Pub Date : 2001-06-16DOI: 10.1109/LICS.2001.932483
S. Stoller
Electronic payment protocols are designed to work correctly in the presence of an adversary that can prompt honest principals to engage in an unbounded number of concurrent instances of the protocol. This paper establishes an upper bound on the number of protocol instances needed to attack a large class of protocols, which contains versions of some well-known electronic payment protocols, including SET and 1KP. Such bounds clarify the nature of attacks on and provide a rigorous basis for automated verification of payment protocols.
{"title":"A bound on attacks on payment protocols","authors":"S. Stoller","doi":"10.1109/LICS.2001.932483","DOIUrl":"https://doi.org/10.1109/LICS.2001.932483","url":null,"abstract":"Electronic payment protocols are designed to work correctly in the presence of an adversary that can prompt honest principals to engage in an unbounded number of concurrent instances of the protocol. This paper establishes an upper bound on the number of protocol instances needed to attack a large class of protocols, which contains versions of some well-known electronic payment protocols, including SET and 1KP. Such bounds clarify the nature of attacks on and provide a rigorous basis for automated verification of payment protocols.","PeriodicalId":366313,"journal":{"name":"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121551362","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 : 2001-06-16DOI: 10.1109/LICS.2001.932510
David Janin, G. Lenzi
As is already known from the work of D. Janin & I. Walukiewicz (1996), the mu-calculus is as expressive as the bisimulation-invariant fragment of monadic second-order logic. In this paper, we relate the expressiveness of levels of the fixpoint alternation depth hierarchy of the mu-calculus (the mu-calculus hierarchy) with the expressiveness of the bisimulation-invariant fragment of levels of the monadic quantifiers alternation-depth hierarchy (the monadic hierarchy). From J. van Benthem's (1976) results, we know already that the fixpoint free fragment of the mu-calculus (i.e. polymodal logic) is as expressive as the bisimulation-invariant fragment of monadic /spl Sigma//sub 0/ (i.e. first-order logic). We show that the /spl nu/-level of the mu-calculus hierarchy is as expressive as the bisimulation-invariant fragment of monadic /spl Sigma//sub 1/ and that the /spl nu//spl mu/-level of the mu-calculus hierarchy is as expressive as the bisimulation-invariant fragment of monadic /spl Sigma//sub 2/, and we show that no other level /spl Sigma//sub k/ (for k>2) of the monadic hierarchy can be related similarly with any other level of the mu-calculus hierarchy. The possible inclusion of all the mu-calculus in some level /spl Sigma//sub k/ of the monadic hierarchy, for some k>2, is also discussed.
{"title":"Relating levels of the mu-calculus hierarchy and levels of the monadic hierarchy","authors":"David Janin, G. Lenzi","doi":"10.1109/LICS.2001.932510","DOIUrl":"https://doi.org/10.1109/LICS.2001.932510","url":null,"abstract":"As is already known from the work of D. Janin & I. Walukiewicz (1996), the mu-calculus is as expressive as the bisimulation-invariant fragment of monadic second-order logic. In this paper, we relate the expressiveness of levels of the fixpoint alternation depth hierarchy of the mu-calculus (the mu-calculus hierarchy) with the expressiveness of the bisimulation-invariant fragment of levels of the monadic quantifiers alternation-depth hierarchy (the monadic hierarchy). From J. van Benthem's (1976) results, we know already that the fixpoint free fragment of the mu-calculus (i.e. polymodal logic) is as expressive as the bisimulation-invariant fragment of monadic /spl Sigma//sub 0/ (i.e. first-order logic). We show that the /spl nu/-level of the mu-calculus hierarchy is as expressive as the bisimulation-invariant fragment of monadic /spl Sigma//sub 1/ and that the /spl nu//spl mu/-level of the mu-calculus hierarchy is as expressive as the bisimulation-invariant fragment of monadic /spl Sigma//sub 2/, and we show that no other level /spl Sigma//sub k/ (for k>2) of the monadic hierarchy can be related similarly with any other level of the mu-calculus hierarchy. The possible inclusion of all the mu-calculus in some level /spl Sigma//sub k/ of the monadic hierarchy, for some k>2, is also discussed.","PeriodicalId":366313,"journal":{"name":"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117248558","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 : 2001-06-16DOI: 10.1109/LICS.2001.932499
F. Pfenning
We develop a uniform type theory that integrates intensionality, extensionality and proof irrelevance as judgmental concepts. Any object may be treated intensionally (subject only to /spl alpha/-conversion), extensionally (subject also to /spl beta//spl eta/-conversion), or as irrelevant (equal to any other object at the same type), depending on where it occurs. Modal restrictions developed by R. Harper et al. (2000) for single types are generalized and employed to guarantee consistency between these views of objects. Potential applications are in logical frameworks, functional programming and the foundations of first-order modal logics. Our type theory contrasts with previous approaches that, a priori, distinguished propositions (whose proofs are all identified - only their existence is important) from specifications (whose implementations are subject to some definitional equalities).
