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2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)最新文献

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Upper Bounds on the Quantifier Depth for Graph Differentiation in First Order Logic 一阶逻辑图微分的量词深度上界
2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2016-05-11 DOI: 10.1145/2933575.2933595
Sandra Kiefer, Pascal Schweitzer
{"title":"Upper Bounds on the Quantifier Depth for Graph Differentiation in First Order Logic","authors":"Sandra Kiefer, Pascal Schweitzer","doi":"10.1145/2933575.2933595","DOIUrl":"https://doi.org/10.1145/2933575.2933595","url":null,"abstract":"We show that on graphs with n vertices the 2-dimensional Weisfei-ler-Leman algorithm requires at most O(n2/log(n)) iterations to reach stabilization. This in particular shows that the previously best, trivial upper bound of O(n2) is asymptotically not tight. In the logic setting this translates to the statement that if two graphs of size n can be distinguished by a formula in first order logic with counting with 3 variables (i.e., in C3) then they can also be distinguished by a C3-formula that has quantifier depth at most O (n2/log(n)).To prove the result we define a game between two players that enables us to decouple the causal dependencies between the processes happening simultaneously over several iterations of the algorithm. This allows us to treat large color classes and small color classes separately. As part of our proof we show that for graphs with bounded color class size, the number of iterations until stabilization is at most linear in the number of vertices. This also yields a corresponding statement in first order logic with counting.Similar results can be obtained for the respective logic without counting quantifiers, i.e., for the logic L3.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"173 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129435766","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}
引用次数: 22
A Mechanization of the Blakers–Massey Connectivity Theorem in Homotopy Type Theory 同伦型理论中Blakers-Massey连通性定理的机械化
2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2016-05-10 DOI: 10.1145/2933575.2934545
Kuen-Bang Hou, Eric Finster, Daniel R. Licata, P. Lumsdaine
{"title":"A Mechanization of the Blakers–Massey Connectivity Theorem in Homotopy Type Theory","authors":"Kuen-Bang Hou, Eric Finster, Daniel R. Licata, P. Lumsdaine","doi":"10.1145/2933575.2934545","DOIUrl":"https://doi.org/10.1145/2933575.2934545","url":null,"abstract":"This paper contributes to recent investigations of the use of homotopy type theory to give machine-checked proofs of constructions from homotopy theory. We present a mechanized proof of a result called the Blakers–Massey connectivity theorem, which relates the higher-dimensional loop structures of two spaces sharing a common part (represented by a pushout type, which is a generalization of a disjoint sum type) to those of the common part itself. This theorem gives important information about the pushout type, and has a number of useful corollaries, including the Freudenthal suspension theorem, which was used in previous formalizations. The proof is more direct than existing ones that apply in general category-theoretic settings for homotopy theory, and its mechanization is concise and high-level, due to novel combinations of ideas from homotopy theory and from type theory.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123045160","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}
引用次数: 33
Definability equals recognizability for graphs of bounded treewidth * 可定义性等于有界树宽*图的可识别性
2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2016-05-10 DOI: 10.1145/2933575.2934508
M. Bojanczyk, Michal Pilipczuk
{"title":"Definability equals recognizability for graphs of bounded treewidth *","authors":"M. Bojanczyk, Michal Pilipczuk","doi":"10.1145/2933575.2934508","DOIUrl":"https://doi.org/10.1145/2933575.2934508","url":null,"abstract":"We prove a conjecture of Courcelle, which states that a graph property is definable in MSO with modular counting predicates on graphs of constant treewidth if, and only if it is recognizable in the following sense: constant-width tree decompositions of graphs satisfying the property can be recognized by tree automata. While the forward implication is a classic fact known as Courcelle’s theorem, the converse direction remained open.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117186642","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}
引用次数: 41
Proving Liveness of Parameterized Programs 证明参数化程序的活动性
2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2016-05-08 DOI: 10.1145/2933575.2935310
Azadeh Farzan, Zachary Kincaid, A. Podelski
