Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science最新文献_第6页

A Generalized Modality for Recursion 递归的广义模态

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-05-28 DOI: 10.1145/3209108.3209148

Adrien Guatto

{"title":"A Generalized Modality for Recursion","authors":"Adrien Guatto","doi":"10.1145/3209108.3209148","DOIUrl":"https://doi.org/10.1145/3209108.3209148","url":null,"abstract":"Nakano's later modality allows types to express that the output of a function does not immediately depend on its input, and thus that computing its fixpoint is safe. This idea, guarded recursion, has proved useful in various contexts, from functional programming with infinite data structures to formulations of step-indexing internal to type theory. Categorical models have revealed that the later modality corresponds in essence to a simple reindexing of the discrete time scale. Unfortunately, existing guarded type theories suffer from significant limitations for programming purposes. These limitations stem from the fact that the later modality is not expressive enough to capture precise input-output dependencies of functions. As a consequence, guarded type theories reject many productive definitions. Combining insights from guarded type theories and synchronous programming languages, we propose a new modality for guarded recursion. This modality can apply any well-behaved reindexing of the time scale to a type. We call such reindexings time warps. Several modalities from the literature, including later, correspond to fixed time warps, and thus arise as special cases of ours.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125900308","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: 16

A sequent calculus with dependent types for classical arithmetic 经典算术中具有相关类型的连续演算

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-05-24 DOI: 10.1145/3209108.3209199

Étienne Miquey

{"title":"A sequent calculus with dependent types for classical arithmetic","authors":"Étienne Miquey","doi":"10.1145/3209108.3209199","DOIUrl":"https://doi.org/10.1145/3209108.3209199","url":null,"abstract":"In a recent paper [11], Herbelin developed dPAω, a calculus in which constructive proofs for the axioms of countable and dependent choices could be derived via the encoding of a proof of countable universal quantification as a stream of it components. However, the property of normalization (and therefore the one of soundness) was only conjectured. The difficulty for the proof of normalization is due to the simultaneous presence of dependent types (for the constructive part of the choice), of control operators (for classical logic), of coinductive objects (to encode functions of type N→A into streams (a0, a1, ...)) and of lazy evaluation with sharing (for these coinductive objects). Elaborating on previous works, we introduce in this paper a variant of dPAω presented as a sequent calculus. On the one hand, we take advantage of a variant of Krivine classical realizability that we developed to prove the normalization of classical call-by-need [20]. On the other hand, we benefit from dLtp, a classical sequent calculus with dependent types in which type safety is ensured by using delimited continuations together with a syntactic restriction [19]. By combining the techniques developed in these papers, we manage to define a realizability interpretation à la Krivine of our calculus that allows us to prove normalization and soundness.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127463014","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: 9

Conditional Value-at-Risk for Reachability and Mean Payoff in Markov Decision Processes 马尔可夫决策过程中可达性和平均收益的条件风险值

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-05-08 DOI: 10.1145/3209108.3209176

Jan Křetínský, Tobias Meggendorfer

引用次数: 11

Free Higher Groups in Homotopy Type Theory 同伦型论中的自由高群

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-05-05 DOI: 10.1145/3209108.3209183

Nicolai Kraus, Thorsten Altenkirch

引用次数: 9

One Theorem to Rule Them All: A Unified Translation of LTL into ω-Automata 一个支配一切的定理:LTL到ω-自动机的统一翻译

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-05-02 DOI: 10.1145/3209108.3209161

J. Esparza, Jan Křetínský, Salomon Sickert

引用次数: 31

Computable decision making on the reals and other spaces: via partiality and nondeterminism 实数和其他空间上的可计算决策:通过偏爱和不确定性

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-05-01 DOI: 10.1145/3209108.3209193

Benjamin Sherman, Luke Sciarappa, A. Chlipala, Michael Carbin

{"title":"Computable decision making on the reals and other spaces: via partiality and nondeterminism","authors":"Benjamin Sherman, Luke Sciarappa, A. Chlipala, Michael Carbin","doi":"10.1145/3209108.3209193","DOIUrl":"https://doi.org/10.1145/3209108.3209193","url":null,"abstract":"Though many safety-critical software systems use floating point to represent real-world input and output, the mathematical specifications of these systems' behaviors use real numbers. Significant deviations from those specifications can cause errors and jeopardize safety. To ensure system safety, some programming systems offer exact real arithmetic, which often enables a program's computation to match its mathematical specification exactly. However, exact real arithmetic complicates decision-making: in these systems, it is impossible to compute (total and deterministic) discrete decisions based on connected spaces such as R. We present programming-language semantics based on constructive topology with variants allowing nondeterminism and/or partiality. Either nondeterminism or partiality suffices to allow computable decision making on connected spaces such as R. We then introduce pattern matching on spaces, a language construct for creating programs on spaces, generalizing pattern matching in functional programming, where patterns need not represent decidable predicates and also may overlap or be inexhaustive, giving rise to nondeterminism or partiality, respectively. Nondeterminism and/or partiality also yield formal logics for constructing approximate decision procedures. We extended the Marshall language for exact real arithmetic with these constructs and implemented some programs with it.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130520456","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

