Probabilistic pushdown automata (recursive state machines) are a widely known model of probabilistic computation associated with many decidable problems concerning termination (time) and linear-time model checking. Higher-order recursion schemes (HORS) are a prominent formalism for the analysis of higher-order computation. Recent studies showed that, for the probabilistic variant of HORS, even the basic problem of determining whether a scheme terminates almost surely is undecidable. Moreover, the undecidability already holds for order-2 schemes (order-1 schemes are known to correspond to pushdown automata). Motivated by these results, we study restricted probabilistic tree-stack automata (rPTSA), which in the nondeterministic setting are known to characterise a proper extension of context-free languages, namely, the multiple context-free languages. We show that several verification problems, such as almost-sure termination, positive almost-sure termination and ω-regular model checking are decidable for this class. At the level of higher-order recursion schemes, this corresponds to being able to verify a probabilistic version of MAHORS (which are a multiplicative-additive version of higher-order recursion schemes). MAHORS extend order-1 recursion schemes and are incomparable with order-2 schemes.
{"title":"Probabilistic Verification Beyond Context-Freeness","authors":"Guanyan Li, A. Murawski, C. Ong","doi":"10.1145/3531130.3533351","DOIUrl":"https://doi.org/10.1145/3531130.3533351","url":null,"abstract":"Probabilistic pushdown automata (recursive state machines) are a widely known model of probabilistic computation associated with many decidable problems concerning termination (time) and linear-time model checking. Higher-order recursion schemes (HORS) are a prominent formalism for the analysis of higher-order computation. Recent studies showed that, for the probabilistic variant of HORS, even the basic problem of determining whether a scheme terminates almost surely is undecidable. Moreover, the undecidability already holds for order-2 schemes (order-1 schemes are known to correspond to pushdown automata). Motivated by these results, we study restricted probabilistic tree-stack automata (rPTSA), which in the nondeterministic setting are known to characterise a proper extension of context-free languages, namely, the multiple context-free languages. We show that several verification problems, such as almost-sure termination, positive almost-sure termination and ω-regular model checking are decidable for this class. At the level of higher-order recursion schemes, this corresponds to being able to verify a probabilistic version of MAHORS (which are a multiplicative-additive version of higher-order recursion schemes). MAHORS extend order-1 recursion schemes and are incomparable with order-2 schemes.","PeriodicalId":373589,"journal":{"name":"Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132267260","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}
Algorithms for solving computational problems related to the modal μ-calculus generally do not take the formulas themselves as input, but operate on some kind of representation of formulas. This representation is usually based on a graph structure that one may associate with a μ-calculus formula. Recent work by Kupke, Marti & Venema showed that the operation of renaming bound variables may incur an exponential blow-up of the size of such a graph representation. Their example revealed the undesirable situation that standard constructions, on which algorithms for model checking and satisfiability depend, are sensitive to the specific choice of bound variables used in a formula. Our work discusses how the notion of alphabetic equivalence interacts with the construction of graph representations of μ-calculus formulas, and with the induced size measures of formulas. We introduce the condition of α-invariance on such constructions, requiring that alphabetically equivalent formulas are given the same (or isomorphic) graph representations. Our main results are the following. First we show that if two μ-calculus formulas are α-equivalent, then their respective Fischer-Ladner closures have the same cardinality, up to α-equivalence. We then continue with the definition of an α-invariant construction which represents an arbitrary μ-calculus formula by a graph that has exactly the size of the quotient of the closure of the formula, up to α-equivalence. This definition, which is itself based on a renaming of variables, solves the above-mentioned problem discovered by Kupke et al.
