International Journal of Foundations of Computer Science最新文献_第2页

Synthesizing Computable Functions from Rational Specifications Over Infinite Words 从无限字上的有理规范合成可计算函数

4区计算机科学

International Journal of Foundations of Computer Science Pub Date : 2023-11-15 DOI: 10.1142/s012905412348009x

Emmanuel Filiot, Sarah Winter

{"title":"Synthesizing Computable Functions from Rational Specifications Over Infinite Words","authors":"Emmanuel Filiot, Sarah Winter","doi":"10.1142/s012905412348009x","DOIUrl":"https://doi.org/10.1142/s012905412348009x","url":null,"abstract":"The synthesis problem asks to automatically generate, if it exists, an algorithm from a specification of correct input-output pairs. In this paper, we consider the synthesis of computable functions of infinite words, for a classical Turing computability notion over infinite inputs. We consider specifications which are rational relations of infinite words, i.e., specifications defined by non-deterministic parity transducers. We prove that the synthesis problem of computable functions from rational specifications is undecidable. We provide an incomplete but sound reduction to some parity game, such that if Eve wins the game, then the rational specification is realizable by a computable function. We prove that this function is even computable by a deterministic two-way transducer. We provide a sufficient condition under which the latter game reduction is complete. This entails the decidability of the synthesis problem of computable functions, which we proved to be ExpTime-complete, for a large subclass of rational specifications, namely deterministic rational specifications. This subclass contains the class of automatic relations over infinite words, a yardstick in reactive synthesis.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":"10 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136227556","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Rainbow Domination in Cartesian Product of Paths and Cycles 路径与循环笛卡尔积中的彩虹支配

4区计算机科学

International Journal of Foundations of Computer Science Pub Date : 2023-11-11 DOI: 10.1142/s0129054123500272

Hong Gao, Yunlei Zhang, Yuqi Wang, Yuanyuan Guo, Xing Liu, Renbang Liu, Changqing Xi, Yuansheng Yang

{"title":"Rainbow Domination in Cartesian Product of Paths and Cycles","authors":"Hong Gao, Yunlei Zhang, Yuqi Wang, Yuanyuan Guo, Xing Liu, Renbang Liu, Changqing Xi, Yuansheng Yang","doi":"10.1142/s0129054123500272","DOIUrl":"https://doi.org/10.1142/s0129054123500272","url":null,"abstract":"Let [Formula: see text] be a graph and [Formula: see text] be an integer representing [Formula: see text] colors. There is a function [Formula: see text] from [Formula: see text] to the power set of [Formula: see text] colors satisfying every vertex [Formula: see text] assigned [Formula: see text] under [Formula: see text] in its neighborhood has all the colors, then [Formula: see text] is called a [Formula: see text]-rainbow dominating function ([Formula: see text]RDF) on [Formula: see text]. The weight of [Formula: see text] is the sum of the number of colors on each vertex all over the graph. The [Formula: see text]-rainbow domination number of [Formula: see text] is the minimum weight of [Formula: see text]RDFs on [Formula: see text], denoted by [Formula: see text]. The aim of this paper is to investigate the [Formula: see text]-rainbow ([Formula: see text]) domination number of the Cartesian product of paths [Formula: see text] and the Cartesian product of paths and cycles [Formula: see text]. For [Formula: see text], we determine the value [Formula: see text] and present [Formula: see text] for [Formula: see text]. For [Formula: see text], we determine the values of [Formula: see text] for [Formula: see text] or [Formula: see text] and [Formula: see text] for [Formula: see text] or [Formula: see text].","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":"19 15","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135087194","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Quantum and Approximation Algorithms for Maximum Witnesses of Boolean Matrix Products 布尔矩阵乘积最大见证的量子和近似算法

4区计算机科学

International Journal of Foundations of Computer Science Pub Date : 2023-11-10 DOI: 10.1142/s0129054123500259

Mirosław Kowaluk, Andrzej Lingas

{"title":"Quantum and Approximation Algorithms for Maximum Witnesses of Boolean Matrix Products","authors":"Mirosław Kowaluk, Andrzej Lingas","doi":"10.1142/s0129054123500259","DOIUrl":"https://doi.org/10.1142/s0129054123500259","url":null,"abstract":"The problem of finding maximum (or minimum) witnesses of the Boolean product of two Boolean matrices (MW for short) has a number of important applications, in particular the all-pairs lowest common ancestor (LCA) problem in directed acyclic graphs (dags). The best known upper time-bound on the MW problem for [Formula: see text] Boolean matrices of the form [Formula: see text] has not been substantially improved since 2006. In order to obtain faster algorithms for this problem, we study quantum algorithms for MW and approximation algorithms for MW (in the classical computational model). Some of our quantum algorithms are input or output sensitive. Our fastest quantum algorithm for the MW problem, and consequently for the related problems, runs in time [Formula: see text], where [Formula: see text] satisfies the equation [Formula: see text] and [Formula: see text] is the exponent of the multiplication of an [Formula: see text] matrix by an [Formula: see text] matrix. Next, we consider a relaxed version of the MW problem (in the classical model) asking for reporting a witness of bounded rank (the maximum witness has rank 1) for each non-zero entry of the matrix product. First, by adapting the fastest known algorithm for maximum witnesses, we obtain an algorithm for the relaxed problem that reports for each non-zero entry of the product matrix a witness of rank at most [Formula: see text] in time [Formula: see text] Then, by reducing the relaxed problem to the so called [Formula: see text]-witness problem, we provide an algorithm that reports for each non-zero entry [Formula: see text] of the product matrix [Formula: see text] a witness of rank [Formula: see text], where [Formula: see text] is the number of witnesses for [Formula: see text], with high probability. The algorithm runs in [Formula: see text] time, where [Formula: see text].","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":"85 21","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135087720","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