{"title":"Proving Liveness of Parameterized Programs","authors":"Azadeh Farzan, Zachary Kincaid, A. Podelski","doi":"10.1145/2933575.2935310","DOIUrl":"https://doi.org/10.1145/2933575.2935310","url":null,"abstract":"Correctness of multi-threaded programs typically requires that they satisfy liveness properties. For example, a program may require that no thread is starved of a shared resource, or that all threads eventually agree on a single value. This paper presents a method for proving that such liveness properties hold. Two particular challenges which are addressed in this work are that (1) the correctness argument may rely on global behaviour of the system (e.g., the correctness argument may require that all threads collectively progress towards \"the good thing\" rather than one thread progressing while the others do not interfere), and (2) such programs are often designed to be executed by any number of threads, and the desired liveness properties must hold no matter how many threads are active in the system.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"102 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134453322","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}
引用次数: 28
Type Theory based on Dependent Inductive and Coinductive Types 基于依赖归纳型和共归纳型的类型论
2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2016-05-07 DOI: 10.1145/2933575.2934514
Henning Basold, H. Geuvers
{"title":"Type Theory based on Dependent Inductive and Coinductive Types","authors":"Henning Basold, H. Geuvers","doi":"10.1145/2933575.2934514","DOIUrl":"https://doi.org/10.1145/2933575.2934514","url":null,"abstract":"We develop a dependent type theory that is based purely on inductive and coinductive types, and the corresponding recursion and corecursion principles. This results in a type theory with a small set of rules, while still being fairly expressive. For example, all well-known basic types and type formers that are needed for using this type theory as a logic are definable: propositional connectives, like falsity, conjunction, disjunction, and function space, dependent function space, existential quantification, equality, natural numbers, vectors etc. The reduction relation on terms consists solely of a rule for recursion and a rule for corecursion. The reduction relations for well-known types arise from that. To further support the introduction of this new type theory, we also prove fundamental properties of its term calculus. Most importantly, we prove subject reduction and strong normalisation of the reduction relation, which gives computational meaning to the terms.The presented type theory is based on ideas from categorical logic that have been investigated before by the first author, and it extends Hagino’s categorical data types to a dependently typed setting. By basing the type theory on concepts from category theory we maintain the duality between inductive and coinductive types, and it allows us to describe, for example, the function space as a coinductive type.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128322700","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}
引用次数: 12
Monadic second order logic as the model companion of temporal logic 一元二阶逻辑作为时间逻辑的模型伴侣
2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2016-05-03 DOI: 10.1145/2933575.2933609
S. Ghilardi, S. V. Gool
{"title":"Monadic second order logic as the model companion of temporal logic","authors":"S. Ghilardi, S. V. Gool","doi":"10.1145/2933575.2933609","DOIUrl":"https://doi.org/10.1145/2933575.2933609","url":null,"abstract":"The main focus of this paper is on bisimulation-invariant MSO, and more particularly on giving a novel model-theoretic approach to it. In model theory, a model companion of a theory is a first- order description of the class of models in which all potentially solvable systems of equations and non-equations have solutions. We show that bisimulation-invariant MSO on trees gives the model companion for a new temporal logic, \"fair CTL\", an enrichment of CTL with local fairness constraints. To achieve this, we give a completeness proof for the logic fair CTL which combines tableaux and Stone duality, and a fair CTL encoding of the automata for the modal μ-calculus. Moreover, we also show that MSO on binary trees is the model companion of binary deterministic fair CTL.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132301386","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}
引用次数: 8
Weak consistency notions for all the CSPs of bounded width∗ 所有有界宽度的csp的弱相合性概念
2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2016-05-02 DOI: 10.1145/2933575.2934510
M. Kozik
