Pub Date : 2000-06-26DOI: 10.1109/LICS.2000.855781
Gian Luca Cattani, Peter Sewell
We study syntax-free models for name-passing processes. For interleaving semantics, we identify the indexing structure required of an early labelled transition system to support the usual /spl pi/-calculus operations, defining indexed labelled transition systems. For non-interleaving causal semantics, we define indexed labelled asynchronous transition systems, smoothly generalizing both our interleaving model and the standard asynchronous transition systems model for CCS-like calculi. In each case we relate a denotational semantics to an operational view for bisimulation and causal bisimulation respectively. This is a first step towards a uniform understanding of the semantics and operations of name-passing calculi.
{"title":"Models for name-passing processes: interleaving and causal","authors":"Gian Luca Cattani, Peter Sewell","doi":"10.1109/LICS.2000.855781","DOIUrl":"https://doi.org/10.1109/LICS.2000.855781","url":null,"abstract":"We study syntax-free models for name-passing processes. For interleaving semantics, we identify the indexing structure required of an early labelled transition system to support the usual /spl pi/-calculus operations, defining indexed labelled transition systems. For non-interleaving causal semantics, we define indexed labelled asynchronous transition systems, smoothly generalizing both our interleaving model and the standard asynchronous transition systems model for CCS-like calculi. In each case we relate a denotational semantics to an operational view for bisimulation and causal bisimulation respectively. This is a first step towards a uniform understanding of the semantics and operations of name-passing calculi.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"11 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":"122516009","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.2000.855785
H. Xi
The article enriches imperative programming with a form of dependent types. We start by explaining some motivations for this enrichment and mentioning some major obstacles that need to be overcome. We then present the design of a source level dependently typed imperative programming language Xanadu, forming both static and dynamic semantics and then establishing the type soundness theorem. We also present realistic examples, which have all been verified in a prototype implementation, in support of the practicality of Xanadu. We claim that the language design of Xanadu is novel and it serves as an informative example that demonstrates a means to combine imperative programming with dependent types.
{"title":"Imperative programming with dependent types","authors":"H. Xi","doi":"10.1109/LICS.2000.855785","DOIUrl":"https://doi.org/10.1109/LICS.2000.855785","url":null,"abstract":"The article enriches imperative programming with a form of dependent types. We start by explaining some motivations for this enrichment and mentioning some major obstacles that need to be overcome. We then present the design of a source level dependently typed imperative programming language Xanadu, forming both static and dynamic semantics and then establishing the type soundness theorem. We also present realistic examples, which have all been verified in a prototype implementation, in support of the practicality of Xanadu. We claim that the language design of Xanadu is novel and it serves as an informative example that demonstrates a means to combine imperative programming with dependent types.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"43 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":"127801153","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.2000.855750
Ronald Fagin
In this talk, I will discuss an approach to the P = NP question via the correspondence between logic and complexity. The focus will be on the possible use of Ehrenfeucht-Fraisse games.
{"title":"Logic, complexity, and games","authors":"Ronald Fagin","doi":"10.1109/LICS.2000.855750","DOIUrl":"https://doi.org/10.1109/LICS.2000.855750","url":null,"abstract":"In this talk, I will discuss an approach to the P = NP question via the correspondence between logic and complexity. The focus will be on the possible use of Ehrenfeucht-Fraisse games.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"60 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":"115931667","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.2000.855780
A. Jeffrey, J. Rathke
Concurrent ML is an extension of Standard ML with /spl pi/-calculus-like primitives for multi-threaded programming. CML has a reduction semantics, but to date there has been no labelled transitions semantics provided for the entire language. We present a labelled transition semantics for a fragment of CML called /spl mu/vCML which includes features not covered before: dynamically generated local channels and thread identifiers. We show that weak bisimulation for /spl mu/vCML is a congruence, and coincides with barbed bisimulation congruence. We also provide a variant of D. Sangiorgi's (1993) normal bisimulation for /spl mu/vCML, and show that this too coincides with bisimulation.