{"title":"Intensionality, extensionality, and proof irrelevance in modal type theory","authors":"F. Pfenning","doi":"10.1109/LICS.2001.932499","DOIUrl":"https://doi.org/10.1109/LICS.2001.932499","url":null,"abstract":"We develop a uniform type theory that integrates intensionality, extensionality and proof irrelevance as judgmental concepts. Any object may be treated intensionally (subject only to /spl alpha/-conversion), extensionally (subject also to /spl beta//spl eta/-conversion), or as irrelevant (equal to any other object at the same type), depending on where it occurs. Modal restrictions developed by R. Harper et al. (2000) for single types are generalized and employed to guarantee consistency between these views of objects. Potential applications are in logical frameworks, functional programming and the foundations of first-order modal logics. Our type theory contrasts with previous approaches that, a priori, distinguished propositions (whose proofs are all identified - only their existence is important) from specifications (whose implementations are subject to some definitional equalities).","PeriodicalId":366313,"journal":{"name":"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science","volume":"1862 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129906945","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 : 2001-06-16DOI: 10.1109/LICS.2001.932488
M. Escardó, A. Simpson
We propose a notion of interval object in a category with finite products, providing a universal property for closed and bounded real line segments. The universal property gives rise to an analogue of primitive recursion for defining computable functions on the interval. We use this to define basic arithmetic operations and to verify equations between them. We test the notion in categories of interest. In the category of sets, any closed and bounded interval of real numbers is an interval object. In the category of topological spaces, the interval objects are closed and bounded intervals with the Euclidean topology. We also prove that an interval object exists in and elementary topos with natural numbers object.
{"title":"A universal characterization of the closed Euclidean interval","authors":"M. Escardó, A. Simpson","doi":"10.1109/LICS.2001.932488","DOIUrl":"https://doi.org/10.1109/LICS.2001.932488","url":null,"abstract":"We propose a notion of interval object in a category with finite products, providing a universal property for closed and bounded real line segments. The universal property gives rise to an analogue of primitive recursion for defining computable functions on the interval. We use this to define basic arithmetic operations and to verify equations between them. We test the notion in categories of interest. In the category of sets, any closed and bounded interval of real numbers is an interval object. In the category of topological spaces, the interval objects are closed and bounded intervals with the Euclidean topology. We also prove that an interval object exists in and elementary topos with natural numbers object.","PeriodicalId":366313,"journal":{"name":"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121960144","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 : 2001-06-16DOI: 10.1109/LICS.2001.932516
G. Bruns, Patrice Godefroid
A temporal logic query checker takes as input a Kripke structure and a temporal logic formula with a hole, and returns the set of propositional formulas that, when put in the hole, are satisfied by the Kripke structure. By allowing the temporal properties of a system to be discovered, query checking is useful in the study and reverse engineering of systems. Temporal logic query checking was first proposed by W. Chan (2000). In this paper, we generalize and simplify Chan's work by showing how a new class of alternating automata can be used for query checking with a wide range of temporal logics.
