Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science最新文献_第2页

Reasoning on Data Words over Numeric Domains 数字域上数据词的推理

Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2022-08-02 DOI: 10.1145/3531130.3533354

Diego Figueira, A. Lin

引用次数: 4

A Functorial Excursion Between Algebraic Geometry and Linear Logic 代数几何与线性逻辑之间的函数偏移

Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2022-08-02 DOI: 10.1145/3531130.3532488

Paul-André Melliès

引用次数: 2

On the Skolem Problem and the Skolem Conjecture 论Skolem问题和Skolem猜想

Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2022-08-02 DOI: 10.1145/3531130.3533328

R. Lipton, F. Luca, Joris Nieuwveld, J. Ouaknine, David Purser, J. Worrell

{"title":"On the Skolem Problem and the Skolem Conjecture","authors":"R. Lipton, F. Luca, Joris Nieuwveld, J. Ouaknine, David Purser, J. Worrell","doi":"10.1145/3531130.3533328","DOIUrl":"https://doi.org/10.1145/3531130.3533328","url":null,"abstract":"It is a longstanding open problem whether there is an algorithm to decide the Skolem Problem for linear recurrence sequences (LRS) over the integers, namely whether a given such sequence has a zero term (i.e., whether un = 0 for some n). A major breakthrough in the early 1980s established decidability for LRS of order 4 or less, i.e., for LRS in which every new term depends linearly on the previous four (or fewer) terms. The Skolem Problem for LRS of order 5 or more, in particular, remains a major open challenge to this day. Our main contributions in this paper are as follows: First, we show that the Skolem Problem is decidable for reversible LRS of order 7 or less. (An integer LRS is reversible if its unique extension to a bi-infinite LRS also takes exclusively integer values; a typical example is the classical Fibonacci sequence, whose bi-infinite extension is ⟨…, 5, −3, 2, −1, 1, 0, 1, 1, 2, 3, 5, …⟩.) Second, assuming the Skolem Conjecture (a central hypothesis in Diophantine analysis, also known as the Exponential Local-Global Principle), we show that the Skolem Problem for LRS of order 5 is decidable, and exhibit a concrete procedure for solving it.","PeriodicalId":373589,"journal":{"name":"Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124945018","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

Logical Foundations of Quantitative Equality 数量相等的逻辑基础

Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2022-08-02 DOI: 10.1145/3531130.3533337

Francesco Dagnino, Fabio Pasquali

引用次数: 6

Transducers of polynomial growth 多项式生长的传感器

Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2022-08-02 DOI: 10.1145/3531130.3533326

M. Bojanczyk

引用次数: 12

On Almost-Uniform Generation of SAT Solutions: The power of 3-wise independent hashing 关于SAT解的几乎一致的生成:3-wise独立哈希的力量

Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2022-08-02 DOI: 10.1145/3531130.3533338

Remi Delannoy, Kuldeep S. Meel

{"title":"On Almost-Uniform Generation of SAT Solutions: The power of 3-wise independent hashing","authors":"Remi Delannoy, Kuldeep S. Meel","doi":"10.1145/3531130.3533338","DOIUrl":"https://doi.org/10.1145/3531130.3533338","url":null,"abstract":"Given a Boolean formula φ and a distribution parameter ε, the problem of almost-uniform generation seeks to design a randomized generator such that every solution of φ is output with probability within (1 + ε)-factor of where sol(φ) is the set of all the solutions of φ. The prior state of the art scheme due to Jerrum, Valiant, and Vazirani, makes calls to a SAT oracle and employs 2 − wise independent hash functions. In this work, we design a new randomized algorithm that makes calls to a SAT oracle and employs 3 − wise independent hash functions. The widely used 2 − wise independent hashing is tabulation hashing proposed by Carter and Wegman. Since this classical scheme is also 3 − wise independent, we observe that practical implementation of our technique does not incur additional overhead. We demonstrate that theoretical improvements translate to practice; in particular, we conduct a comprehensive study over 562 benchmarks and demonstrate that while JVV would time out for 544 out of 562 instances, our proposed scheme can handle all the 562 instances. To the best of our knowledge, this is the first almost-uniform generation scheme that can handle practical instances from real-world applications. We also present a nuanced analysis focusing on the both the size of SAT queries as well as the number of queries.","PeriodicalId":373589,"journal":{"name":"Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116849341","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

