We show that the Scott topology induces a topology for real-valued Lipschitz maps on Banach spaces which we call the L-topology. It is the weakest topology with respect to which the L-derivative operator, as a second order functional which maps the space of Lipschitz functions into the function space of non-empty weak* compact and convex valued maps equipped with the Scott topology, is continuous. For finite dimensional Euclidean spaces, where the L-derivative and the Clarke gradient coincide, we provide a simple characterisation of the basic open subsets of the L-topology in terms of ties or primitive maps of functions. We use this to verify that the L-topology is strictly coarser than the well-known Lipschitz norm topology. We then develop a fundamental theorem of calculus of second order in finite dimensions showing that the continuous integral operator from the continuous Scott domain of non-empty convex and compact valued functions to the continuous Scott domain of ties is inverse to the continuous operator induced by the L-derivative.
{"title":"Weak Topology and a Differentiable Operator for Lipschitz Maps","authors":"A. Edalat","doi":"10.1109/LICS.2008.49","DOIUrl":"https://doi.org/10.1109/LICS.2008.49","url":null,"abstract":"We show that the Scott topology induces a topology for real-valued Lipschitz maps on Banach spaces which we call the L-topology. It is the weakest topology with respect to which the L-derivative operator, as a second order functional which maps the space of Lipschitz functions into the function space of non-empty weak* compact and convex valued maps equipped with the Scott topology, is continuous. For finite dimensional Euclidean spaces, where the L-derivative and the Clarke gradient coincide, we provide a simple characterisation of the basic open subsets of the L-topology in terms of ties or primitive maps of functions. We use this to verify that the L-topology is strictly coarser than the well-known Lipschitz norm topology. We then develop a fundamental theorem of calculus of second order in finite dimensions showing that the continuous integral operator from the continuous Scott domain of non-empty convex and compact valued functions to the continuous Scott domain of ties is inverse to the continuous operator induced by the L-derivative.","PeriodicalId":298300,"journal":{"name":"2008 23rd Annual IEEE Symposium on Logic in Computer Science","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114571447","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}
We present a logic for algebraic effects, based on the algebraic representation of computational effects by operations and equations. We begin with the a-calculus, a minimal calculus which separates values, effects, and computations and thereby canonises the order of evaluation. This is extended to obtain the logic, which is a classical first-order multi-sorted logic with higher-order value and computation types, as in Levy's call-by-push-value, a principle of induction over computations, a free algebra principle, and predicate fixed points. This logic embraces Moggi's computational lambda-calculus, and also, via definable modalities, Hennessy-Milner logic, and evaluation logic, though Hoare logic presents difficulties.
{"title":"A Logic for Algebraic Effects","authors":"G. Plotkin, Matija Pretnar","doi":"10.1109/LICS.2008.45","DOIUrl":"https://doi.org/10.1109/LICS.2008.45","url":null,"abstract":"We present a logic for algebraic effects, based on the algebraic representation of computational effects by operations and equations. We begin with the a-calculus, a minimal calculus which separates values, effects, and computations and thereby canonises the order of evaluation. This is extended to obtain the logic, which is a classical first-order multi-sorted logic with higher-order value and computation types, as in Levy's call-by-push-value, a principle of induction over computations, a free algebra principle, and predicate fixed points. This logic embraces Moggi's computational lambda-calculus, and also, via definable modalities, Hennessy-Milner logic, and evaluation logic, though Hoare logic presents difficulties.","PeriodicalId":298300,"journal":{"name":"2008 23rd Annual IEEE Symposium on Logic in Computer Science","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129742080","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}
This paper presents a new bisimulation theory for parametric polymorphism which enables straight forward co-inductive proofs of program equivalences involving existential types. The theory is an instance of typed normal form bisimulation and demonstrates the power of this recent framework for modeling typed lambda calculi as labelled transition systems.We develop our theory for a continuation-passing style calculus, Jump-With-Argument, where normal form bisimulation takes a simple form. We equip the calculus with both existential and recursive types. An "ultimate pattern matching theorem" enables us to define bisimilarity and we show it to be a congruence. We apply our theory to proving program equivalences, type isomorphisms and genericity.