{"title":"A theory of bisimulation for a fragment of Concurrent ML with local names","authors":"A. Jeffrey, J. Rathke","doi":"10.1109/LICS.2000.855780","DOIUrl":"https://doi.org/10.1109/LICS.2000.855780","url":null,"abstract":"Concurrent ML is an extension of Standard ML with /spl pi/-calculus-like primitives for multi-threaded programming. CML has a reduction semantics, but to date there has been no labelled transitions semantics provided for the entire language. We present a labelled transition semantics for a fragment of CML called /spl mu/vCML which includes features not covered before: dynamically generated local channels and thread identifiers. We show that weak bisimulation for /spl mu/vCML is a congruence, and coincides with barbed bisimulation congruence. We also provide a variant of D. Sangiorgi's (1993) normal bisimulation for /spl mu/vCML, and show that this too coincides with bisimulation.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"4 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":"114187759","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.2000.855752
Alexandre Miquel
We introduce a novel model based on coherence spaces for interpreting large impredicative type systems such as the Extended Calculus of Constructions (ECC). Moreover we show that this model is well-suited for interpreting intersection types and subtyping too, and we illustrate this by interpreting a variant of ECC with an additional intersection type binder. Furthermore, we propose a general method for interpreting the impredicative level in a non-syntactical way, by allowing the model to be parametrized by an arbitrarily large coherence space in order to interpret inhabitants of impredicative types. As an application, we show that uncountable types such as the type of real numbers or Zermelo-Frankel sets can safely be axiomatized on the impredicative level of, say, ECC, without harm for consistency.
{"title":"A model for impredicative type systems, universes, intersection types and subtyping","authors":"Alexandre Miquel","doi":"10.1109/LICS.2000.855752","DOIUrl":"https://doi.org/10.1109/LICS.2000.855752","url":null,"abstract":"We introduce a novel model based on coherence spaces for interpreting large impredicative type systems such as the Extended Calculus of Constructions (ECC). Moreover we show that this model is well-suited for interpreting intersection types and subtyping too, and we illustrate this by interpreting a variant of ECC with an additional intersection type binder. Furthermore, we propose a general method for interpreting the impredicative level in a non-syntactical way, by allowing the model to be parametrized by an arbitrarily large coherence space in order to interpret inhabitants of impredicative types. As an application, we show that uncountable types such as the type of real numbers or Zermelo-Frankel sets can safely be axiomatized on the impredicative level of, say, ECC, without harm for consistency.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"11 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":"121732228","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.2000.855763
L. D. Alfaro, T. Henzinger
We consider two-player games which are played on a finite state space for an infinite number of rounds. The games are concurrent, that is, in each round, the two players choose their moves independently and simultaneously; the current state and the two moves determine a successor state. We consider omega-regular winning conditions on the resulting infinite state sequence. To model the independent choice of moves, both players are allowed to use randomization for selecting their moves. This gives rise to the following qualitative modes of winning, which can be studied without numerical considerations concerning probabilities: sure-win (player 1 can ensure winning with certainty); almost-sure-win (player 1 can ensure winning with probability 1); limit-win (player 1 can ensure winning with probability arbitrarily close to 1); bounded-win (player 1 can ensure winning with probability bounded away from 0); positive-win (player 1 can ensure winning with positive probability); and exist-win (player 1 can ensure that at least one possible outcome of the game satisfies the winning condition). We provide algorithms for computing the sets of winning states for each of these winning modes. In particular, we solve concurrent Rabin-chain games in n/sup O/(m) time, where n is the size of the game structure and m is the number of pairs in the Rabin-chain condition. While this complexity is in line with traditional turn-based games, our algorithms are considerably more involved. This is because concurrent games violate two of the most basic properties of turn-based games: concurrent games are not determined, but rather exhibit a more general duality property which involves multiple modes of winning; and winning strategies for concurrent games may require infinite memory.
{"title":"Concurrent omega-regular games","authors":"L. D. Alfaro, T. Henzinger","doi":"10.1109/LICS.2000.855763","DOIUrl":"https://doi.org/10.1109/LICS.2000.855763","url":null,"abstract":"We consider two-player games which are played on a finite state space for an infinite number of rounds. The games are concurrent, that is, in each round, the two players choose their moves independently and simultaneously; the current state and the two moves determine a successor state. We consider omega-regular winning conditions on the resulting infinite state sequence. To model the independent choice of moves, both players are allowed to use randomization for selecting their moves. This gives rise to the following qualitative modes of winning, which can be studied without numerical considerations concerning probabilities: sure-win (player 1 can ensure winning with certainty); almost-sure-win (player 1 can ensure winning with probability 1); limit-win (player 1 can ensure winning with probability arbitrarily close to 1); bounded-win (player 1 can ensure winning with probability bounded away from 0); positive-win (player 1 can ensure winning with positive probability); and exist-win (player 1 can ensure that at least one possible outcome of the game satisfies the winning condition). We provide algorithms for computing the sets of winning states for each of these winning modes. In particular, we solve concurrent Rabin-chain games in n/sup O/(m) time, where n is the size of the game structure and m is the number of pairs in the Rabin-chain condition. While this complexity is in line with traditional turn-based games, our algorithms are considerably more involved. This is because concurrent games violate two of the most basic properties of turn-based games: concurrent games are not determined, but rather exhibit a more general duality property which involves multiple modes of winning; and winning strategies for concurrent games may require infinite memory.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"80 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":"131993900","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.2000.855779