{"title":"Temporal logic query checking","authors":"G. Bruns, Patrice Godefroid","doi":"10.1109/LICS.2001.932516","DOIUrl":"https://doi.org/10.1109/LICS.2001.932516","url":null,"abstract":"A temporal logic query checker takes as input a Kripke structure and a temporal logic formula with a hole, and returns the set of propositional formulas that, when put in the hole, are satisfied by the Kripke structure. By allowing the temporal properties of a system to be discovered, query checking is useful in the study and reverse engineering of systems. Temporal logic query checking was first proposed by W. Chan (2000). In this paper, we generalize and simplify Chan's work by showing how a new class of alternating automata can be used for query checking with a wide range of temporal logics.","PeriodicalId":366313,"journal":{"name":"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133006804","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 : 2001-06-16DOI: 10.1109/LICS.2001.932514
O. Kupermann, M.Y. Varfi
In system synthesis, we transform a specification into a system that is guaranteed to satisfy the specification. When the system is distributed, the goal is to construct the system's underlying processes. Results on multi-player games imply that the synthesis problem for linear specifications is undecidable for general architectures, and is nonelementary decidable for hierarchical architectures, where the processes are linearly ordered and information among them flows in one direction. In this paper, we present a significant extension of this result. We handle both linear and branching specifications, and we show that a sufficient condition for decidability of the synthesis problem is a linear or cyclic order among the processes, in which information flows in either one or both directions. We also allow the processes to have internal hidden variables, and we consider communications with and without delay. Many practical applications fall into this class.
{"title":"Synthesizing distributed systems","authors":"O. Kupermann, M.Y. Varfi","doi":"10.1109/LICS.2001.932514","DOIUrl":"https://doi.org/10.1109/LICS.2001.932514","url":null,"abstract":"In system synthesis, we transform a specification into a system that is guaranteed to satisfy the specification. When the system is distributed, the goal is to construct the system's underlying processes. Results on multi-player games imply that the synthesis problem for linear specifications is undecidable for general architectures, and is nonelementary decidable for hierarchical architectures, where the processes are linearly ordered and information among them flows in one direction. In this paper, we present a significant extension of this result. We handle both linear and branching specifications, and we show that a sufficient condition for decidability of the synthesis problem is a linear or cyclic order among the processes, in which information flows in either one or both directions. We also allow the processes to have internal hidden variables, and we consider communications with and without delay. Many practical applications fall into this class.","PeriodicalId":366313,"journal":{"name":"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115745956","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 : 2001-06-16DOI: 10.1109/LICS.2001.932478
F. Blanqui
Considers an extension of the calculus of constructions where predicates can be defined with a general form of rewrite rules. We prove the strong normalization of the reduction relation generated by the /spl beta/-rule and user-defined rules under some general syntactic conditions, including confluence. As examples, we show that two important systems satisfy these conditions: (i) a sub-system of the calculus of inductive constructions, which is the basis of the proof assistant Cog, and (ii) natural deduction modulo a large class of equational theories.
{"title":"Definitions by rewriting in the calculus of constructions","authors":"F. Blanqui","doi":"10.1109/LICS.2001.932478","DOIUrl":"https://doi.org/10.1109/LICS.2001.932478","url":null,"abstract":"Considers an extension of the calculus of constructions where predicates can be defined with a general form of rewrite rules. We prove the strong normalization of the reduction relation generated by the /spl beta/-rule and user-defined rules under some general syntactic conditions, including confluence. As examples, we show that two important systems satisfy these conditions: (i) a sub-system of the calculus of inductive constructions, which is the basis of the proof assistant Cog, and (ii) natural deduction modulo a large class of equational theories.","PeriodicalId":366313,"journal":{"name":"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122281267","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 : 2001-06-16DOI: 10.1109/LICS.2001.932496
D. M. Barrington, N. Immerman, C. Lautemann, Nicole Schweikardt, D. Thérien
A language L over an alphabet A is said to have a neutral letter if there is a letter e/spl isin/A such that inserting or deleting e's from any word in A* does not change its membership (or non-membership) in L. The presence of a neutral letter affects the definability of a language in first-order logic. It was conjectured that it renders all numerical predicates apart from the order predicate useless, i.e., that if a language L with a neutral letter is not definable in first-order logic with linear order then it is not definable in first-order. Logic with any set /spl Nscr/ of numerical predicates. We investigate this conjecture in detail, showing that it fails already for /spl Nscr/={+, *}, or possibly stronger for any set /spl Nscr/ that allows counting up to the m times iterated logarithm, 1g/sup (m)/, for any constant m. On the positive side, we prove the conjecture for the case of all monadic numerical predicates, for /spl Nscr/={+}, for the fragment BC(/spl Sigma/) of first-order logic, and for binary alphabets.