{"title":"Typed Normal Form Bisimulation for Parametric Polymorphism","authors":"Søren B. Lassen, P. Levy","doi":"10.1109/LICS.2008.26","DOIUrl":"https://doi.org/10.1109/LICS.2008.26","url":null,"abstract":"This paper presents a new bisimulation theory for parametric polymorphism which enables straight forward co-inductive proofs of program equivalences involving existential types. The theory is an instance of typed normal form bisimulation and demonstrates the power of this recent framework for modeling typed lambda calculi as labelled transition systems.We develop our theory for a continuation-passing style calculus, Jump-With-Argument, where normal form bisimulation takes a simple form. We equip the calculus with both existential and recursive types. An \"ultimate pattern matching theorem\" enables us to define bisimilarity and we show it to be a congruence. We apply our theory to proving program equivalences, type isomorphisms and genericity.","PeriodicalId":298300,"journal":{"name":"2008 23rd Annual IEEE Symposium on Logic in Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130118306","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 : 2008-06-24DOI: 10.2168/LMCS-8(3:26)2012
M. Bojanczyk, L. Segoufin, Howard Straubing
This paper presents a decidable characterization of tree languages that can be defined by a boolean combination of Sigma1 formulas. This is a tree extension of the Simon theorem, which says that a string language can be defined by a boolean combination of Sigma1 formulas if and only if its syntactic monoid is J-trivial.
{"title":"Piecewise Testable Tree Languages","authors":"M. Bojanczyk, L. Segoufin, Howard Straubing","doi":"10.2168/LMCS-8(3:26)2012","DOIUrl":"https://doi.org/10.2168/LMCS-8(3:26)2012","url":null,"abstract":"This paper presents a decidable characterization of tree languages that can be defined by a boolean combination of Sigma1 formulas. This is a tree extension of the Simon theorem, which says that a string language can be defined by a boolean combination of Sigma1 formulas if and only if its syntactic monoid is J-trivial.","PeriodicalId":298300,"journal":{"name":"2008 23rd Annual IEEE Symposium on Logic in Computer Science","volume":"103 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128584563","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}
Separation logic involves two dual forms of modularity: local reasoning makes part of the store invisible within a static scope, whereas hiding local state makes part of the store invisible outside a static scope. In the recent literature, both idioms are explained in terms of a higher-order frame rule. I point out that this approach to hiding local state imposes continuation-passing style, which is impractical. Instead, I introduce a higher-order anti-frame rule, which permits hiding local state in direct style. I formalize this rule in the setting of a type system, equipped with linear capabilities, for an ML-like programming language, and prove type soundness via a syntactic argument. Several applications illustrate the expressive power of the new rule.
{"title":"Hiding Local State in Direct Style: A Higher-Order Anti-Frame Rule","authors":"F. Pottier","doi":"10.1109/LICS.2008.16","DOIUrl":"https://doi.org/10.1109/LICS.2008.16","url":null,"abstract":"Separation logic involves two dual forms of modularity: local reasoning makes part of the store invisible within a static scope, whereas hiding local state makes part of the store invisible outside a static scope. In the recent literature, both idioms are explained in terms of a higher-order frame rule. I point out that this approach to hiding local state imposes continuation-passing style, which is impractical. Instead, I introduce a higher-order anti-frame rule, which permits hiding local state in direct style. I formalize this rule in the setting of a type system, equipped with linear capabilities, for an ML-like programming language, and prove type soundness via a syntactic argument. Several applications illustrate the expressive power of the new rule.","PeriodicalId":298300,"journal":{"name":"2008 23rd Annual IEEE Symposium on Logic in Computer Science","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133022142","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}
We introduce a notion of definable tree decompositions of graphs. Actually, a definable tree decomposition of a graph is not just a tree decomposition, but a more complicated structure that represents many different tree decompositions of the graph. It is definable in the graph by a tuple of formulas of some logic. In this paper, only study tree decomposition definable in fixed-point logic. We say that a definable tree decomposition is over a class of graphs if the pieces of the decomposition are in this class. We prove two general theorems lifting definability results from the pieces of a tree decomposition of a graph to the whole graph. Besides unifying earlier work on fixed-point definability and descriptive complexity theory on planar graphs and graphs of bounded tree width, these general results can be used to prove that the class of all graphs without a K5-minor is definable infixed-point logic and that fixed-point logic with counting captures polynomial time on this class.
