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2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science最新文献

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Two-Variable Logic with Counting and Trees 具有计数和树的二变量逻辑
2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2016-11-03 DOI: 10.1145/2983622
Witold Charatonik, Piotr Witkowski
{"title":"Two-Variable Logic with Counting and Trees","authors":"Witold Charatonik, Piotr Witkowski","doi":"10.1145/2983622","DOIUrl":"https://doi.org/10.1145/2983622","url":null,"abstract":"We consider the two-variable logic with counting quantifiers (C2) interpreted over finite structures that contain two forests of ranked trees. This logic is strictly more expressive than standard C2 and it is no longer a fragment of the first order logic. In particular, it can express that a structure is a ranked tree, a cycle or a connected graph of bounded degree. It is also strictly more expressive than the first-order logic with two variables and two successor relations of two finite linear orders. We give a decision procedure for the satisfiability problem for this logic. The procedure runs in NEXPTIME, which is optimal since the satisfiability problem for plain C2 is NEXPTIME-complete.","PeriodicalId":425745,"journal":{"name":"2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131409876","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: 34
Weighted Relational Models of Typed Lambda-Calculi 类型化λ -微积分的加权关系模型
2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2013-06-25 DOI: 10.1109/LICS.2013.36
J. Laird, Giulio Manzonetto, G. McCusker, Michele Pagani
{"title":"Weighted Relational Models of Typed Lambda-Calculi","authors":"J. Laird, Giulio Manzonetto, G. McCusker, Michele Pagani","doi":"10.1109/LICS.2013.36","DOIUrl":"https://doi.org/10.1109/LICS.2013.36","url":null,"abstract":"The category Rel of sets and relations yields one of the simplest denotational semantics of Linear Logic (LL). It is known that Rel is the biproduct completion of the Boolean ring. We consider the generalization of this construction to an arbitrary continuous semiring R, producing a cpo-enriched category which is a semantics of LL, and its (co)Kleisli category is an adequate model of an extension of PCF, parametrized by R. Specific instances of R allow us to compare programs not only with respect to “what they can do”, but also “in how many steps” or “in how many different ways” (for non-deterministic PCF) or even “with what probability” (for probabilistic PCF).","PeriodicalId":425745,"journal":{"name":"2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122890966","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: 84
Pumping by Typing 输入式泵送
2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2013-06-25 DOI: 10.1109/LICS.2013.46
N. Kobayashi
{"title":"Pumping by Typing","authors":"N. Kobayashi","doi":"10.1109/LICS.2013.46","DOIUrl":"https://doi.org/10.1109/LICS.2013.46","url":null,"abstract":"Higher-order recursion schemes (HORS), which are higher-order grammars for generating infinite trees, have recently been studied extensively in the context of model checking and its applications to higher-order program verification. We develop a pumping lemma for HORS by using a novel but simple intersection type system for reasoning about reductions of λ-terms. Our proof is arguably much simpler than the proof of Kartzow and Parys' pumping lemma for collapsible pushdown automata. As an application, we give an alternative proof of Kartzow and Parys' result about the strictness of the hierarchy of trees generated by HORS.","PeriodicalId":425745,"journal":{"name":"2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"342 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132544675","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: 14
On the Query Complexity of Real Functionals 实函数的查询复杂度
2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2013-06-25 DOI: 10.1109/LICS.2013.15
Hugo Férée, M. Hoyrup, W. Gomaa
{"title":"On the Query Complexity of Real Functionals","authors":"Hugo Férée, M. Hoyrup, W. Gomaa","doi":"10.1109/LICS.2013.15","DOIUrl":"https://doi.org/10.1109/LICS.2013.15","url":null,"abstract":"Recently Kawamura and Cook developed a framework to define the computational complexity of operators arising in analysis. Our goal is to understand the effects of complexity restrictions on the analytical properties of the operator. We focus on the case of norms over C[0,1] and introduce the notion of dependence of a norm on a point and relate it to the query complexity of the norm. We show that the dependence of almost every point is of the order of the query complexity of the norm. A norm with small complexity depends on a few points but, as compensation, highly depends on them. We characterize the functionals that are computable using one oracle call only and discuss the uniformity of that characterization.","PeriodicalId":425745,"journal":{"name":"2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116996802","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: 5