Probabilistic Stable Functions on Discrete Cones are Power Series 离散锥上的概率稳定函数是幂级数

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-05-01 DOI: 10.1145/3209108.3209198

Raphaëlle Crubillé

引用次数: 17

A General Framework for Relational Parametricity 关系参数的一般框架

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-04-30 DOI: 10.1145/3209108.3209141

Kristina Sojakova, Patricia Johann

{"title":"A General Framework for Relational Parametricity","authors":"Kristina Sojakova, Patricia Johann","doi":"10.1145/3209108.3209141","DOIUrl":"https://doi.org/10.1145/3209108.3209141","url":null,"abstract":"Reynolds' original theory of relational parametricity was intended to capture the observation that polymorphically typed System F programs preserve all relations between inputs. But as Reynolds himself later showed, his theory can only be formulated in a metatheory with an impredicative universe, such as the Calculus of Inductive Constructions. A number of more abstract treatments of relational parametricity have since appeared; however, as we show, none of these seem to express Reynolds' original theory in a satisfactory way. To correct this, we develop an abstract framework for relational parametricity that delivers a model expressing Reynolds' theory in a direct and natural way. This framework is uniform with respect to a choice of meta-theory, which allows us to obtain the well-known PER model of Longo and Moggi as a direct instance in a natural way as well. Underlying the framework is the novel notion of a λ2-fibration with isomorphisms, which relaxes certain strictness requirements on split λ2-fibrations. Our main theorem is a generalization of Seely's classical construction of sound models of System F from split λ2-fibrations: we prove that the canonical interpretation of System F induced by every λ2-fibration with isomorphisms validates System F's entire equational theory on the nose, independently of the parameterizing meta-theory. Moreover, we offer a novel relationally parametric model of System F (after Orsanigo), which is proof-relevant in the sense that witnesses of relatedness are themselves suitably related. We show that, unlike previous frameworks for parametricity, ours recognizes this new model in a natural way. Our framework is thus descriptive, in that it accounts for well-known models, as well as prescriptive, in that it identifies abstract properties that good models of relational parametricity should satisfy and suggests new constructions of such models.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122448188","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

Stochastic Shortest Paths and Weight-Bounded Properties in Markov Decision Processes 马尔可夫决策过程中的随机最短路径和权有界性质

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-04-30 DOI: 10.1145/3209108.3209184

C. Baier, N. Bertrand, Clemens Dubslaff, Daniel Gburek, O. Sankur

引用次数: 14

Efficient Algorithms for Asymptotic Bounds on Termination Time in VASS VASS中终止时间渐近界的有效算法

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-04-29 DOI: 10.1145/3209108.3209191

T. Brázdil, K. Chatterjee, A. Kucera, Petr Novotný, Dominik Velan, Florian Zuleger

{"title":"Efficient Algorithms for Asymptotic Bounds on Termination Time in VASS","authors":"T. Brázdil, K. Chatterjee, A. Kucera, Petr Novotný, Dominik Velan, Florian Zuleger","doi":"10.1145/3209108.3209191","DOIUrl":"https://doi.org/10.1145/3209108.3209191","url":null,"abstract":"Vector Addition Systems with States (VASS) provide a well-known and fundamental model for the analysis of concurrent processes, parameterized systems, and are also used as abstract models of programs in resource bound analysis. In this paper we study the problem of obtaining asymptotic bounds on the termination time of a given VASS. In particular, we focus on the practically important case of obtaining polynomial bounds on termination time. Our main contributions are as follows: First, we present a polynomial-time algorithm for deciding whether a given VASS has a linear asymptotic complexity. We also show that if the complexity of a VASS is not linear, it is at least quadratic. Second, we classify VASS according to quantitative properties of their cycles. We show that certain singularities in these properties are the key reason for non-polynomial asymptotic complexity of VASS. In absence of singularities, we show that the asymptotic complexity is always polynomial and of the form Θ(nk), for some integer k ≤ d, where d is the dimension of the VASS. We present a polynomial-time algorithm computing the optimal k. For general VASS, the same algorithm, which is based on a complete technique for the construction of ranking functions in VASS, produces a valid lower bound, i.e., a k such that the termination complexity is Ω(nk). Our results are based on new insights into the geometry of VASS dynamics, which hold the potential for further applicability to VASS analysis.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"96 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132418660","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