In software verification, it is often required to prove statements about heterogeneous domains containing elements of various sorts, such as counters, stacks, lists, trees and queues. Any domain with counters, stacks, lists, and trees (but not queues) can be easily seen as a special case of the term algebra, and hence a decision procedure for term algebras can be applied to decide the first-order theory of such a domain. We present a quantifier-elimination procedure for the first-order theory of term algebras extended with queues. The complete axiomatization and decidability of this theory can be immediately derived from the procedure.
{"title":"A decision procedure for term algebras with queues","authors":"T. Rybina, A. Voronkov","doi":"10.1145/371316.371494","DOIUrl":"https://doi.org/10.1145/371316.371494","url":null,"abstract":"In software verification, it is often required to prove statements about heterogeneous domains containing elements of various sorts, such as counters, stacks, lists, trees and queues. Any domain with counters, stacks, lists, and trees (but not queues) can be easily seen as a special case of the term algebra, and hence a decision procedure for term algebras can be applied to decide the first-order theory of such a domain. We present a quantifier-elimination procedure for the first-order theory of term algebras extended with queues. The complete axiomatization and decidability of this theory can be immediately derived from the procedure.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126384525","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.2000.855768
A. Murawski, C. Ong
We consider the following decision problems. PROOFNET: given a multiplicative linear logic (MLL) proof structure, is it a proof net? ESSNET: given an essential net (of an intuitionistic MLL sequent), is it correct? The authors show that linear-time algorithms for ESSNET can be obtained by constructing the dominator tree of the input essential net. As a corollary, by showing that PROOFNET is linear-time reducible to ESSNET (by the trip translation), we obtain a linear-time algorithm for PROOFNET. We show further that these linear-time algorithms can be optimized to simple one-pass algorithms: each node of the input structure is visited at most once. As another application of dominator trees, we obtain linear time algorithms for sequentializing proof nets (i.e. given a proof net, find a derivation for the underlying MLL sequent) and essential nets.
{"title":"Dominator trees and fast verification of proof nets","authors":"A. Murawski, C. Ong","doi":"10.1109/LICS.2000.855768","DOIUrl":"https://doi.org/10.1109/LICS.2000.855768","url":null,"abstract":"We consider the following decision problems. PROOFNET: given a multiplicative linear logic (MLL) proof structure, is it a proof net? ESSNET: given an essential net (of an intuitionistic MLL sequent), is it correct? The authors show that linear-time algorithms for ESSNET can be obtained by constructing the dominator tree of the input essential net. As a corollary, by showing that PROOFNET is linear-time reducible to ESSNET (by the trip translation), we obtain a linear-time algorithm for PROOFNET. We show further that these linear-time algorithms can be optimized to simple one-pass algorithms: each node of the input structure is visited at most once. As another application of dominator trees, we obtain linear time algorithms for sequentializing proof nets (i.e. given a proof net, find a derivation for the underlying MLL sequent) and essential nets.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"17 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":"116563118","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.2000.855762
P. Abdulla, Aletta Nylén
Many existing algorithms for model checking of infinite-state systems operate on constraints which are used to represent (potentially infinite) sets of states. A general powerful technique which can be employed for proving termination of these algorithms is that of well quasi-orderings. Several methodologies have been proposed for derivation of new well quasi-ordered constraint systems. However, many of these constraint systems suffer from a "constraint explosion problem", as the number of the generated constraints grows exponentially with the size of the problem. We demonstrate that a refinement of the theory of well quasi-orderings, called the theory of better quasi-orderings is more appropriate for symbolic model checking, since it allows inventing constraint systems which are both well quasi-ordered and compact. We apply our methodology to derive new constraint systems for verification of systems with unboundedly many clocks, broadcast protocols, lossy channel systems, and integral relational automata. The new constraint systems are exponentially more succinct than existing ones, and their well quasi-ordering cannot be shown by previous methods in the literature.
{"title":"Better is better than well: on efficient verification of infinite-state systems","authors":"P. Abdulla, Aletta Nylén","doi":"10.1109/LICS.2000.855762","DOIUrl":"https://doi.org/10.1109/LICS.2000.855762","url":null,"abstract":"Many existing algorithms for model checking of infinite-state systems operate on constraints which are used to represent (potentially infinite) sets of states. A general powerful technique which can be employed for proving termination of these algorithms is that of well quasi-orderings. Several methodologies have been proposed for derivation of new well quasi-ordered constraint systems. However, many of these constraint systems suffer from a \"constraint explosion problem\", as the number of the generated constraints grows exponentially with the size of the problem. We demonstrate that a refinement of the theory of well quasi-orderings, called the theory of better quasi-orderings is more appropriate for symbolic model checking, since it allows inventing constraint systems which are both well quasi-ordered and compact. We apply our methodology to derive new constraint systems for verification of systems with unboundedly many clocks, broadcast protocols, lossy channel systems, and integral relational automata. The new constraint systems are exponentially more succinct than existing ones, and their well quasi-ordering cannot be shown by previous methods in the literature.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"61 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":"127096976","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.2000.855786
J. Palsberg, Tian Zhao
Equality and subtyping of recursive types have been studied in the 1990s by: R.M. Amadaio and L. Cardelli (1993); D. Kozen et al. (1993); M. Brandt and F. Henglein (1997) and others. Potential applications include automatic generation of bridge code for multi-language systems and type-based retrieval of software modules from libraries. J. Auerbach et al. (1998) advocate a highly flexible combination of matching rules for which there, until now, are no efficient algorithmic techniques. We present an efficient decision procedure for a notion of type equality that includes unfolding of recursive types, and associativity and commutativity of product types, as advocated by Auerbach et al. For two types of size at most n, our algorithm decides equality in O(n/sup 2/) time. The algorithm iteratively prunes a set of type pairs, and eventually it produces a set of pairs of equal types. In each iteration, the algorithm exploits a so-called coherence property of the set of type pairs produced in the preceding iteration. The algorithm takes O(n) iterations, each of which takes O(n) time, for a total of O(n/sup 2/) time.