{"title":"Weak consistency notions for all the CSPs of bounded width∗","authors":"M. Kozik","doi":"10.1145/2933575.2934510","DOIUrl":"https://doi.org/10.1145/2933575.2934510","url":null,"abstract":"The characterization of all the Constraint Satisfaction Problems of bounded width, proposed by Feder and Vardi [SICOMP’98], was confirmed in [Bulatov’09] and independently in [FOCS’09, JACM’14]. Both proofs are based on the (2,3)-consistency (using Prague consistency in [FOCS’09], directly in [Bulatov’09]) which is costly to verify.We introduce a new consistency notion, Singleton Linear Arc Consistency (SLAC), and show that it solves the same family of problems. SLAC is weaker than Singleton Arc Consistency (SAC) and thus the result answers the question from [JLC’13] by showing that SAC solves all the problems of bounded width. At the same time the problem of verifying weaker consistency (even SAC) offers significant computational advantages over the problem of verifying (2,3)-consistency which improves the algorithms solving the CSPs of bounded width.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"124 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122084198","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}
引用次数: 27
Healthiness from Duality 健康来自对偶
2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2016-05-02 DOI: 10.1145/2933575.2935319
W. Hino, H. Kobayashi, I. Hasuo, B. Jacobs
{"title":"Healthiness from Duality","authors":"W. Hino, H. Kobayashi, I. Hasuo, B. Jacobs","doi":"10.1145/2933575.2935319","DOIUrl":"https://doi.org/10.1145/2933575.2935319","url":null,"abstract":"Healthiness is a good old question in program logics that dates back to Dijkstra. It asks for an intrinsic characterization of those predicate transformers which arise as the (backward) interpretation of a certain class of programs. There are several results known for healthiness conditions: for deterministic programs, nondeterministic ones, probabilistic ones, etc. Building upon our previous works on so-called state-and-effect triangles, we contribute a unified categorical framework for investigating healthiness conditions. This framework is based on a dual adjunction induced by a dualizing object and on our notion of relative Eilenberg-Moore algebra. The latter notion seems interesting in its own right in the context of monads, Lawvere theories and enriched categories.Categories and Subject Descriptors F.3.2 [Semantics of Programming Languages]: Algebraic Approaches to Semantics","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133882267","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}
引用次数: 18
The Diagonal Problem for Higher-Order Recursion Schemes is Decidable* 高阶递推格式的对角问题是可判定的
2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2016-05-02 DOI: 10.1145/2933575.2934527
Lorenzo Clemente, P. Parys, Sylvain Salvati, I. Walukiewicz
{"title":"The Diagonal Problem for Higher-Order Recursion Schemes is Decidable*","authors":"Lorenzo Clemente, P. Parys, Sylvain Salvati, I. Walukiewicz","doi":"10.1145/2933575.2934527","DOIUrl":"https://doi.org/10.1145/2933575.2934527","url":null,"abstract":"A non-deterministic recursion scheme recognizes a language of fi-nite trees. This very expressive model can simulate, among others, higher-order pushdown automata with collapse. We show decidability of the diagonal problem for schemes. This result has several interesting consequences. In particular, it gives an algorithm that computes the downward closure of languages of words recognized by schemes. In turn, this has immediate application to separability problems and reachability analysis of concurrent systems.Categories and Subject Descriptors 500 [Theory of computation]: Grammars and context-free languages; 500 [Theory of computation]: Tree languages; 500 [Theory of computation]: Regular languages","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132634103","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}
引用次数: 29
The Power of Arc Consistency for CSPs Defined by Partially-Ordered Forbidden Patterns* 由部分有序禁止模式定义的csp的弧一致性幂
2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2016-04-27 DOI: 10.1145/2933575.2933587
Martin C. Cooper, Stanislav Živný
{"title":"The Power of Arc Consistency for CSPs Defined by Partially-Ordered Forbidden Patterns*","authors":"Martin C. Cooper, Stanislav Živný","doi":"10.1145/2933575.2933587","DOIUrl":"https://doi.org/10.1145/2933575.2933587","url":null,"abstract":"Characterising tractable fragments of the constraint satisfaction problem (CSP) is an important challenge in theoretical computer science and artificial intelligence. Forbidding patterns (generic sub-instances) provides a means of defining CSP fragments which are neither exclusively language-based nor exclusively structure-based. It is known that the class of binary CSP instances in which the broken-triangle pattern (BTP) does not occur, a class which includes all tree-structured instances, are decided by arc consistency (AC), a ubiquitous reduction operation in constraint solvers. We provide a characterisation of simple partially-ordered forbidden patterns which have this AC-solvability property. It turns out that BTP is just one of five such AC-solvable patterns. The four other patterns allow us to exhibit new tractable classes.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"1087 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116037631","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}
引用次数: 12
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