{"title":"Definable Tree Decompositions","authors":"Martin Grohe","doi":"10.1109/LICS.2008.10","DOIUrl":"https://doi.org/10.1109/LICS.2008.10","url":null,"abstract":"We introduce a notion of definable tree decompositions of graphs. Actually, a definable tree decomposition of a graph is not just a tree decomposition, but a more complicated structure that represents many different tree decompositions of the graph. It is definable in the graph by a tuple of formulas of some logic. In this paper, only study tree decomposition definable in fixed-point logic. We say that a definable tree decomposition is over a class of graphs if the pieces of the decomposition are in this class. We prove two general theorems lifting definability results from the pieces of a tree decomposition of a graph to the whole graph. Besides unifying earlier work on fixed-point definability and descriptive complexity theory on planar graphs and graphs of bounded tree width, these general results can be used to prove that the class of all graphs without a K5-minor is definable infixed-point logic and that fixed-point logic with counting captures polynomial time on this class.","PeriodicalId":298300,"journal":{"name":"2008 23rd Annual IEEE Symposium on Logic in Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128397004","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}
The question of whether there is a logic that captures polynomial time is the central open problem in descriptive complexity theory. In my talk, I will review the question and the early, mostly negative results that were obtained until the mid 1990s, and then move on to positive results about capturing polynomial time on specific classes of graphs. This will include recent results on definability in fixed-point logic and graph structure theory. Finally, I will dicuss stronger logics and propose directions for further research.The purpose of this accompanying note is to give the basic definitions in detail, state the main results, mention some open problems, and give a list of references.
{"title":"The Quest for a Logic Capturing PTIME","authors":"Martin Grohe","doi":"10.1109/LICS.2008.11","DOIUrl":"https://doi.org/10.1109/LICS.2008.11","url":null,"abstract":"The question of whether there is a logic that captures polynomial time is the central open problem in descriptive complexity theory. In my talk, I will review the question and the early, mostly negative results that were obtained until the mid 1990s, and then move on to positive results about capturing polynomial time on specific classes of graphs. This will include recent results on definability in fixed-point logic and graph structure theory. Finally, I will dicuss stronger logics and propose directions for further research.The purpose of this accompanying note is to give the basic definitions in detail, state the main results, mention some open problems, and give a list of references.","PeriodicalId":298300,"journal":{"name":"2008 23rd Annual IEEE Symposium on Logic in Computer Science","volume":"9 48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124684311","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}
Collapsible pushdown automata (CPDA) are a new kind of higher-order pushdown automata in which every symbol in the stack has a link to a stack situated somewhere below it. In addition to the higher-order push and pop operations, CPDA have an important operation called collapse, whose effect is to "collapse" a stack s to the prefix as indicated by the link from the topmost symbol of s. Our first result is that CPDA are equi-expressive with recursion schemes as generators of (possibly infinite) ranked trees. In one direction, we give a simple algorithm that transforms an order-n CPDA to an order-n recursion scheme that generates the same tree, uniformly for all n Gt= 0. In the other direction, using ideas from game semantics, we give an effective transformation of order-n recursion schemes (not assumed to be homogeneously typed, and hence not necessarily safe) to order-n CPDA that compute traversals over an abstract syntax graph of the scheme, and hence paths in the tree generated by the scheme. Our equi-expressivity result is the first automata-theoretic characterization of higher-order recursion schemes. Thus CPDA are also a characterization of the simply-typed lambda calculus with recursion (generated from uninterpreted 1st-order symbols) and of (pure) innocent strategies. An important consequence of the equi-expressivity result is that it allows us to reduce decision problems on trees generated by recursion schemes to equivalent problems on CPDA and vice versa. Thus we show, as a consequence of a recent result by Ong (modal mu-calculus model-checking of trees generated by recursion schemes is n-EXPTIME complete), that the problem of solving parity games over the configuration graphs of order-n CPDA is n-EXPTIME complete, subsuming several well-known results about the solvability of games over higher-order pushdown graphs by (respectively) Walukiewicz, Cachat, and Knapik et al. Another contribution of our work is a self-contained proof of the same solvability result by generalizing standard techniques in the field. By appealing to our equi-expressivity result, we obtain a new proof of Ong's result. In contrast to higher-order pushdown graphs, we show that the monadic second-order theories of the configuration graphs of CPDA are undecidable. It follows that -- as generators of graphs -- CPDA are strictly more expressive than higher-order pushdown automata.
