outputs of L/sub /spl infin//spl omega//*(C)-definable queries. We also specialize some of the results for structures of small degree.","PeriodicalId":173462,"journal":{"name":"Proceedings. Thirteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.98CB36226)","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127270085","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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