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

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Reachability in Two-Dimensional Unary Vector Addition Systems with States is NL-Complete* 具有状态的二维一元向量加法系统的可达性是nl完全的*
2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2016-02-01 DOI: 10.1145/2933575.2933577
Matthias Englert, R. Lazic, Patrick Totzke
{"title":"Reachability in Two-Dimensional Unary Vector Addition Systems with States is NL-Complete*","authors":"Matthias Englert, R. Lazic, Patrick Totzke","doi":"10.1145/2933575.2933577","DOIUrl":"https://doi.org/10.1145/2933575.2933577","url":null,"abstract":"Blondin et al. showed at LICS 2015 that two-dimensional vector addition systems with states have reachability witnesses of length exponential in the number of states and polynomial in the norm of vectors. The resulting guess-and-verify algorithm is optimal (PSPACE), but only if the input vectors are given in binary. We answer positively the main question left open by their work, namely establish that reachability witnesses of pseudo-polynomial length always exist. Hence, when the input vectors are given in unary, the improved guess-and-verify algorithm requires only logarithmic space.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"281 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131714329","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: 32
A bifibrational reconstruction of Lawvere’s presheaf hyperdoctrine 对Lawvere的前页超主义的一种震颤式的重建
2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2016-01-22 DOI: 10.1145/2933575.2934525
Paul-André Melliès, N. Zeilberger
{"title":"A bifibrational reconstruction of Lawvere’s presheaf hyperdoctrine","authors":"Paul-André Melliès, N. Zeilberger","doi":"10.1145/2933575.2934525","DOIUrl":"https://doi.org/10.1145/2933575.2934525","url":null,"abstract":"Combining insights from the study of type refinement systems and of monoidal closed chiralities, we show how to reconstruct Lawvere’s hyperdoctrine of presheaves using a full and faithful embedding into a monoidal closed bifibration living now over the compact closed category of small categories and distributors. Besides revealing dualities which are not immediately apparent in the traditional presentation of the presheaf hyperdoctrine, this reconstruction leads us to an axiomatic treatment of directed equality predicates (modelled by hom presheaves), realizing a vision initially set out by Lawvere (1970). It also leads to a simple calculus of string diagrams (representing presheaves) that is highly reminiscent of C. S. Peirce’s existential graphs for predicate logic, refining an earlier interpretation of existential graphs in terms of Boolean hyperdoctrines by Brady and Trimble. Finally, we illustrate how this work extends to a bifibrational setting a number of fundamental ideas of linear logic.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"263 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126053021","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
Interacting Frobenius Algebras are Hopf 相互作用的Frobenius代数是Hopf
2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2016-01-19 DOI: 10.1145/2933575.2934550
Ross Duncan, Kevin Dunne
{"title":"Interacting Frobenius Algebras are Hopf","authors":"Ross Duncan, Kevin Dunne","doi":"10.1145/2933575.2934550","DOIUrl":"https://doi.org/10.1145/2933575.2934550","url":null,"abstract":"Theories featuring the interaction between a Frobenius algebra and a Hopf algebra have recently appeared in several areas in computer science: concurrent programming, control theory, and quantum computing, among others. Bonchi, Sobocinski, and Zanasi [9] have shown that, given a suitable distribution law, a pair of Hopf algebras forms two Frobenius algebras. Here we take the opposite approach, and show that interacting Frobenius algebras form Hopf algebras. We generalise [9] by including non-trivial dynamics of the underlying object—the so-called phase group—and investigate the effects of finite dimensionality of the underlying model, and recover the system of Bonchi et al as a subtheory in the prime power dimensional case. However the more general theory does not arise from a distributive law.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130723195","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: 38
Solvability of Matrix-Exponential Equations 矩阵-指数方程的可解性
2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2016-01-19 DOI: 10.1145/2933575.2934538
J. Ouaknine, Amaury Pouly, João Sousa Pinto, J. Worrell
{"title":"Solvability of Matrix-Exponential Equations","authors":"J. Ouaknine, Amaury Pouly, João Sousa Pinto, J. Worrell","doi":"10.1145/2933575.2934538","DOIUrl":"https://doi.org/10.1145/2933575.2934538","url":null,"abstract":"We consider a continuous analogue of (Babai et al. 1996)’s and (Cai et al. 2000)’s problem of solving multiplicative matrix equations. Given k + 1 square matrices A1,…, Ak, C, all of the same dimension, whose entries are real algebraic, we examine the problem of deciding whether there exist non-negative reals t1, …, tk such thatbegin{equation*} prodlimits_{i = 1}^k {exp ({A_i}{t_i})} = C. end{equation*}We show that this problem is undecidable in general, but decidable under the assumption that the matrices A1, …, Ak commute. Our results have applications to reachability problems for linear hybrid automata.Our decidability proof relies on a number of theorems from algebraic and transcendental number theory, most notably those of Baker, Kronecker, Lindemann, and Masser, as well as some useful geometric and linear-algebraic results, including the Minkowski-Weyl theorem and a new (to the best of our knowledge) result about the uniqueness of strictly upper triangular matrix logarithms of upper unitriangular matrices. On the other hand, our undecidability result is shown by reduction from Hilbert’s Tenth Problem.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114684914","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: 4