{"title":"Size measures and alphabetic equivalence in the μ-calculus","authors":"C. Kupke, J. Marti, Y. Venema","doi":"10.1145/3531130.3533339","DOIUrl":"https://doi.org/10.1145/3531130.3533339","url":null,"abstract":"Algorithms for solving computational problems related to the modal μ-calculus generally do not take the formulas themselves as input, but operate on some kind of representation of formulas. This representation is usually based on a graph structure that one may associate with a μ-calculus formula. Recent work by Kupke, Marti & Venema showed that the operation of renaming bound variables may incur an exponential blow-up of the size of such a graph representation. Their example revealed the undesirable situation that standard constructions, on which algorithms for model checking and satisfiability depend, are sensitive to the specific choice of bound variables used in a formula. Our work discusses how the notion of alphabetic equivalence interacts with the construction of graph representations of μ-calculus formulas, and with the induced size measures of formulas. We introduce the condition of α-invariance on such constructions, requiring that alphabetically equivalent formulas are given the same (or isomorphic) graph representations. Our main results are the following. First we show that if two μ-calculus formulas are α-equivalent, then their respective Fischer-Ladner closures have the same cardinality, up to α-equivalence. We then continue with the definition of an α-invariant construction which represents an arbitrary μ-calculus formula by a graph that has exactly the size of the quotient of the closure of the formula, up to α-equivalence. This definition, which is itself based on a renaming of variables, solves the above-mentioned problem discovered by Kupke et al.","PeriodicalId":373589,"journal":{"name":"Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125421985","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}
David Baelde, Amina Doumane, Denis Kuperberg, A. Saurin
Given that (co)inductive types are naturally modelled as fixed points, it is unsurprising that fixed-point logics are of interest in the study of programming languages, via the Curry-Howard (or proofs-as-programs) correspondence. This motivates investigations of the structural proof-theory of fixed-point logics and of their cut-elimination procedures. Among the various approaches to proofs in fixed-point logics, circular – or cyclic – proofs, are of interest in this regard but suffer from a number of limitations, most notably from a quite restricted use of cuts. Indeed, the validity condition which ensures soundness of non-wellfounded derivations and productivity of their cut-elimination prevents some computationally-relevant patterns of cuts. As a result, traditional circular proofs cannot serve as a basis for a theory of (co)recursive programming by lack of compositionality: there are not enough circular proofs and they compose badly. The present paper addresses some of these limitations by developing the circular and non-wellfounded proof-theory of multiplicative additive linear logic with fixed points () beyond the scope of the seminal works of Santocanale and Fortier and of Baelde et al. We define bouncing-validity: a new, generalized, validity criterion for , which takes axioms and cuts into account. We show soundness and cut elimination theorems for bouncing-valid non-wellfounded proofs: as a result, even though bouncing-validity proves the same sequents (or judgments) as before, we have many more valid proofs at our disposal. We illustrate the computational relevance of bouncing-validity on a number of examples. Finally, we study the decidability of the criterion in the circular case: we prove that it is undecidable in general but identify a hierarchy of decidable sub-criteria.
{"title":"Bouncing Threads for Circular and Non-Wellfounded Proofs: Towards Compositionality with Circular Proofs","authors":"David Baelde, Amina Doumane, Denis Kuperberg, A. Saurin","doi":"10.1145/3531130.3533375","DOIUrl":"https://doi.org/10.1145/3531130.3533375","url":null,"abstract":"Given that (co)inductive types are naturally modelled as fixed points, it is unsurprising that fixed-point logics are of interest in the study of programming languages, via the Curry-Howard (or proofs-as-programs) correspondence. This motivates investigations of the structural proof-theory of fixed-point logics and of their cut-elimination procedures. Among the various approaches to proofs in fixed-point logics, circular – or cyclic – proofs, are of interest in this regard but suffer from a number of limitations, most notably from a quite restricted use of cuts. Indeed, the validity condition which ensures soundness of non-wellfounded derivations and productivity of their cut-elimination prevents some computationally-relevant patterns of cuts. As a result, traditional circular proofs cannot serve as a basis for a theory of (co)recursive programming by lack of compositionality: there are not enough circular proofs and they compose badly. The present paper addresses some of these limitations by developing the circular and non-wellfounded proof-theory of multiplicative additive linear logic with fixed points () beyond the scope of the seminal works of Santocanale and Fortier and of Baelde et al. We define bouncing-validity: a new, generalized, validity criterion for , which takes axioms and cuts into account. We show soundness and cut elimination theorems for bouncing-valid non-wellfounded proofs: as a result, even though bouncing-validity proves the same sequents (or judgments) as before, we have many more valid proofs at our disposal. We illustrate the computational relevance of bouncing-validity on a number of examples. Finally, we study the decidability of the criterion in the circular case: we prove that it is undecidable in general but identify a hierarchy of decidable sub-criteria.","PeriodicalId":373589,"journal":{"name":"Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121554570","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}
N. Ackerman, Julian Asilis, Jieqi Di, Cameron E. Freer, Jean-Baptiste Tristan
We introduce definitions of computable PAC learning for binary classification over computable metric spaces. We provide sufficient conditions on a hypothesis class to ensure than an empirical risk minimizer (ERM) is computable, and bound the strong Weihrauch degree of an ERM under more general conditions. We also give a presentation of a hypothesis class that does not admit any proper computable PAC learner with computable sample function, despite the underlying class being PAC learnable.