J. Krivine
This talk presents a system of typed lambda-calculus for the Zermelo-Frankel set theory, in the framework of classical logic [10]. The Curry-Howard correspondence between proofs and programs was originally discovered with the system of simple types, which uses the intuitionistic propositional calculus, with the only connective. It was extended to second order intuitionistic logic, in 1970, by J.-Y. Girard [4], under the name of system F for which he proved the normalization property .The relation with programming languages was made by Reynolds [13].More recently, in 1990, the Curry-Howard correspondence was extended to classical logic, following Felleisen and Griffin [6] who discovered that the law of Peirce corresponds to control instructions in functional programming languages. It is interesting to notice that, as early as 1972, Clint and Hoare [1] had made an analogous remark for the law of excluded middle and controlled jump instructions in imperative languages.There are now many type systems, which are based on classical logic, among the best known are the system LC of J.-Y. Girard [5] and the e µ-calculus of M. Parigot [12]. We use a system closely related to the latter, called the e c calculus [8, 9]. Both systems use classical second order logic and have the normalization property.In order to extend the Curry -Howard correspondence to classical Zermelo-Frankel set theory, we give realizability models, which are built recursively like in the well-known construction of forcing. We show that each axiom of ZF is then realized; we obtain in this way a type s stem in which set-theoretic proofs are formalizable and give rise to programs, which are e -terms with control instructions. In this system, the normalization property is ?essentially true? in the sense that we get correct computations on data types. Of course, not every typable term is normalizable since, for example, Y has the type of the foundation axiom. These realizability models differ deeply from forcing models and pose several interesting problems. In particular, they do not seem to be end extensions of the original model of ZFC. In addition, it is likely that the negation of the axiom of choice is realized in them.
{"title":"The curry-howard correspondence in set theory","authors":"J. Krivine","doi":"10.1109/LICS.2000.855779","DOIUrl":"https://doi.org/10.1109/LICS.2000.855779","url":null,"abstract":"This talk presents a system of typed lambda-calculus for the Zermelo-Frankel set theory, in the framework of classical logic [10]. The Curry-Howard correspondence between proofs and programs was originally discovered with the system of simple types, which uses the intuitionistic propositional calculus, with the only connective. It was extended to second order intuitionistic logic, in 1970, by J.-Y. Girard [4], under the name of system F for which he proved the normalization property .The relation with programming languages was made by Reynolds [13].More recently, in 1990, the Curry-Howard correspondence was extended to classical logic, following Felleisen and Griffin [6] who discovered that the law of Peirce corresponds to control instructions in functional programming languages. It is interesting to notice that, as early as 1972, Clint and Hoare [1] had made an analogous remark for the law of excluded middle and controlled jump instructions in imperative languages.There are now many type systems, which are based on classical logic, among the best known are the system LC of J.-Y. Girard [5] and the e µ-calculus of M. Parigot [12]. We use a system closely related to the latter, called the e c calculus [8, 9]. Both systems use classical second order logic and have the normalization property.In order to extend the Curry -Howard correspondence to classical Zermelo-Frankel set theory, we give realizability models, which are built recursively like in the well-known construction of forcing. We show that each axiom of ZF is then realized; we obtain in this way a type s stem in which set-theoretic proofs are formalizable and give rise to programs, which are e -terms with control instructions. In this system, the normalization property is ?essentially true? in the sense that we get correct computations on data types. Of course, not every typable term is normalizable since, for example, Y has the type of the foundation axiom. These realizability models differ deeply from forcing models and pose several interesting problems. In particular, they do not seem to be end extensions of the original model of ZFC. In addition, it is likely that the negation of the axiom of choice is realized in them.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"40 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":"121673548","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.2000.855766
Saul A. Kripke
This paper was conceived in reaction to Soare's paper in the Bulletin of Symbolic Logic 1996. From Godel in the 30s, to Gandy, Soare, and many others today, the obvious fundamental importance of Turing's work both for logic and computer science has led to an overemphasis on his paper as the justification for the Church-Turing thesis. It is even said that Turing proved a theorem that every ?function computable by a human being in a routine way? is Turing computable. Though several have endorsed this claim, it is hard for me to see ho w it could really meet modern standards of rigor. Moreover, Gandy worried that Turing's analysis did not cover modern computers, which may use parallel processing. He proved a very complicated result (now much simplified by Byrne and Sieg) to deal with this. My paper argues that an alternative approach {once this subject has been properly analyzed and delimited} allows us to state a simple theorem that covers computations either by machines or by humans. A thesis believed by all contemporary logicians is needed for this theorem to cover all likely future cases. It should be obvious that the theorem covers all computations known hitherto.
