Pub Date : 1997-06-29DOI: 10.1109/LICS.1997.614944
E. Asarin, P. Caspi, O. Maler
In this paper we define timed regular expressions, and extension of regular expressions for specifying sets of dense-time discrete-valued signals. We show that this formalism is equivalent in expressive power to the timed automata of Alur and Dill by providing a translation procedure from expressions to automata and vice versa. the result is extended to /spl omega/-regular expressions (Buchi's theorem).
{"title":"A Kleene theorem for timed automata","authors":"E. Asarin, P. Caspi, O. Maler","doi":"10.1109/LICS.1997.614944","DOIUrl":"https://doi.org/10.1109/LICS.1997.614944","url":null,"abstract":"In this paper we define timed regular expressions, and extension of regular expressions for specifying sets of dense-time discrete-valued signals. We show that this formalism is equivalent in expressive power to the timed automata of Alur and Dill by providing a translation procedure from expressions to automata and vice versa. the result is extended to /spl omega/-regular expressions (Buchi's theorem).","PeriodicalId":272903,"journal":{"name":"Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128056120","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 : 1997-06-29DOI: 10.1109/LICS.1997.614933
Patrick Baillot, V. Danos, T. Ehrhard, L. Regnier
A general category of games is constructed. A subcategory of saturated strategies, closed under all possible codings in copy games, is shown to model reduction in classical linear logic.
{"title":"Believe it or not, AJM's games model is a model of classical linear logic","authors":"Patrick Baillot, V. Danos, T. Ehrhard, L. Regnier","doi":"10.1109/LICS.1997.614933","DOIUrl":"https://doi.org/10.1109/LICS.1997.614933","url":null,"abstract":"A general category of games is constructed. A subcategory of saturated strategies, closed under all possible codings in copy games, is shown to model reduction in classical linear logic.","PeriodicalId":272903,"journal":{"name":"Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science","volume":"13 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114025941","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 : 1997-06-29DOI: 10.1109/LICS.1997.614960
N. Heintze, David A. McAllester
We prove that certain data-flow and control-flow problems are 2NPDA-complete. This means that these problems are in the class 2NPDA and that they are hard for that class. The fact that they are in 2NPDA demonstrates the richness of the class. The fact that they are hard for 2NPDA can be interpreted as evidence they can not be solved in sub-cubic time-the cubic time decision procedure for an arbitrary 2NPDA problem has not been improved since its discovery in 1968.
{"title":"On the cubic bottleneck in subtyping and flow analysis","authors":"N. Heintze, David A. McAllester","doi":"10.1109/LICS.1997.614960","DOIUrl":"https://doi.org/10.1109/LICS.1997.614960","url":null,"abstract":"We prove that certain data-flow and control-flow problems are 2NPDA-complete. This means that these problems are in the class 2NPDA and that they are hard for that class. The fact that they are in 2NPDA demonstrates the richness of the class. The fact that they are hard for 2NPDA can be interpreted as evidence they can not be solved in sub-cubic time-the cubic time decision procedure for an arbitrary 2NPDA problem has not been improved since its discovery in 1968.","PeriodicalId":272903,"journal":{"name":"Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science","volume":"146 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127250347","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 : 1997-06-29DOI: 10.1109/LICS.1997.614927
R. D. Cosmo, D. Kesner
In this paper, we show the correspondence existing between normalization in calculi with explicit substitution and cut elimination in sequent calculus for linear logic, via proof nets. This correspondence allows us to prove that a typed version of the /spl lambda/x-calculus is strongly normalizing, as well as of all the calculi that can be translated to it keeping normalization properties such as /spl lambda//sub v/, /spl lambda//sub s/, /spl lambda//sub d/ and /spl lambda//sub f/. In order to achieve this result, we introduce a new notion of reduction in proof nets: this extended reduction is still confluent and strongly normalizing, and is of interest of its own, as it corresponds to more identifications of proofs in linear logic that differ by inessential details. These results show that calculi with explicit substitutions are really an intermediate formalism between lambda calculus and proof nets, and suggest a completely new way to look at the problems still open in the field of explicit substitutions.
{"title":"Strong normalization of explicit substitutions via cut elimination in proof nets","authors":"R. D. Cosmo, D. Kesner","doi":"10.1109/LICS.1997.614927","DOIUrl":"https://doi.org/10.1109/LICS.1997.614927","url":null,"abstract":"In this paper, we show the correspondence existing between normalization in calculi with explicit substitution and cut elimination in sequent calculus for linear logic, via proof nets. This correspondence allows us to prove that a typed version of the /spl lambda/x-calculus is strongly normalizing, as well as of all the calculi that can be translated to it keeping normalization properties such as /spl lambda//sub v/, /spl lambda//sub s/, /spl lambda//sub d/ and /spl lambda//sub f/. In order to achieve this result, we introduce a new notion of reduction in proof nets: this extended reduction is still confluent and strongly normalizing, and is of interest of its own, as it corresponds to more identifications of proofs in linear logic that differ by inessential details. These results show that calculi with explicit substitutions are really an intermediate formalism between lambda calculus and proof nets, and suggest a completely new way to look at the problems still open in the field of explicit substitutions.","PeriodicalId":272903,"journal":{"name":"Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122012719","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 : 1997-06-29DOI: 10.1109/LICS.1997.614956
S. Vorobyov
We prove that any decision procedure for a modest fragment of L. Henkin's theory of pure propositional types requires time exceeding a tower of 2's of height exponential in the length of input. Until now the highest known lower bounds for natural decidable theories were at most linearly high towers of 2's and since mid-seventies it was an open problem whether natural decidable theories requiring more than that exist. We give the affirmative answer. As an application of this today's strongest lower bound we improve known and settle new lower bounds for several problems in the simply typed lambda calculus.