{"title":"Computable PAC Learning of Continuous Features","authors":"N. Ackerman, Julian Asilis, Jieqi Di, Cameron E. Freer, Jean-Baptiste Tristan","doi":"10.1145/3531130.3533330","DOIUrl":"https://doi.org/10.1145/3531130.3533330","url":null,"abstract":"We introduce definitions of computable PAC learning for binary classification over computable metric spaces. We provide sufficient conditions on a hypothesis class to ensure than an empirical risk minimizer (ERM) is computable, and bound the strong Weihrauch degree of an ERM under more general conditions. We also give a presentation of a hypothesis class that does not admit any proper computable PAC learner with computable sample function, despite the underlying class being PAC learnable.","PeriodicalId":373589,"journal":{"name":"Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115510729","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 prove the following completeness result about classical realizability: given any Boolean algebra with at least two elements, there exists a Krivine-style classical realizability model whose characteristic Boolean algebra is elementarily equivalent to it. This is done by controlling precisely which combinations of so-called “angelic” (or “may”) and “demonic” (or “must”) nondeterminism exist in the underlying model of computation.
{"title":"A first-order completeness result about characteristic Boolean algebras in classical realizability","authors":"Guillaume Geoffroy","doi":"10.1145/3531130.3532484","DOIUrl":"https://doi.org/10.1145/3531130.3532484","url":null,"abstract":"We prove the following completeness result about classical realizability: given any Boolean algebra with at least two elements, there exists a Krivine-style classical realizability model whose characteristic Boolean algebra is elementarily equivalent to it. This is done by controlling precisely which combinations of so-called “angelic” (or “may”) and “demonic” (or “must”) nondeterminism exist in the underlying model of computation.","PeriodicalId":373589,"journal":{"name":"Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115734169","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 article redevelops and deepens the probability theory of Ewens and others from the 1970s in population biology. At the heart of this theory are the so-called Ewens distributions describing biolological mutations. These distributions have a particularly rich (and beautiful) mathematical structure. The original work is formulated in terms of partitions, which are special multisets on natural numbers. The current redevelopment starts from multisets on arbitrary sets, with partitions as a special form that captures only the multiplicities of multiplicities, without naming the elements themselves. This ‘element-free’ approach will be developed in parallel to the usual element-based theory. Ewens’ famous sampling formula describes a cone of (parametrised) distributions on partitions. Another cone for this chain is described in terms of new (element-free) multinomials. They are well-defined because of a novel ‘partitions multinomial theorem’ that extends the familiar multinomial theorem. This is based on a new concept of ‘division’, as element-free distribution, in terms of multisets of probabilities that add up to one.