Fibred Data Types 光纤数据类型
2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2013-06-25 DOI: 10.1109/LICS.2013.30
Neil Ghani, Lorenzo Malatesta, F. Forsberg, A. Setzer
{"title":"Fibred Data Types","authors":"Neil Ghani, Lorenzo Malatesta, F. Forsberg, A. Setzer","doi":"10.1109/LICS.2013.30","DOIUrl":"https://doi.org/10.1109/LICS.2013.30","url":null,"abstract":"Data types are undergoing a major leap forward in their sophistication driven by a conjunction of i) theoretical advances in the foundations of data types; and ii) requirements of programmers for ever more control of the data structures they work with. In this paper we develop a theory of indexed data types where, crucially, the indices are generated inductively at the same time as the data. In order to avoid commitment to any specific notion of indexing we take an axiomatic approach to such data types using fibrations - thus giving us a theory of what we call fibred data types. The genesis of these fibred data types can be traced within the literature, most notably to Dybjer and Setzer's introduction of the concept of induction-recursion. This paper, while drawing heavily on their seminal work for inspiration, gives a categorical reformulation of Dybjer and Setzer's original work which leads to a large number of extensions of induction-recursion. Concretely, the paper provides i) conceptual clarity as to what inductionrecursion fundamentally is about; ii) greater expressiveness in allowing not just the inductive-recursive definition of families of sets, or even indexed families of sets, but rather the inductiverecursive definition of a whole host of other structures; iii) a semantics for induction-recursion based not on the specific model of families, but rather an axiomatic model based upon fibrations which therefore encompasses diverse structures (domain theoretic, realisability, games etc) arising in the semantics of programming languages; and iv) technical justification as to why these fibred data types exist using large cardinals from set theory.","PeriodicalId":425745,"journal":{"name":"2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"128 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123445562","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: 6
The Logic of Exact Covers: Completeness and Uniform Interpolation 精确覆盖的逻辑:完备性和一致插值
2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2013-06-25 DOI: 10.1109/LICS.2013.48
D. Pattinson
{"title":"The Logic of Exact Covers: Completeness and Uniform Interpolation","authors":"D. Pattinson","doi":"10.1109/LICS.2013.48","DOIUrl":"https://doi.org/10.1109/LICS.2013.48","url":null,"abstract":"We show that all (not necessarily normal or monotone) modal logics that can be axiomatised in rank-1 have the interpolation property, and that in fact interpolation is uniform if the logics just have finitely many modal operators. As immediate applications, we obtain previously unknown interpolation theorems for a range of modal logics, containing probabilistic and graded modal logic, alternating temporal logic and some variants of conditional logic. Technically, this is achieved by translating to and from a new (coalgebraic) logic introduced in this paper, the logic of exact covers. It is interpreted over coalgebrasfor an endofunctor on the category of sets that also directly determines the syntax. Apart from closure under bisimulation quantifiers (and hence interpolation), we also provide a complete tableaux calculus and establish both the Hennessy-Milner and the small model property for this logic.","PeriodicalId":425745,"journal":{"name":"2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127278848","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: 14
Presburger Vector Addition Systems Presburger向量加法系统
2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2013-06-25 DOI: 10.1109/LICS.2013.7
Jérôme Leroux
{"title":"Presburger Vector Addition Systems","authors":"Jérôme Leroux","doi":"10.1109/LICS.2013.7","DOIUrl":"https://doi.org/10.1109/LICS.2013.7","url":null,"abstract":"The reachability problem for Vector Addition Systems (VAS) is a central problem of net theory. The problem is known to be decidable by inductive invariants definable in the Presburger arithmetic. When the reachability set is definable in the Presburger arithmetic, the existence of such an inductive invariant is immediate. However, in this case, the computation of a Presburger formula denoting the reachability set is an open problem. In this paper we close this problem by proving that if the reachability set of a VAS is definable in the Presburger arithmetic, then the VAS is flatable, i.e. its reachability set can be obtained by runs labeled by words in a bounded language. As a direct consequence, classical algorithms based on acceleration techniques effectively compute a formula in the Presburger arithmetic denoting the reachability set.","PeriodicalId":425745,"journal":{"name":"2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127295711","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: 31