{"title":"The \"Hardest\" natural decidable theory","authors":"S. Vorobyov","doi":"10.1109/LICS.1997.614956","DOIUrl":"https://doi.org/10.1109/LICS.1997.614956","url":null,"abstract":"We prove that any decision procedure for a modest fragment of L. Henkin's theory of pure propositional types requires time exceeding a tower of 2's of height exponential in the length of input. Until now the highest known lower bounds for natural decidable theories were at most linearly high towers of 2's and since mid-seventies it was an open problem whether natural decidable theories requiring more than that exist. We give the affirmative answer. As an application of this today's strongest lower bound we improve known and settle new lower bounds for several problems in the simply typed lambda calculus.","PeriodicalId":272903,"journal":{"name":"Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129425527","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 : 1997-06-29DOI: 10.1109/LICS.1997.614938
H. Andersen, H. Hulgaard
This paper presents a new data structure called Boolean Expression Diagrams (BEDs) for representing and manipulating Boolean functions. BEDs are a generalization of Binary Decision Diagrams (BDDs) which can represent any Boolean circuit in linear space and still maintain many of the desirable properties of BDDs. Two algorithms are described for transforming a BED into a reduced ordered BDD. One closely mimics the BDD apply-operator while the other can exploit the structural information of the Boolean expression. The efficacy of the BED representation is demonstrated by verifying that the redundant and non-redundant versions of the ISCAS 85 benchmark circuits are identical. In particular, it is verified that the two 16-bit multiplication circuits (c6288 and c6288nr) implement the same Boolean functions. Using BEDs, this verification problem is solved in less than a second, while using standard BDD techniques this problem is infeasible. BEDs are useful in applications where the end-result as a reduced ordered BDD is small, for example for tautology checking.
{"title":"Boolean expression diagrams","authors":"H. Andersen, H. Hulgaard","doi":"10.1109/LICS.1997.614938","DOIUrl":"https://doi.org/10.1109/LICS.1997.614938","url":null,"abstract":"This paper presents a new data structure called Boolean Expression Diagrams (BEDs) for representing and manipulating Boolean functions. BEDs are a generalization of Binary Decision Diagrams (BDDs) which can represent any Boolean circuit in linear space and still maintain many of the desirable properties of BDDs. Two algorithms are described for transforming a BED into a reduced ordered BDD. One closely mimics the BDD apply-operator while the other can exploit the structural information of the Boolean expression. The efficacy of the BED representation is demonstrated by verifying that the redundant and non-redundant versions of the ISCAS 85 benchmark circuits are identical. In particular, it is verified that the two 16-bit multiplication circuits (c6288 and c6288nr) implement the same Boolean functions. Using BEDs, this verification problem is solved in less than a second, while using standard BDD techniques this problem is infeasible. BEDs are useful in applications where the end-result as a reduced ordered BDD is small, for example for tautology checking.","PeriodicalId":272903,"journal":{"name":"Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134152793","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 : 1997-06-29DOI: 10.1109/LICS.1997.614939
Stefan Dziembowski, M. Jurdzinski, I. Walukiewicz
We consider a class of infinite two-player games on finitely coloured graphs. Our main question is: given a winning condition, what is the inherent blow-up (additional memory) of the size of the I/O automata realizing winning strategies in games with this condition. This problem is relevant to synthesis of reactive programs and to the theory of automata on infinite objects. We provide matching upper and lower bounds for the size of memory needed by winning strategies in games with a fixed winning condition. We also show that in the general case the LAR (latest appearance record) data structure of Gurevich and Harrington is optimal. Then we propose a more succinct way of representing winning strategies by means of parallel compositions of transition systems. We study the question: which classes of winning conditions admit only polynomial-size blowup of strategies in this representation.
