{"title":"An Observationally Complete Program Logic for Imperative Higher-Order Frame Rules","authors":"Kohei Honda, N. Yoshida, Martin Berger","doi":"10.1109/LICS.2005.5","DOIUrl":"https://doi.org/10.1109/LICS.2005.5","url":null,"abstract":"","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2005-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91063834","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 : 2004-07-13DOI: 10.1109/LICS.2004.1319632
Phuong Nguyen, S. Cook
We introduce a finitely axiomatizable second-order theory, which is VTC/sup 0/ associated with the class FO-uniform TC/sup 0/. It consists of the base theory V/sup 0/ for AC/sup 0/ reasoning together with the axiom NUMONES, which states the existence of a "counting array" Y for any string X: the ith row of Y contains only the number of 1 bits up to (excluding) bit i of X. We introduce the notion of "strong /spl Delta//sub 1//sup B/-definability" for relations in a theory, and use a recursive characterization of the TC/sup 0/ relations (rather than functions) to show that the TC/sup 0/ relations are strongly /spl Delta//sub 1//sup B/-definable. It follows that the TC/sup 0/ functions are /spl Sigma//sub 1//sup B/-definable in VTC/sup 0/. We prove a general witnessing theorem for second-order theories and conclude that the/spl Sigma//sub 1//sup B/ theorems of VTC/sup 0/ are witnessed by TC/sup 0/ functions. We prove that VTC/sup 0/ is RSUV isomorphic to the first order theory /spl Delta//sub 1//sup b/-CR of Johannsen and Pollett (the "minimal theory for TC/sup 0/"), /spl Delta//sub 1//sup b/-CR includes the /spl Delta//sub 1//sup b/ comprehension rule, and J and P ask whether there is an upper bound to the nesting depth required for this rule. We answer "yes", because VTC/sup 0/ , and therefore /spl Delta//sub 1//sup b/-CR, are finitely axiomatizable. Finally, we show that /spl Sigma//sub 1//sup B/ theorems of VTC/sup 0/ translate to families of tautologies which have polynomial-size constant-depth TC/sup 0/-Frege proofs. We also show that PHP is a /spl Sigma//sub 0//sup B/ theorem of VTC/sup 0/. These together imply that the family of propositional tautologies associated with PHP has polynomial-size constant-depth TC/sup 0/-Frege proofs.
{"title":"VTC circ: A Second-Order Theory for TCcirc","authors":"Phuong Nguyen, S. Cook","doi":"10.1109/LICS.2004.1319632","DOIUrl":"https://doi.org/10.1109/LICS.2004.1319632","url":null,"abstract":"We introduce a finitely axiomatizable second-order theory, which is VTC/sup 0/ associated with the class FO-uniform TC/sup 0/. It consists of the base theory V/sup 0/ for AC/sup 0/ reasoning together with the axiom NUMONES, which states the existence of a \"counting array\" Y for any string X: the ith row of Y contains only the number of 1 bits up to (excluding) bit i of X. We introduce the notion of \"strong /spl Delta//sub 1//sup B/-definability\" for relations in a theory, and use a recursive characterization of the TC/sup 0/ relations (rather than functions) to show that the TC/sup 0/ relations are strongly /spl Delta//sub 1//sup B/-definable. It follows that the TC/sup 0/ functions are /spl Sigma//sub 1//sup B/-definable in VTC/sup 0/. We prove a general witnessing theorem for second-order theories and conclude that the/spl Sigma//sub 1//sup B/ theorems of VTC/sup 0/ are witnessed by TC/sup 0/ functions. We prove that VTC/sup 0/ is RSUV isomorphic to the first order theory /spl Delta//sub 1//sup b/-CR of Johannsen and Pollett (the \"minimal theory for TC/sup 0/\"), /spl Delta//sub 1//sup b/-CR includes the /spl Delta//sub 1//sup b/ comprehension rule, and J and P ask whether there is an upper bound to the nesting depth required for this rule. We answer \"yes\", because VTC/sup 0/ , and therefore /spl Delta//sub 1//sup b/-CR, are finitely axiomatizable. Finally, we show that /spl Sigma//sub 1//sup B/ theorems of VTC/sup 0/ translate to families of tautologies which have polynomial-size constant-depth TC/sup 0/-Frege proofs. We also show that PHP is a /spl Sigma//sub 0//sup B/ theorem of VTC/sup 0/. These together imply that the family of propositional tautologies associated with PHP has polynomial-size constant-depth TC/sup 0/-Frege proofs.","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88711628","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 : 2004-07-13DOI: 10.1109/LICS.2004.1319614
B. Intrigila, R. Statman
We give a many-one reduction of the set of true /spl Pi//sub 2//sup 0/ sentences to the set of consequences of the lambda calculus with the omega rule. This solves in the affirmative a well known problem of H. Barendregt. The technique of proof has interest in itself and can be extended to prove that the theory which identifies all unsolvable terms together with the omega rule is H/sub 1//sup 1/-complete which solves another long-standing conjecture of H. Barendregt.
