Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science最新文献_第9页

Differential Equation Axiomatization: The Impressive Power of Differential Ghosts 微分方程公理化:微分幽灵令人印象深刻的力量

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-02-05 DOI: 10.1145/3209108.3209147

André Platzer, Yong Kiam Tan

{"title":"Differential Equation Axiomatization: The Impressive Power of Differential Ghosts","authors":"André Platzer, Yong Kiam Tan","doi":"10.1145/3209108.3209147","DOIUrl":"https://doi.org/10.1145/3209108.3209147","url":null,"abstract":"We prove the completeness of an axiomatization for differential equation invariants. First, we show that the differential equation axioms in differential dynamic logic are complete for all algebraic invariants. Our proof exploits differential ghosts, which introduce additional variables that can be chosen to evolve freely along new differential equations. Cleverly chosen differential ghosts are the proof-theoretical counterpart of dark matter. They create new hypothetical state, whose relationship to the original state variables satisfies invariants that did not exist before. The reflection of these new invariants in the original system then enables its analysis. We then show that extending the axiomatization with existence and uniqueness axioms makes it complete for all local progress properties, and further extension with a real induction axiom makes it complete for all real arithmetic invariants. This yields a parsimonious axiomatization, which serves as the logical foundation for reasoning about invariants of differential equations. Moreover, our results are purely axiomatic, and so the axiomatization is suitable for sound implementation in foundational theorem provers.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"93 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130298716","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: 43

On Higher Inductive Types in Cubical Type Theory 论三次型论中的高归纳型

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-02-04 DOI: 10.1145/3209108.3209197

T. Coquand, Simon Huber, Anders Mörtberg

引用次数: 71

A van Benthem Theorem for Fuzzy Modal Logic 模糊模态逻辑的van Benthem定理

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-02-01 DOI: 10.1145/3209108.3209180

P. Wild, Lutz Schröder, D. Pattinson, B. König

引用次数: 17

Diagrammatic Reasoning beyond Clifford+T Quantum Mechanics 超越Clifford+T量子力学的图解推理

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-01-30 DOI: 10.1145/3209108.3209139

E. Jeandel, S. Perdrix, R. Vilmart

引用次数: 54

Quantitative Behavioural Reasoning for Higher-order Effectful Programs: Applicative Distances 高阶有效规划的定量行为推理:应用距离

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-01-27 DOI: 10.1145/3209108.3209149

Francesco Gavazzo

引用次数: 41

Type-two polynomial-time and restricted lookahead 二类多项式时间和受限前瞻

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-01-23 DOI: 10.1145/3209108.3209124

B. Kapron, Florian Steinberg

{"title":"Type-two polynomial-time and restricted lookahead","authors":"B. Kapron, Florian Steinberg","doi":"10.1145/3209108.3209124","DOIUrl":"https://doi.org/10.1145/3209108.3209124","url":null,"abstract":"This paper provides an alternate characterization of second-order polynomial-time computability, with the goal of making second-order complexity theory more approachable. We rely on the usual oracle machines to model programs with subroutine calls. In contrast to previous results, the use of higher-order objects as running times is avoided, either explicitly or implicitly. Instead, regular polynomials are used. This is achieved by refining the notion of oracle-poly-time computability introduced by Cook. We impose a further restriction on oracle interactions to force feasibility. Both the restriction and its purpose are very simple: it is well-known that Cook's model allows polynomial depth iteration of functional inputs with no restrictions on size, and thus does not preserve poly-time computability. To mend this we restrict the number of lookahead revisions, that is the number of times a query whose size exceeds that of any previous query may be asked. We prove that this leads to a class of feasible functionals and that all feasible problems can be solved within this class if one is allowed to separate a task into efficiently solvable subtasks. Formally, the closure of our class under lambda-abstraction and application are the basic feasible functionals. We also revisit the very similar class of strongly poly-time computable operators previously introduced by Kawamura and Steinberg. We prove it to be strictly included in our class and, somewhat surprisingly, to have the same closure property. This is due to the nature of the limited recursion operator: it is not strongly poly-time but decomposes into two such operations and lies in our class.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125333257","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

Work Analysis with Resource-Aware Session Types 具有资源感知会话类型的工作分析

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2017-12-22 DOI: 10.1145/3209108.3209146