{"title":"Partitions and Ewens Distributions in element-free Probability Theory","authors":"B. Jacobs","doi":"10.1145/3531130.3532419","DOIUrl":"https://doi.org/10.1145/3531130.3532419","url":null,"abstract":"This article redevelops and deepens the probability theory of Ewens and others from the 1970s in population biology. At the heart of this theory are the so-called Ewens distributions describing biolological mutations. These distributions have a particularly rich (and beautiful) mathematical structure. The original work is formulated in terms of partitions, which are special multisets on natural numbers. The current redevelopment starts from multisets on arbitrary sets, with partitions as a special form that captures only the multiplicities of multiplicities, without naming the elements themselves. This ‘element-free’ approach will be developed in parallel to the usual element-based theory. Ewens’ famous sampling formula describes a cone of (parametrised) distributions on partitions. Another cone for this chain is described in terms of new (element-free) multinomials. They are well-defined because of a novel ‘partitions multinomial theorem’ that extends the familiar multinomial theorem. This is based on a new concept of ‘division’, as element-free distribution, in terms of multisets of probabilities that add up to one.","PeriodicalId":373589,"journal":{"name":"Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"90 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115966764","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}
Quantitative Σ-algebras, where Σ is a signature with countable arities, are Σ-algebras equipped with a metric making all operations nonexpanding. They have been studied by Mardare, Panangaden and Plotkin who also introduced c-basic quantitative equations for regular cardinals c. Categories of quantitative algebras that can be presented by such equations for c = ℵ1 are called ω1-varieties. We prove that they are precisely the monadic categories , where is a countably basic monad on the category of metric spaces For Σ finitary one speaks about ω-varieties for c = ℵ0. If all spaces used are restricted to UMet, the category of ultrametric spaces, then ω-varieties are precisely the monadic categories , where is a finitely basic monad.
{"title":"Varieties of Quantitative Algebras and Their Monads","authors":"J. Adámek","doi":"10.1145/3531130.3532405","DOIUrl":"https://doi.org/10.1145/3531130.3532405","url":null,"abstract":"Quantitative Σ-algebras, where Σ is a signature with countable arities, are Σ-algebras equipped with a metric making all operations nonexpanding. They have been studied by Mardare, Panangaden and Plotkin who also introduced c-basic quantitative equations for regular cardinals c. Categories of quantitative algebras that can be presented by such equations for c = ℵ1 are called ω1-varieties. We prove that they are precisely the monadic categories , where is a countably basic monad on the category of metric spaces For Σ finitary one speaks about ω-varieties for c = ℵ0. If all spaces used are restricted to UMet, the category of ultrametric spaces, then ω-varieties are precisely the monadic categories , where is a finitely basic monad.","PeriodicalId":373589,"journal":{"name":"Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"120 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114076042","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}
Can the λ-calculus be considered a reasonable computational model? Can we use it for measuring the time and space consumption of algorithms? While the literature contains positive answers about time, much less is known about space. This paper presents a new reasonable space cost model for the λ-calculus, based on a variant over the Krivine abstract machine. For the first time, this cost model is able to accommodate logarithmic space. Moreover, we study the time behavior of our machine and show how to transport our results to the call-by-value λ-calculus.
{"title":"Reasonable Space for the λ-Calculus, Logarithmically","authors":"Beniamino Accattoli, Ugo Dal Lago, G. Vanoni","doi":"10.1145/3531130.3533362","DOIUrl":"https://doi.org/10.1145/3531130.3533362","url":null,"abstract":"Can the λ-calculus be considered a reasonable computational model? Can we use it for measuring the time and space consumption of algorithms? While the literature contains positive answers about time, much less is known about space. This paper presents a new reasonable space cost model for the λ-calculus, based on a variant over the Krivine abstract machine. For the first time, this cost model is able to accommodate logarithmic space. Moreover, we study the time behavior of our machine and show how to transport our results to the call-by-value λ-calculus.","PeriodicalId":373589,"journal":{"name":"Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117023184","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 characterize the strength of the algebraic proof systems Sherali-Adams () and Nullstellensatz () in terms of Frege-style proof systems. Unlike bounded-depth Frege, has polynomial-size proofs of the pigeonhole principle (). A natural question is whether adding to bounded-depth Frege is enough to simulate . We show that , with unary integer coefficients, lies strictly between tree-like and tree-like Resolution. We introduce a weighted version of () and we show that with integer coefficients lies strictly between tree-like and Resolution. Analogous results are shown for using the bijective (i.e. onto and functional) pigeonhole principle and a weighted version of it.