{"title":"The Omega Rule is II_2^0-Hard in the lambda beta -Calculus","authors":"B. Intrigila, R. Statman","doi":"10.1109/LICS.2004.1319614","DOIUrl":"https://doi.org/10.1109/LICS.2004.1319614","url":null,"abstract":"We give a many-one reduction of the set of true /spl Pi//sub 2//sup 0/ sentences to the set of consequences of the lambda calculus with the omega rule. This solves in the affirmative a well known problem of H. Barendregt. The technique of proof has interest in itself and can be extended to prove that the theory which identifies all unsolvable terms together with the omega rule is H/sub 1//sup 1/-complete which solves another long-standing conjecture of H. Barendregt.","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90533804","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 : 2004-01-01DOI: 10.1109/LICS.2004.1319609
S. Abramsky, Ghica, A. Murawski, C. Ong, I. Stark
{"title":"Logic in Computer Science, 2004. Proceedings of the 19th Annual IEEE Symposium on","authors":"S. Abramsky, Ghica, A. Murawski, C. Ong, I. Stark","doi":"10.1109/LICS.2004.1319609","DOIUrl":"https://doi.org/10.1109/LICS.2004.1319609","url":null,"abstract":"","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91397575","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 : 2004-01-01DOI: 10.1109/LICS.2004.1319630
I. Walukiewicz
{"title":"A Landscape with Games in the Backgroun","authors":"I. Walukiewicz","doi":"10.1109/LICS.2004.1319630","DOIUrl":"https://doi.org/10.1109/LICS.2004.1319630","url":null,"abstract":"","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86671771","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 : 2002-07-22DOI: 10.1109/LICS.2002.1029826
M. Faella, S. L. Torre, A. Murano
The rapid development of complex and safety-critical systems requires the use of reliable verification methods and tools for system design (synthesis). Many systems of interest are reactive, in the sense that their behavior depends on the interaction with the environment. A natural framework to model them is a two-player game: the system versus the environment. In this context, the central problem is to determine the existence of a winning strategy according to a given winning condition. We focus on real-time systems, and choose to model the related game as a nondeterministic timed automaton. We express winning conditions by formulas of the branching-time temporal logic TCTL. While timed games have been studied in the literature, timed games with dense-time winning conditions constitute a new research topic. The main result of this paper is an exponential-time algorithm to check for the existence of a winning strategy for TCTL games where equality is not allowed in the timing constraints. Our approach consists on translating to timed tree automata both the game graph and the winning condition, thus reducing the considered decision problem to the emptiness problem for this class of automata. The proposed algorithm matches the known lower bound on timed games. Moreover, if we relax the limitation we have placed on the timing constraints, the problem becomes undecidable.