{"title":"Collapsible Pushdown Automata and Recursion Schemes","authors":"M. Hague, A. Murawski, C. Ong, O. Serre","doi":"10.1145/3091122","DOIUrl":"https://doi.org/10.1145/3091122","url":null,"abstract":"Collapsible pushdown automata (CPDA) are a new kind of higher-order pushdown automata in which every symbol in the stack has a link to a stack situated somewhere below it. In addition to the higher-order push and pop operations, CPDA have an important operation called collapse, whose effect is to \"collapse\" a stack s to the prefix as indicated by the link from the topmost symbol of s. Our first result is that CPDA are equi-expressive with recursion schemes as generators of (possibly infinite) ranked trees. In one direction, we give a simple algorithm that transforms an order-n CPDA to an order-n recursion scheme that generates the same tree, uniformly for all n Gt= 0. In the other direction, using ideas from game semantics, we give an effective transformation of order-n recursion schemes (not assumed to be homogeneously typed, and hence not necessarily safe) to order-n CPDA that compute traversals over an abstract syntax graph of the scheme, and hence paths in the tree generated by the scheme. Our equi-expressivity result is the first automata-theoretic characterization of higher-order recursion schemes. Thus CPDA are also a characterization of the simply-typed lambda calculus with recursion (generated from uninterpreted 1st-order symbols) and of (pure) innocent strategies. An important consequence of the equi-expressivity result is that it allows us to reduce decision problems on trees generated by recursion schemes to equivalent problems on CPDA and vice versa. Thus we show, as a consequence of a recent result by Ong (modal mu-calculus model-checking of trees generated by recursion schemes is n-EXPTIME complete), that the problem of solving parity games over the configuration graphs of order-n CPDA is n-EXPTIME complete, subsuming several well-known results about the solvability of games over higher-order pushdown graphs by (respectively) Walukiewicz, Cachat, and Knapik et al. Another contribution of our work is a self-contained proof of the same solvability result by generalizing standard techniques in the field. By appealing to our equi-expressivity result, we obtain a new proof of Ong's result. In contrast to higher-order pushdown graphs, we show that the monadic second-order theories of the configuration graphs of CPDA are undecidable. It follows that -- as generators of graphs -- CPDA are strictly more expressive than higher-order pushdown automata.","PeriodicalId":298300,"journal":{"name":"2008 23rd Annual IEEE Symposium on Logic in Computer Science","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126803051","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}
We propose a setting in which the search for a proof of B or a refutation of B (a proof of not B) can be carried out simultaneously. In contrast with the usual approach in automated deduction, we do not need to first commit to either proving B or to proving not B: instead we devise a neutral setting for attempting both a proof and a refutation. This setting is described as a two player game in which each player follows the same rules. A winning strategy translates to a proof of the formula and a winning counter-strategy translates to a refutation of the formula. The game is described for multiplicative and additive linear logic without atomic formulas. A game theoretic treatment of the multiplicative connectives is intricate and our approach to it involves two important ingredients. First, labeled graph structures are used to represent positions in a game and, second, the game playing must deal with the failure of a given player and with an appropriate resumption of play. This latter ingredient accounts for the fact that neither players might win (that is, neither B nor not B might be provable).