{"title":"Efficient and flexible matching of recursive types","authors":"J. Palsberg, Tian Zhao","doi":"10.1109/LICS.2000.855786","DOIUrl":"https://doi.org/10.1109/LICS.2000.855786","url":null,"abstract":"Equality and subtyping of recursive types have been studied in the 1990s by: R.M. Amadaio and L. Cardelli (1993); D. Kozen et al. (1993); M. Brandt and F. Henglein (1997) and others. Potential applications include automatic generation of bridge code for multi-language systems and type-based retrieval of software modules from libraries. J. Auerbach et al. (1998) advocate a highly flexible combination of matching rules for which there, until now, are no efficient algorithmic techniques. We present an efficient decision procedure for a notion of type equality that includes unfolding of recursive types, and associativity and commutativity of product types, as advocated by Auerbach et al. For two types of size at most n, our algorithm decides equality in O(n/sup 2/) time. The algorithm iteratively prunes a set of type pairs, and eventually it produces a set of pairs of equal types. In each iteration, the algorithm exploits a so-called coherence property of the set of type pairs produced in the preceding iteration. The algorithm takes O(n) iterations, each of which takes O(n) time, for a total of O(n/sup 2/) time.","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":"130745411","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.2000.855767
B. Selman
Recently, there has been much progress in the area of prepositional reasoning and search. Current techniques can handle problem instances with thousands of variables and up to a million clauses. This has led to new applications in areas such as planning, scheduling, protocol verification, and software testing. Much of the recent progress has resulted from a better understanding of the computational characteristics of the satisfiability problem. In particular, by exploiting connections between combinatorial problems and models from statistical physics, we now have methods that enable a much finer-grained characterization of computational complexity than the standard worst-case complexity measures. These findings provide insights into new algorithmic strategies based on randomization and distributed algorithm portfolios. I will survey the recent progress in this area and I will discuss the current state-of-the-art in propositional reasoning focusing on a series of challenge problems concerning propositional encodings, compilation techniques, approximate reasoning, robustness, and scalability.
{"title":"Satisfiability testing: recent developments and challenge problems","authors":"B. Selman","doi":"10.1109/LICS.2000.855767","DOIUrl":"https://doi.org/10.1109/LICS.2000.855767","url":null,"abstract":"Recently, there has been much progress in the area of prepositional reasoning and search. Current techniques can handle problem instances with thousands of variables and up to a million clauses. This has led to new applications in areas such as planning, scheduling, protocol verification, and software testing. Much of the recent progress has resulted from a better understanding of the computational characteristics of the satisfiability problem. In particular, by exploiting connections between combinatorial problems and models from statistical physics, we now have methods that enable a much finer-grained characterization of computational complexity than the standard worst-case complexity measures. These findings provide insights into new algorithmic strategies based on randomization and distributed algorithm portfolios. I will survey the recent progress in this area and I will discuss the current state-of-the-art in propositional reasoning focusing on a series of challenge problems concerning propositional encodings, compilation techniques, approximate reasoning, robustness, and scalability.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"17 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":"130848214","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.2000.855777
Konstantin Korovin, A. Voronkov
The authors show the decidability of the existential theory of term algebras with any Knuth-Bendix ordering. They achieve this by giving a procedure for solving Knuth-Bendix ordering constraints. As for complexity, NP-hardness of the set of satisfiable quantifier-free formulas can be shown in the same way as by R. Nieuwenhuis (1993). The algorithm presented does not give an NP upper bound; we point out parts of our algorithm that may cause nonpolynomial behavior.
{"title":"A decision procedure for the existential theory of term algebras with the Knuth-Bendix ordering","authors":"Konstantin Korovin, A. Voronkov","doi":"10.1109/LICS.2000.855777","DOIUrl":"https://doi.org/10.1109/LICS.2000.855777","url":null,"abstract":"The authors show the decidability of the existential theory of term algebras with any Knuth-Bendix ordering. They achieve this by giving a procedure for solving Knuth-Bendix ordering constraints. As for complexity, NP-hardness of the set of satisfiable quantifier-free formulas can be shown in the same way as by R. Nieuwenhuis (1993). The algorithm presented does not give an NP upper bound; we point out parts of our algorithm that may cause nonpolynomial behavior.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"266 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":"124331161","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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