Proving Differential Privacy via Probabilistic Couplings 通过概率耦合证明差分隐私
2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2016-01-19 DOI: 10.1145/2933575.2934554
G. Barthe, Marco Gaboardi, B. Grégoire, Justin Hsu, Pierre-Yves Strub
{"title":"Proving Differential Privacy via Probabilistic Couplings","authors":"G. Barthe, Marco Gaboardi, B. Grégoire, Justin Hsu, Pierre-Yves Strub","doi":"10.1145/2933575.2934554","DOIUrl":"https://doi.org/10.1145/2933575.2934554","url":null,"abstract":"Over the last decade, differential privacy has achieved widespread adoption within the privacy community. Moreover, it has attracted significant attention from the verification community, resulting in several successful tools for formally proving differential privacy. Although their technical approaches vary greatly, all existing tools rely on reasoning principles derived from the composition theorem of differential privacy. While this suffices to verify most common private algorithms, there are several important algorithms whose privacy analysis does not rely solely on the composition theorem. Their proofs are significantly more complex, and are currently beyond the reach of verification tools.In this paper, we develop compositional methods for formally verifying differential privacy for algorithms whose analysis goes beyond the composition theorem. Our methods are based on deep connections between differential privacy and probabilistic couplings, an established mathematical tool for reasoning about stochastic processes. Even when the composition theorem is not helpful, we can often prove privacy by a coupling argument.We demonstrate our methods on two algorithms: the Exponential mechanism and the Above Threshold algorithm, the critical component of the famous Sparse Vector algorithm. We verify these examples in a relational program logic apRHL+, which can construct approximate couplings. This logic extends the existing apRHL logic with more general rules for the Laplace mechanism and the one-sided Laplace mechanism, and new structural rules enabling pointwise reasoning about privacy; all the rules are inspired by the connection with coupling. While our paper is presented from a formal verification perspective, we believe that its main insight is of independent interest for the differential privacy community.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126194452","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: 88
Reducts of finitely bounded homogeneous structures, and lifting tractability from finite-domain constraint satisfaction 有限有界齐次结构的约简，以及从有限域约束满足中提升可追溯性
2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2016-01-18 DOI: 10.1145/2933575.2934515
M. Bodirsky, A. Mottet
{"title":"Reducts of finitely bounded homogeneous structures, and lifting tractability from finite-domain constraint satisfaction","authors":"M. Bodirsky, A. Mottet","doi":"10.1145/2933575.2934515","DOIUrl":"https://doi.org/10.1145/2933575.2934515","url":null,"abstract":"Many natural decision problems can be formulated as constraint satisfaction problems for reducts of finitely bounded homogeneous structures. This class of problems is a large generalisation of the class of CSPs over finite domains. Our first result is a general polynomial-time reduction from such infinite-domain CSPs to finite-domain CSPs. We use this reduction to obtain new powerful polynomial-time tractability conditions that can be expressed in terms of topological polymorphism clones. Moreover, we study the subclass $mathcal{C}$ of CSPs for structures that are first-order definable over equality with parameters. Also this class $mathcal{C}$ properly extends the class of all finite-domain CSPs. We show that the tractability conjecture for reducts of finitely bounded homogeneous structures is for $mathcal{C}$ equivalent to the finite-domain tractability conjecture.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130017350","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: 21
Semi-galois Categories I: The Classical Eilenberg Variety Theory 半伽罗瓦范畴1:经典的艾伦伯格变异理论
2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2015-12-14 DOI: 10.1145/2933575.2934528
Takeo Uramoto