{"title":"Dense Real-Time Games","authors":"M. Faella, S. L. Torre, A. Murano","doi":"10.1109/LICS.2002.1029826","DOIUrl":"https://doi.org/10.1109/LICS.2002.1029826","url":null,"abstract":"The rapid development of complex and safety-critical systems requires the use of reliable verification methods and tools for system design (synthesis). Many systems of interest are reactive, in the sense that their behavior depends on the interaction with the environment. A natural framework to model them is a two-player game: the system versus the environment. In this context, the central problem is to determine the existence of a winning strategy according to a given winning condition. We focus on real-time systems, and choose to model the related game as a nondeterministic timed automaton. We express winning conditions by formulas of the branching-time temporal logic TCTL. While timed games have been studied in the literature, timed games with dense-time winning conditions constitute a new research topic. The main result of this paper is an exponential-time algorithm to check for the existence of a winning strategy for TCTL games where equality is not allowed in the timing constraints. Our approach consists on translating to timed tree automata both the game graph and the winning condition, thus reducing the considered decision problem to the emptiness problem for this class of automata. The proposed algorithm matches the known lower bound on timed games. Moreover, if we relax the limitation we have placed on the timing constraints, the problem becomes undecidable.","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2002-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81160284","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 : 2002-01-01DOI: 10.1109/LICS.2002.1029818
Amal J. Ahmed, A. Appel, Roberto Virga
With a packaged semiconductor device of this invention, an IC pellet or chip supported on a mounting unit is encapsulated in plastics material, for example, epoxy resin or silicone resin. A plurality of lead strips are disposed at one end in the proximity of the mounting part of the mounting unit. The lead strips are electrically connected to the respective conductive pads of the IC pellet set on the mounting part of the mounting unit. The lead strips extend at the other end outside of an plastics material. Mounting unit-reinforcing side walls project substantially at right angles from the edges of the flat part of the mounting unit. The heat-radiating legs of the mounting unit extend substantially at right angles from the low edges of the side walls with the bottom surface of said legs exposed to the outside of the plastics material.
{"title":"A Stratified Semantics of General References A Stratified Semantics of General References","authors":"Amal J. Ahmed, A. Appel, Roberto Virga","doi":"10.1109/LICS.2002.1029818","DOIUrl":"https://doi.org/10.1109/LICS.2002.1029818","url":null,"abstract":"With a packaged semiconductor device of this invention, an IC pellet or chip supported on a mounting unit is encapsulated in plastics material, for example, epoxy resin or silicone resin. A plurality of lead strips are disposed at one end in the proximity of the mounting part of the mounting unit. The lead strips are electrically connected to the respective conductive pads of the IC pellet set on the mounting part of the mounting unit. The lead strips extend at the other end outside of an plastics material. Mounting unit-reinforcing side walls project substantially at right angles from the edges of the flat part of the mounting unit. The heat-radiating legs of the mounting unit extend substantially at right angles from the low edges of the side walls with the bottom surface of said legs exposed to the outside of the plastics material.","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2002-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81042363","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.1998.705685
J. L. Bars
We prove that there is a Monadic /spl Sigma//sub 1//sup 1/ (Minimal Scott without equality) sentence without an asymptotic probability. Our result entails that the 0-1 law fails for the logics /spl Sigma//sub 1//sup 1/(FO/sup 2/) and /spl Sigma//sub 1//sup 1/ (Minimal Godel without equality). Therefore we achieve the classification of first-order prefix classes with or without equality. According to the existence of the 0-1 law for the corresponding /spl Sigma//sub 1//sup 1/ fragment. In addition, our counterexample can be viewed as a single explanation of the failure of the 0-1 law of all the fragments of existential second-order logic for which the failure is already known.
{"title":"Fragments of Existential Second-Order Logic without 0-1 Laws","authors":"J. L. Bars","doi":"10.1109/LICS.1998.705685","DOIUrl":"https://doi.org/10.1109/LICS.1998.705685","url":null,"abstract":"We prove that there is a Monadic /spl Sigma//sub 1//sup 1/ (Minimal Scott without equality) sentence without an asymptotic probability. Our result entails that the 0-1 law fails for the logics /spl Sigma//sub 1//sup 1/(FO/sup 2/) and /spl Sigma//sub 1//sup 1/ (Minimal Godel without equality). Therefore we achieve the classification of first-order prefix classes with or without equality. According to the existence of the 0-1 law for the corresponding /spl Sigma//sub 1//sup 1/ fragment. In addition, our counterexample can be viewed as a single explanation of the failure of the 0-1 law of all the fragments of existential second-order logic for which the failure is already known.","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1998-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74837791","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 : 1997-01-01DOI: 10.1109/LICS.1997.614950
K. Etessami, Moshe Y. Vardi, T. Wilke
{"title":"Proceedings, 12th Annual IEEE Symposium on Logic in Computer Science, Warsaw, Poland, June 29 - July 2, 1997","authors":"K. Etessami, Moshe Y. Vardi, T. Wilke","doi":"10.1109/LICS.1997.614950","DOIUrl":"https://doi.org/10.1109/LICS.1997.614950","url":null,"abstract":"","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1997-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90279849","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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