{"title":"A Neutral Approach to Proof and Refutation in MALL","authors":"Olivier Delande, D. Miller","doi":"10.1109/LICS.2008.35","DOIUrl":"https://doi.org/10.1109/LICS.2008.35","url":null,"abstract":"We propose a setting in which the search for a proof of B or a refutation of B (a proof of not B) can be carried out simultaneously. In contrast with the usual approach in automated deduction, we do not need to first commit to either proving B or to proving not B: instead we devise a neutral setting for attempting both a proof and a refutation. This setting is described as a two player game in which each player follows the same rules. A winning strategy translates to a proof of the formula and a winning counter-strategy translates to a refutation of the formula. The game is described for multiplicative and additive linear logic without atomic formulas. A game theoretic treatment of the multiplicative connectives is intricate and our approach to it involves two important ingredients. First, labeled graph structures are used to represent positions in a game and, second, the game playing must deal with the failure of a given player and with an appropriate resumption of play. This latter ingredient accounts for the fact that neither players might win (that is, neither B nor not B might be provable).","PeriodicalId":298300,"journal":{"name":"2008 23rd Annual IEEE Symposium on Logic in Computer Science","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116530835","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}
Dataflow analysis for concurrent programs is a problem of critical importance but, unfortunately, also an undecidable one. A key obstacle is to determine precisely how dataflow facts at a location in a given thread could be affected by operations of other threads.This problem, in turn, boils down to pairwise reachability, i.e., given program locations c1 and c2 in two threads T1 and T2, respectively, determining whether c1 and c2 are simultaneously reachable in the presence of constraints imposed by synchronization primitives. Unfortunately, pairwise reachability is undecidable for most synchronization primitives. However, we leverage the surprising result that the closely related problem of parameterized pairwise reachability of c1 and c2, i.e., whether for some n1 and n2, c1 and c2 are simultaneously reachable in the program T1 n1||T2 n2 comprised of n1 copies of T1 and n2 copies of T2,is not only decidable for many primitives, but efficiently so. Although parameterization makes pairwise reachability tractable it may over-approximate the set of pairwise reachable locations and can, therefore, be looked upon as an abstraction technique.Where as abstract interpretation is used for control and data abstractions, we propose the use of parameterization as an abstraction for concurrency. Leveraging abstract interpretation in conjunction with parameterization allows us to lift two desirable properties of sequential dataflow analysis to the concurrent domain, i.e., precision and scalability.
{"title":"Parameterization as Abstraction: A Tractable Approach to the Dataflow Analysis of Concurrent Programs","authors":"Vineet Kahlon","doi":"10.1109/LICS.2008.37","DOIUrl":"https://doi.org/10.1109/LICS.2008.37","url":null,"abstract":"Dataflow analysis for concurrent programs is a problem of critical importance but, unfortunately, also an undecidable one. A key obstacle is to determine precisely how dataflow facts at a location in a given thread could be affected by operations of other threads.This problem, in turn, boils down to pairwise reachability, i.e., given program locations c<sub>1</sub> and c<sub>2</sub> in two threads T<sub>1</sub> and T<sub>2</sub>, respectively, determining whether c1 and c2 are simultaneously reachable in the presence of constraints imposed by synchronization primitives. Unfortunately, pairwise reachability is undecidable for most synchronization primitives. However, we leverage the surprising result that the closely related problem of parameterized pairwise reachability of c<sub>1</sub> and c<sub>2</sub>, i.e., whether for some n<sub>1</sub> and n<sub>2</sub>, c<sub>1</sub> and c<sub>2</sub> are simultaneously reachable in the program T<sub>1</sub> n<sub>1||</sub>T<sub>2</sub> n<sub>2</sub> comprised of n<sub>1</sub> copies of T<sub>1</sub> and n<sub>2</sub> copies of T<sub>2</sub>,is not only decidable for many primitives, but efficiently so. Although parameterization makes pairwise reachability tractable it may over-approximate the set of pairwise reachable locations and can, therefore, be looked upon as an abstraction technique.Where as abstract interpretation is used for control and data abstractions, we propose the use of parameterization as an abstraction for concurrency. Leveraging abstract interpretation in conjunction with parameterization allows us to lift two desirable properties of sequential dataflow analysis to the concurrent domain, i.e., precision and scalability.","PeriodicalId":298300,"journal":{"name":"2008 23rd Annual IEEE Symposium on Logic in Computer Science","volume":"184 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123011353","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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