{"title":"How much memory is needed to win infinite games?","authors":"Stefan Dziembowski, M. Jurdzinski, I. Walukiewicz","doi":"10.1109/LICS.1997.614939","DOIUrl":"https://doi.org/10.1109/LICS.1997.614939","url":null,"abstract":"We consider a class of infinite two-player games on finitely coloured graphs. Our main question is: given a winning condition, what is the inherent blow-up (additional memory) of the size of the I/O automata realizing winning strategies in games with this condition. This problem is relevant to synthesis of reactive programs and to the theory of automata on infinite objects. We provide matching upper and lower bounds for the size of memory needed by winning strategies in games with a fixed winning condition. We also show that in the general case the LAR (latest appearance record) data structure of Gurevich and Harrington is optimal. Then we propose a more succinct way of representing winning strategies by means of parallel compositions of transition systems. We study the question: which classes of winning conditions admit only polynomial-size blowup of strategies in this representation.","PeriodicalId":272903,"journal":{"name":"Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130980755","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 : 1997-06-29DOI: 10.1109/LICS.1997.614928
M. Kanovich, Takayasu Ito
The aim of the paper is to develop comprehensive logical systems capable of handling both resource-sensitive and time-dependent properties of concurrent processes. As a language for specifying such properties, we introduce 'temporal linear logic' (TLL) an extension of linear logic with certain features of temporal logic. A semantic setting for TLL is given in terms of 'time-state universes'. TLL is proved to be fully adequate for 'time-state' concurrency models.
{"title":"Temporal linear logic specifications for concurrent processes","authors":"M. Kanovich, Takayasu Ito","doi":"10.1109/LICS.1997.614928","DOIUrl":"https://doi.org/10.1109/LICS.1997.614928","url":null,"abstract":"The aim of the paper is to develop comprehensive logical systems capable of handling both resource-sensitive and time-dependent properties of concurrent processes. As a language for specifying such properties, we introduce 'temporal linear logic' (TLL) an extension of linear logic with certain features of temporal logic. A semantic setting for TLL is given in terms of 'time-state universes'. TLL is proved to be fully adequate for 'time-state' concurrency models.","PeriodicalId":272903,"journal":{"name":"Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science","volume":"51 7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126285684","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 : 1997-06-29DOI: 10.1109/LICS.1997.614949
Martin Grohe
Far each /spl kappa//spl ges/3, we show that there is no recursive bound for the size of the smallest finite model of an L/sup /spl kappa//-theory in terms of its /spl kappa/-size. Here L/sup /spl kappa// denotes the /spl kappa/-variable fragment of first-order logic. An L/sup /spl kappa//-theory is a maximal consistent set of L/sup /spl kappa//-sentences, and the /spl kappa/-size of an L/sup /spl kappa//-theory is the number of L/sup /spl kappa//-types realized in its models. Our result answers a question of Dawar (1993). As a corollary, we obtain that for /spl kappa//spl ges/3 the so-called L/sup /spl kappa//-invariants, which characterize structures up to equivalence in L/sup /spl kappa//, cannot be recursively inverted.
{"title":"Large finite structures with few L/sup /spl kappa//-types","authors":"Martin Grohe","doi":"10.1109/LICS.1997.614949","DOIUrl":"https://doi.org/10.1109/LICS.1997.614949","url":null,"abstract":"Far each /spl kappa//spl ges/3, we show that there is no recursive bound for the size of the smallest finite model of an L/sup /spl kappa//-theory in terms of its /spl kappa/-size. Here L/sup /spl kappa// denotes the /spl kappa/-variable fragment of first-order logic. An L/sup /spl kappa//-theory is a maximal consistent set of L/sup /spl kappa//-sentences, and the /spl kappa/-size of an L/sup /spl kappa//-theory is the number of L/sup /spl kappa//-types realized in its models. Our result answers a question of Dawar (1993). As a corollary, we obtain that for /spl kappa//spl ges/3 the so-called L/sup /spl kappa//-invariants, which characterize structures up to equivalence in L/sup /spl kappa//, cannot be recursively inverted.","PeriodicalId":272903,"journal":{"name":"Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126121436","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 : 1997-06-29DOI: 10.1109/LICS.1997.614945
David Janin
Fixpoint expressions built from functional signatures interpreted over arbitrary complete lattices are considered. A generic notion of automaton is defined and shown, by means of a tableau technique, to capture the expressive power of fixpoint expressions. For interpretation over continuous and complete lattices when, moreover, the meet symbol /spl Lambda/ commutes in a rough sense with all other functional symbols, it is shown that any closed fixpoint expression is equivalent to a fixpoint expression built without the meet symbol /spl lambda/. This result generalizes Muller and Schupp's simulation theorem for alternating automata on the binary tree.
{"title":"Automata, tableaus and a reduction theorem for fixpoint calculi in arbitrary complete lattices","authors":"David Janin","doi":"10.1109/LICS.1997.614945","DOIUrl":"https://doi.org/10.1109/LICS.1997.614945","url":null,"abstract":"Fixpoint expressions built from functional signatures interpreted over arbitrary complete lattices are considered. A generic notion of automaton is defined and shown, by means of a tableau technique, to capture the expressive power of fixpoint expressions. For interpretation over continuous and complete lattices when, moreover, the meet symbol /spl Lambda/ commutes in a rough sense with all other functional symbols, it is shown that any closed fixpoint expression is equivalent to a fixpoint expression built without the meet symbol /spl lambda/. This result generalizes Muller and Schupp's simulation theorem for alternating automata on the binary tree.","PeriodicalId":272903,"journal":{"name":"Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131222355","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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