Resource approximation for the λμ-calculus λμ微积分的资源近似

Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2022-08-02 DOI: 10.1145/3531130.3532469

Davide Barbarossa

引用次数: 1

A direct computational interpretation of second-order arithmetic via update recursion 通过更新递归的二阶算法的直接计算解释

Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2022-08-02 DOI: 10.1145/3531130.3532458

Valentin Blot

引用次数: 1

Geometric decision procedures and the VC dimension of linear arithmetic theories 几何决策程序和VC维的线性算术理论

Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2022-08-02 DOI: 10.1145/3531130.3533372

D. Chistikov, C. Haase, Alessio Mansutti

{"title":"Geometric decision procedures and the VC dimension of linear arithmetic theories","authors":"D. Chistikov, C. Haase, Alessio Mansutti","doi":"10.1145/3531130.3533372","DOIUrl":"https://doi.org/10.1145/3531130.3533372","url":null,"abstract":"This paper resolves two open problems on linear integer arithmetic (LIA), also known as Presburger arithmetic. First, we give a triply exponential geometric decision procedure for LIA, i.e., a procedure based on manipulating semilinear sets. This matches the running time of the best quantifier elimination and automata-based procedures. Second, building upon our first result, we give a doubly exponential upper bound on the Vapnik–Chervonenkis (VC) dimension of sets definable in LIA, proving a conjecture of D. Nguyen and I. Pak [Combinatorica 39, pp. 923–932, 2019]. These results partially rely on an analysis of sets definable in linear real arithmetic (LRA), and analogous results for LRA are also obtained. At the core of these developments are new decomposition results for semilinear and -semilinear sets, the latter being the sets definable in LRA. These results yield new algorithms to compute the complement of (-)semilinear sets that do not cause a non-elementary blowup when repeatedly combined with procedures for other Boolean operations and projection. The existence of such an algorithm for semilinear sets has been a long-standing open problem.","PeriodicalId":373589,"journal":{"name":"Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"244 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128999465","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: 3

Milner’s Proof System for Regular Expressions Modulo Bisimilarity is Complete: Crystallization: Near-Collapsing Process Graph Interpretations of Regular Expressions 正则表达式模双相似的Milner证明系统是完备的:结晶:正则表达式的近坍缩过程图解释

Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2022-08-02 DOI: 10.1145/3531130.3532430

C. Grabmayer

{"title":"Milner’s Proof System for Regular Expressions Modulo Bisimilarity is Complete: Crystallization: Near-Collapsing Process Graph Interpretations of Regular Expressions","authors":"C. Grabmayer","doi":"10.1145/3531130.3532430","DOIUrl":"https://doi.org/10.1145/3531130.3532430","url":null,"abstract":"Milner (1984) defined a process semantics for regular expressions. He formulated a sound proof system for bisimilarity of process interpretations of regular expressions, and asked whether this system is complete. We report conceptually on a proof that shows that Milner’s system is complete, by motivating and describing all of its main steps. We substantially refine the completeness proof by Grabmayer and Fokkink (2020) for the restriction of Milner’s system to ‘1-free’ regular expressions. As a crucial complication we recognize that process graphs with empty-step transitions that satisfy the layered loop-existence/elimination property LLEE are not closed under bisimulation collapse (unlike process graphs with LLEE that only have proper-step transitions). We circumnavigate this obstacle by defining a LLEE-preserving ‘crystallization procedure’ for such process graphs. By that we obtain ‘near-collapsed’ process graphs with LLEE whose strongly connected components are either collapsed or of ‘twin-crystal’ shape. Such near-collapsed process graphs guarantee provable solutions for bisimulation collapses of process interpretations of regular expressions.","PeriodicalId":373589,"journal":{"name":"Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132358130","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