{"title":"On the strength of Sherali-Adams and Nullstellensatz as propositional proof systems","authors":"Ilario Bonacina, Maria Luisa Bonet","doi":"10.1145/3531130.3533344","DOIUrl":"https://doi.org/10.1145/3531130.3533344","url":null,"abstract":"We characterize the strength of the algebraic proof systems Sherali-Adams () and Nullstellensatz () in terms of Frege-style proof systems. Unlike bounded-depth Frege, has polynomial-size proofs of the pigeonhole principle (). A natural question is whether adding to bounded-depth Frege is enough to simulate . We show that , with unary integer coefficients, lies strictly between tree-like and tree-like Resolution. We introduce a weighted version of () and we show that with integer coefficients lies strictly between tree-like and Resolution. Analogous results are shown for using the bijective (i.e. onto and functional) pigeonhole principle and a weighted version of it.","PeriodicalId":373589,"journal":{"name":"Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"602 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123200957","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}
R. Govind, F. Herbreteau, B. Srivathsan, I. Walukiewicz
A timed network is a parallel composition of timed automata synchronizing on common actions. We develop a methodology that allows to use partial-order methods when solving the reachability problem for timed networks. It is based on a local-time semantics proposed by [Bengtsson et al. 1998]. A new simulation based abstraction of local-time zones is proposed. The main technical contribution is an efficient algorithm for testing subsumption between local-time zones with respect to this abstraction operator. The abstraction is not finite for all networks. It turns out that, under relatively mild conditions, there is no finite abstraction for local-time zones that works for arbitrary timed networks. To circumvent this problem, we introduce a notion of a bounded-spread network. The spread of a network is a parameter that says how far the local times of individual processes need to diverge. For bounded-spread networks, we show that it is possible to use subsumption and partial-order methods at the same time.
一个定时网络是一个同步于共同动作的定时自动机的并行组合。我们开发了一种方法，允许使用部分顺序的方法来解决时间网络的可达性问题。它基于[Bengtsson et al. 1998]提出的局部时间语义。提出了一种新的基于仿真的时区抽象方法。主要的技术贡献是一种有效的算法，用于根据该抽象操作符测试本地时区之间的包容。对所有网络的抽象都不是有限的。事实证明，在相对温和的条件下，对于适用于任意时间网络的本地时区，没有有限的抽象。为了避免这个问题，我们引入了有界扩散网络的概念。网络的扩展是一个参数，表示单个进程的局部时间需要偏离多远。对于有界传播网络，我们证明了同时使用包容和部分阶方法是可能的。
{"title":"Abstractions for the local-time semantics of timed automata: a foundation for partial-order methods","authors":"R. Govind, F. Herbreteau, B. Srivathsan, I. Walukiewicz","doi":"10.1145/3531130.3533343","DOIUrl":"https://doi.org/10.1145/3531130.3533343","url":null,"abstract":"A timed network is a parallel composition of timed automata synchronizing on common actions. We develop a methodology that allows to use partial-order methods when solving the reachability problem for timed networks. It is based on a local-time semantics proposed by [Bengtsson et al. 1998]. A new simulation based abstraction of local-time zones is proposed. The main technical contribution is an efficient algorithm for testing subsumption between local-time zones with respect to this abstraction operator. The abstraction is not finite for all networks. It turns out that, under relatively mild conditions, there is no finite abstraction for local-time zones that works for arbitrary timed networks. To circumvent this problem, we introduce a notion of a bounded-spread network. The spread of a network is a parameter that says how far the local times of individual processes need to diverge. For bounded-spread networks, we show that it is possible to use subsumption and partial-order methods at the same time.","PeriodicalId":373589,"journal":{"name":"Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128805425","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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