{"title":"The Crane Beach Conjecture","authors":"D. M. Barrington, N. Immerman, C. Lautemann, Nicole Schweikardt, D. Thérien","doi":"10.1109/LICS.2001.932496","DOIUrl":"https://doi.org/10.1109/LICS.2001.932496","url":null,"abstract":"A language L over an alphabet A is said to have a neutral letter if there is a letter e/spl isin/A such that inserting or deleting e's from any word in A* does not change its membership (or non-membership) in L. The presence of a neutral letter affects the definability of a language in first-order logic. It was conjectured that it renders all numerical predicates apart from the order predicate useless, i.e., that if a language L with a neutral letter is not definable in first-order logic with linear order then it is not definable in first-order. Logic with any set /spl Nscr/ of numerical predicates. We investigate this conjecture in detail, showing that it fails already for /spl Nscr/={+, *}, or possibly stronger for any set /spl Nscr/ that allows counting up to the m times iterated logarithm, 1g/sup (m)/, for any constant m. On the positive side, we prove the conjecture for the case of all monadic numerical predicates, for /spl Nscr/={+}, for the fragment BC(/spl Sigma/) of first-order logic, and for binary alphabets.","PeriodicalId":366313,"journal":{"name":"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science","volume":"101 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117272103","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 : 2001-06-16DOI: 10.1109/LICS.2001.932511
M. Lange, C. Stirling
Introduce a simple game-theoretic approach to satisfiability checking of temporal logic, for LTL (linear time logic) and CTL (computation tree logic), which has the same complexity as using automata. The mechanisms involved are both explicit and transparent, and underpin a novel approach to developing complete axiom systems for temporal logic. The axiom systems are naturally factored into what happens locally and what happens in the limit. The completeness proofs utilise the game-theoretic construction for satisfiability: if a finite set of formulas is consistent then there is a winning strategy (and therefore construction of an explicit model is avoided).
{"title":"Focus games for satisfiability and completeness of temporal logic","authors":"M. Lange, C. Stirling","doi":"10.1109/LICS.2001.932511","DOIUrl":"https://doi.org/10.1109/LICS.2001.932511","url":null,"abstract":"Introduce a simple game-theoretic approach to satisfiability checking of temporal logic, for LTL (linear time logic) and CTL (computation tree logic), which has the same complexity as using automata. The mechanisms involved are both explicit and transparent, and underpin a novel approach to developing complete axiom systems for temporal logic. The axiom systems are naturally factored into what happens locally and what happens in the limit. The completeness proofs utilise the game-theoretic construction for satisfiability: if a finite set of formulas is consistent then there is a winning strategy (and therefore construction of an explicit model is avoided).","PeriodicalId":366313,"journal":{"name":"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128951208","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 : 2001-06-16DOI: 10.1109/LICS.2001.932490
J. Avigad
In any classical first-order theory that proves the existence of at least two elements, one can eliminate definitions with a polynomial bound on the increase in proof length. The author considers how in any classical first-order theory strong enough to code finite functions, including sequential theories, one can also eliminate Skolem functions with a polynomial bound on the increase in proof length.
{"title":"Eliminating definitions and Skolem functions in first-order logic","authors":"J. Avigad","doi":"10.1109/LICS.2001.932490","DOIUrl":"https://doi.org/10.1109/LICS.2001.932490","url":null,"abstract":"In any classical first-order theory that proves the existence of at least two elements, one can eliminate definitions with a polynomial bound on the increase in proof length. The author considers how in any classical first-order theory strong enough to code finite functions, including sequential theories, one can also eliminate Skolem functions with a polynomial bound on the increase in proof length.","PeriodicalId":366313,"journal":{"name":"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131959759","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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