{"title":"From the church-turing thesis to the first-order algorithm theorem","authors":"Saul A. Kripke","doi":"10.1109/LICS.2000.855766","DOIUrl":"https://doi.org/10.1109/LICS.2000.855766","url":null,"abstract":"This paper was conceived in reaction to Soare's paper in the Bulletin of Symbolic Logic 1996. From Godel in the 30s, to Gandy, Soare, and many others today, the obvious fundamental importance of Turing's work both for logic and computer science has led to an overemphasis on his paper as the justification for the Church-Turing thesis. It is even said that Turing proved a theorem that every ?function computable by a human being in a routine way? is Turing computable. Though several have endorsed this claim, it is hard for me to see ho w it could really meet modern standards of rigor. Moreover, Gandy worried that Turing's analysis did not cover modern computers, which may use parallel processing. He proved a very complicated result (now much simplified by Byrne and Sieg) to deal with this. My paper argues that an alternative approach {once this subject has been properly analyzed and delimited} allows us to state a simple theorem that covers computations either by machines or by humans. A thesis believed by all contemporary logicians is needed for this theorem to cover all likely future cases. It should be obvious that the theorem covers all computations known hitherto.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"1 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":"124736403","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.2000.855765
C. Bergman, G. Slutzki
We prove that several problems concerning congruences on algebras are complete for nondeterministic log-space. These problems are: determining the congruence on a given algebra generated by a set of pairs, and determining whether a given algebra is simple or subdirectly irreducible. We also consider the problem of determining the smallest fully invariant congruence on a given algebra containing a given set of pairs. We prove that this problem is complete for nondeterministic polynomial time.
{"title":"Computational complexity of some problems involving congruences on algebras","authors":"C. Bergman, G. Slutzki","doi":"10.1109/LICS.2000.855765","DOIUrl":"https://doi.org/10.1109/LICS.2000.855765","url":null,"abstract":"We prove that several problems concerning congruences on algebras are complete for nondeterministic log-space. These problems are: determining the congruence on a given algebra generated by a set of pairs, and determining whether a given algebra is simple or subdirectly irreducible. We also consider the problem of determining the smallest fully invariant congruence on a given algebra containing a given set of pairs. We prove that this problem is complete for nondeterministic polynomial time.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"11 1 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":"128846322","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.2000.855756
F. Afrati, Hans Leiss, M. D. Rougemont
A compression algorithm takes a finite structure of a class K as input and produces a finite structure of a different class K' as output. Given a property P on the class K defined in a logic /spl Lscr/, we study the definability of property P on the class K'. We consider two compression schemas on unary ordered structures (words), compression by runlength encoding and the classical Lempel-Ziv. First-order properties of strings are first-order on runlength compressed strings, but this fails for images, i.e. 2-dimensional strings. We present simple first-order properties of strings which are not first-order definable on strings compressed with the Lempel-Ziv compression schema. We show that all properties of strings that are first-order definable on strings are definable on Lempel-Ziv compressed strings in FO(TC), the extension of first-order logic with the transitive closure operator. We define a subclass /spl Fscr/ of the first-order properties of strings such that if L is defined by a property in /spl Fscr/, it is also first-order definable on the Lempel-Ziv compressed strings. Monadic second-order properties of strings are dyadic second order definable on Lempel-Ziv compressed strings.
{"title":"Definability and compression","authors":"F. Afrati, Hans Leiss, M. D. Rougemont","doi":"10.1109/LICS.2000.855756","DOIUrl":"https://doi.org/10.1109/LICS.2000.855756","url":null,"abstract":"A compression algorithm takes a finite structure of a class K as input and produces a finite structure of a different class K' as output. Given a property P on the class K defined in a logic /spl Lscr/, we study the definability of property P on the class K'. We consider two compression schemas on unary ordered structures (words), compression by runlength encoding and the classical Lempel-Ziv. First-order properties of strings are first-order on runlength compressed strings, but this fails for images, i.e. 2-dimensional strings. We present simple first-order properties of strings which are not first-order definable on strings compressed with the Lempel-Ziv compression schema. We show that all properties of strings that are first-order definable on strings are definable on Lempel-Ziv compressed strings in FO(TC), the extension of first-order logic with the transitive closure operator. We define a subclass /spl Fscr/ of the first-order properties of strings such that if L is defined by a property in /spl Fscr/, it is also first-order definable on the Lempel-Ziv compressed strings. Monadic second-order properties of strings are dyadic second order definable on Lempel-Ziv compressed strings.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"41 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":"115877081","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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