{"title":"Semi-galois Categories I: The Classical Eilenberg Variety Theory","authors":"Takeo Uramoto","doi":"10.1145/2933575.2934528","DOIUrl":"https://doi.org/10.1145/2933575.2934528","url":null,"abstract":"Recently, Eilenberg’s variety theorem was reformulated in the light of Stone’s duality theorem. On one level, this reformulation led to a unification of several existing Eilenberg-type theorems and further generalizations of these theorems. On another level, this reformulation is also a natural continuation of a research line on profinite monoids that has been developed since the late 1980s. The current paper concerns the latter in particular. In this relation, this paper introduces and studies the class of semi-galois categories, i.e. an extension of galois categories; and develops a particularly fundamental theory concerning semi-galois categories: That is, (I) a duality theorem between profinite monoids and semi-galois categories; (II) a coherent duality-based reformulation of two classical Eilenberg-type variety theorems due to Straubing [30] and Chaubard et al. [10]; and (III) a Galois-type classification of closed subgroups of profinite monoids in terms of finite discrete cofibrations over semi-galois categories.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134032596","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: 7
Deciding First-Order Satisfiability when Universal and Existential Variables are Separated 确定全称变量与存在变量分离时的一阶可满足性
2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2015-11-29 DOI: 10.1145/2933575.2934532
T. Sturm, Marco Voigt, Christoph Weidenbach
{"title":"Deciding First-Order Satisfiability when Universal and Existential Variables are Separated","authors":"T. Sturm, Marco Voigt, Christoph Weidenbach","doi":"10.1145/2933575.2934532","DOIUrl":"https://doi.org/10.1145/2933575.2934532","url":null,"abstract":"We introduce a new decidable fragment of first-order logic with equality, which strictly generalizes two already well-known ones—the Bernays–Schönfinkel–Ramsey (BSR) Fragment and the Monadic Fragment. The defining principle is the syntactic separation of universally quantified variables from existentially quantified ones at the level of atoms. Thus, our classification neither rests on restrictions on quantifier prefixes (as in the BSR case) nor on restrictions on the arity of predicate symbols (as in the monadic case). We demonstrate that the new fragment exhibits the finite model property and derive a non-elementary upper bound on the computing time required for deciding satisfiability in the new fragment. For the subfragment of prenex sentences with the quantifier prefix ∃*∀*∃* the satisfiability problem is shown to be complete for NEXPTIME. Finally, we discuss how automated reasoning procedures can take advantage of our results.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"80 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127996704","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
Invisible Pushdown Languages 隐形下推语言
2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2015-11-01 DOI: 10.1145/2933575.2933579
Eryk Kopczynski
{"title":"Invisible Pushdown Languages","authors":"Eryk Kopczynski","doi":"10.1145/2933575.2933579","DOIUrl":"https://doi.org/10.1145/2933575.2933579","url":null,"abstract":"Context-free languages allow one to express data with hierarchical structure, at the cost of losing some of the useful properties of languages recognized by finite automata on words. However, it is possible to restore some of these properties by making the structure of the tree visible, such as is done by visibly pushdown languages, or finite automata on trees. In this paper, we show that the structure given by such approaches remains invisible when it is read by a finite automaton (on word). In particular, we show that separability with a regular language is undecidable for visibly pushdown languages, just as it is undecidable for general context-free languages.","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":"2015-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121928964","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
Towards Compositional Feedback in Non-Deterministic and Non-Input-Receptive Systems* 非确定性和非输入可接受系统中的组合反馈研究*
2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2015-10-21 DOI: 10.1145/2933575.2934503
V. Preoteasa, S. Tripakis
{"title":"Towards Compositional Feedback in Non-Deterministic and Non-Input-Receptive Systems*","authors":"V. Preoteasa, S. Tripakis","doi":"10.1145/2933575.2934503","DOIUrl":"https://doi.org/10.1145/2933575.2934503","url":null,"abstract":"Feedback is an essential composition operator in many classes of reactive and other systems. This paper studies feedback in the context of compositional theories with refinement. Such theories allow to reason about systems on a component-by-component basis, and to characterize substitutability as a refinement relation. Although compositional theories of feedback do exist, they are limited either to deterministic systems (functions) or input-receptive systems (total relations). In this work we propose a compositional theory of feedback which applies to non-deterministic and non-input-receptive systems (e.g., partial relations). To achieve this, we use the semantic frameworks of predicate and property transformers, and relations with fail and unknown values. We show how to define instantaneous feedback for stateless systems and feedback with unit delay for stateful systems. Both operations preserve the refinement relation, and both can be applied to non-deterministic and non-input-receptive systems.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115345514","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: 15
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