Compressing Polarized Boxes 压缩极化箱
2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2013-06-25 DOI: 10.1109/LICS.2013.49
Beniamino Accattoli
{"title":"Compressing Polarized Boxes","authors":"Beniamino Accattoli","doi":"10.1109/LICS.2013.49","DOIUrl":"https://doi.org/10.1109/LICS.2013.49","url":null,"abstract":"The sequential nature of sequent calculus provides a simple definition of cut-elimination rules that duplicate or erase sub-proofs. The parallel nature of proof nets, instead, requires the introduction of explicit boxes, which are global and synchronous constraints on the structure of graphs. We show that logical polarity can be exploited to obtain an implicit, compact, and natural representation of boxes: in an expressive polarized dialect of linear logic, boxes may be represented by simply recording some of the polarity changes occurring in the box at level 0. The content of the box can then be recovered locally and unambiguously. Moreover, implicit boxes are more parallel than explicit boxes, as they realize a larger quotient. We provide a correctness criterion and study the novel and subtle cut-elimination dynamics induced by implicit boxes, proving confluence and strong normalization.","PeriodicalId":425745,"journal":{"name":"2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129933216","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: 5
A Relatively Complete Generic Hoare Logic for Order-Enriched Effects 富序效应的一个相对完备的泛型Hoare逻辑
2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2013-06-25 DOI: 10.1109/LICS.2013.33
S. Goncharov, Lutz Schröder
{"title":"A Relatively Complete Generic Hoare Logic for Order-Enriched Effects","authors":"S. Goncharov, Lutz Schröder","doi":"10.1109/LICS.2013.33","DOIUrl":"https://doi.org/10.1109/LICS.2013.33","url":null,"abstract":"Monads are the basis of a well-established method of encapsulating side-effects in semantics and programming. There have been a number of proposals for monadic program logics in the setting of plain monads, while much of the recent work on monadic semantics is concerned with monads on enriched categories, in particular in domain-theoretic settings, which allow for recursive monadic programs. Here, we lay out a definition of order-enriched monad which imposes cpo structure on the monad itself rather than on base category. Starting from the observation that order-enrichment of a monad induces a weak truth-value object, we develop a generic Hoare calculus for monadic side-effecting programs. For this calculus, we prove relative completeness via a calculus of weakest preconditions, which we also relate to strongest postconditions.","PeriodicalId":425745,"journal":{"name":"2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126274410","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: 19
Unifying Classical and Intuitionistic Logics for Computational Control 计算控制中经典逻辑与直觉逻辑的统一
2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2013-06-25 DOI: 10.1109/LICS.2013.34
Chuck C. Liang, D. Miller
{"title":"Unifying Classical and Intuitionistic Logics for Computational Control","authors":"Chuck C. Liang, D. Miller","doi":"10.1109/LICS.2013.34","DOIUrl":"https://doi.org/10.1109/LICS.2013.34","url":null,"abstract":"We show that control operators and other extensions of the Curry-Howard isomorphism can be achieved without collapsing all of intuitionistic logic into classical logic. For this purpose we introduce a unified propositional logic using polarized formulas. We define a Kripke semantics for this logic. Our proof system extends an intuitionistic system that already allows multiple conclusions. This arrangement reveals a greater range of computational possibilities, including a form of dynamic scoping. We demonstrate the utility of this logic by showing how it can improve the formulation of exception handling in programming languages, including the ability to distinguish between different kinds of exceptions and constraining when an exception can be thrown, thus providing more refined control over computation compared to classical logic. We also describe some significant fragments of this logic and discuss its extension to second-order logic.","PeriodicalId":425745,"journal":{"name":"2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"89 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131224623","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: 13
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