Ankush Das, Jan Hoffmann, F. Pfenning

{"title":"Work Analysis with Resource-Aware Session Types","authors":"Ankush Das, Jan Hoffmann, F. Pfenning","doi":"10.1145/3209108.3209146","DOIUrl":"https://doi.org/10.1145/3209108.3209146","url":null,"abstract":"While there exist several successful techniques for supporting programmers in deriving static resource bounds for sequential code, analyzing the resource usage of message-passing concurrent processes poses additional challenges. To meet these challenges, this article presents an analysis for statically deriving worst-case bounds on the total work performed by message-passing processes. To decompose interacting processes into components that can be analyzed in isolation, the analysis is based on novel resource-aware session types, which describe protocols and resource contracts for inter-process communication. A key innovation is that both messages and processes carry potential to share and amortize cost while communicating. To symbolically express resource usage in a setting without static data structures and intrinsic sizes, resource contracts describe bounds that are functions of interactions between processes. Resource-aware session types combine standard binary session types and type-based amortized resource analysis in a linear type system. This type system is formulated for a core session-type calculus of the language SILL and proved sound with respect to a multiset-based operational cost semantics that tracks the total number of messages that are exchanged in a system. The effectiveness of the analysis is demonstrated by analyzing standard examples from amortized analysis and the literature on session types and by a comparative performance analysis of different concurrent programs implementing the same interface.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123695953","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

What's in a game?: A theory of game models 游戏里有什么?:游戏模型的理论

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2017-11-29 DOI: 10.1145/3209108.3209114

Clovis Eberhart, Tom Hirschowitz

引用次数: 6

Satisfiability in multi-valued circuits 多值电路的可满足性

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2017-10-23 DOI: 10.1145/3209108.3209173

P. Idziak, Jacek Krzaczkowski

{"title":"Satisfiability in multi-valued circuits","authors":"P. Idziak, Jacek Krzaczkowski","doi":"10.1145/3209108.3209173","DOIUrl":"https://doi.org/10.1145/3209108.3209173","url":null,"abstract":"Satisfiability of Boolean circuits is among the most known and important problems in theoretical computer science. This problem is NP-complete in general but becomes polynomial time when restricted either to monotone gates or linear gates. We go outside Boolean realm and consider circuits built of any fixed set of gates on an arbitrary large finite domain. From the complexity point of view this is strictly connected with the problems of solving equations (or systems of equations) over finite algebras. The research reported in this work was motivated by a desire to know for which finite algebras A there is a polynomial time algorithm that decides if an equation over A has a solution. We are also looking for polynomial time algorithms that decide if two circuits over a finite algebra compute the same function. Although we have not managed to solve these problems in the most general setting we have obtained such a characterization for a very broad class of algebras from congruence modular varieties. This class includes most known and well-studied algebras such as groups, rings, modules (and their generalizations like quasigroups, loops, near-rings, nonassociative rings, Lie algebras), lattices (and their extensions like Boolean algebras, Heyting algebras or other algebras connected with multi-valued logics including MV-algebras). This paper seems to be the first systematic study of the computational complexity of satisfiability of non-Boolean circuits and solving equations over finite algebras. Our characterization is given in terms of nice structural properties of algebras for which the problems are solvable in polynomial time. Such algebras have to decompose into two factors: a nilpotent one and a factor that essentially behaves as a finite distributive lattice.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128621697","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

Concurrency and Probability: Removing Confusion, Compositionally 并发性和概率:消除混淆，组合

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2017-10-12 DOI: 10.1145/3209108.3209202

R. Bruni, Hernán C. Melgratti, U. Montanari

{"title":"Concurrency and Probability: Removing Confusion, Compositionally","authors":"R. Bruni, Hernán C. Melgratti, U. Montanari","doi":"10.1145/3209108.3209202","DOIUrl":"https://doi.org/10.1145/3209108.3209202","url":null,"abstract":"Assigning a satisfactory truly concurrent semantics to Petri nets with confusion and distributed decisions is a long standing problem, especially if one wants to resolve decisions by drawing from some probability distribution. Here we propose a general solution based on a recursive, static decomposition of (occurrence) nets in loci of decision, called structural branching cells (s-cells). Each s-cell exposes a set of alternatives, called transactions. Our solution transforms a given Petri net into another net whose transitions are the transactions of the s-cells and whose places are those of the original net, with some auxiliary structure for bookkeeping. The resulting net is confusion-free, and thus conflicting alternatives can be equipped with probabilistic choices, while nonintersecting alternatives are purely concurrent and their probability distributions are independent. The validity of the construction is witnessed by a tight correspondence with the recursively stopped configurations of Abbes and Benveniste. Some advantages of our approach are that: i) s-cells are defined statically and locally in a compositional way; ii) our resulting nets faithfully account for concurrency.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123053884","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