State Complexity of Permutation and the Language Inclusion Problem up to Parikh Equivalence on Alphabetical Pattern Constraints and Partially Ordered NFAs 字母模式约束和部分有序NFAs上的排列状态复杂度和Parikh等价的语言包含问题

4区计算机科学

International Journal of Foundations of Computer Science Pub Date : 2023-11-01 DOI: 10.1142/s0129054123430025

Stefan Hoffmann

{"title":"State Complexity of Permutation and the Language Inclusion Problem up to Parikh Equivalence on Alphabetical Pattern Constraints and Partially Ordered NFAs","authors":"Stefan Hoffmann","doi":"10.1142/s0129054123430025","DOIUrl":"https://doi.org/10.1142/s0129054123430025","url":null,"abstract":"We investigate the state complexity of the permutation operation, or the commutative closure, on Alphabetical Pattern Constraints (APCs). This class corresponds to level [Formula: see text] of the Straubing-Thérien hierarchy and includes the finite, the piecewise testable, or [Formula: see text]-trivial, and the [Formula: see text]-trivial and [Formula: see text]-trivial languages. We give a sharp state complexity bound expressed in terms of the longest strings in the unary projection languages of an associated finite language. Additionally, for a subclass, we give sharp bounds expressed in terms of the size of a recognizing input automaton and the size of the alphabet. We also state a related state complexity bound for the commutative closure on finite languages. Lastly, we investigate the language inclusion, equivalence and universality problems on APCs up to permutational, or Parikh, equivalence. These problems are known to be [Formula: see text]-complete on APCs in general, even for fixed alphabets. We show them to be decidable in polynomial time for fixed alphabets if we only want to solve them up to Parikh equivalence. We also correct a mistake from the conference version in a bound on the size of recognizing automata for the commutative closure.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":"227 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135371911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Total 2-Rainbow Domination in Graphs: Complexity and Algorithms 图中的总2-彩虹支配:复杂性和算法

4区计算机科学

International Journal of Foundations of Computer Science Pub Date : 2023-10-28 DOI: 10.1142/s0129054123500260

Manjay Kumar, P. Venkata Subba Reddy

{"title":"Total 2-Rainbow Domination in Graphs: Complexity and Algorithms","authors":"Manjay Kumar, P. Venkata Subba Reddy","doi":"10.1142/s0129054123500260","DOIUrl":"https://doi.org/10.1142/s0129054123500260","url":null,"abstract":"For a simple, undirected graph [Formula: see text] without isolated vertices, a function [Formula: see text] which satisfies the following two conditions is called a total 2-rainbow dominating function (T2RDF) of [Formula: see text]. (i) For all [Formula: see text], if [Formula: see text] then [Formula: see text] and (ii) Every [Formula: see text] with [Formula: see text] is adjacent to a vertex [Formula: see text] with [Formula: see text]. The weight of a T2RDF [Formula: see text] of [Formula: see text] is the value [Formula: see text]. The total 2-rainbow domination number is the minimum weight of a T2RDF on [Formula: see text] and is denoted by [Formula: see text]. The minimum total 2-rainbow domination problem (MT2RDP) is to find a T2RDF of minimum weight in the input graph. In this article, we show that the problem of deciding if [Formula: see text] has a T2RDF of weight at most [Formula: see text] for star convex bipartite graphs, comb convex bipartite graphs, split graphs and planar graphs is NP-complete. On the positive side, we show that MT2RDP is linear time solvable for threshold graphs, chain graphs and bounded tree-width graphs. On the approximation point of view, we show that MT2RDP cannot be approximated within [Formula: see text] for any [Formula: see text] unless [Formula: see text] and also propose [Formula: see text]-approximation algorithm for it. Further, we show that MT2RDP is APX-complete for graphs with maximum degree 4. Next, it is shown that domination problem and the total 2-rainbow domination problems are not equivalent in computational complexity aspects. Finally, an integer linear programming formulation for MT2RDP is presented.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":"10 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136232567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Algorithmic Aspects of Total Vertex-Edge Domination in Graphs 图中总顶点-边缘支配的算法方面

4区计算机科学

International Journal of Foundations of Computer Science Pub Date : 2023-10-19 DOI: 10.1142/s0129054123500247

H. Naresh Kumar, Mustapha Chellali, Y. B. Venkatakrishnan

引用次数: 0

Connectivity Status of Intuitionistic Fuzzy Graphs and Its Applications 直觉模糊图的连通性状态及其应用

4区计算机科学

International Journal of Foundations of Computer Science Pub Date : 2023-10-19 DOI: 10.1142/s0129054123500223

Zengtai Gong, Lele He

引用次数: 0

Relating Various Types of Distributed Reaction Systems 有关各种类型的分布式反应系统

4区计算机科学

International Journal of Foundations of Computer Science Pub Date : 2023-10-18 DOI: 10.1142/s0129054123470044

Bogdan Aman

引用次数: 0

Binary Generalized PCP for Two Periodic Morphisms is Decidable in Polynomial Time 两个周期态射的二元广义PCP在多项式时间内是可判定的

4区计算机科学

International Journal of Foundations of Computer Science Pub Date : 2023-10-16 DOI: 10.1142/s0129054123480076

Vesa Halava, Štěpán Holub

引用次数: 0

Optimal Embedded and Enclosing Isosceles Triangles 最佳嵌入和包围等腰三角形

4区计算机科学

International Journal of Foundations of Computer Science Pub Date : 2023-10-05 DOI: 10.1142/s012905412342008x

Áron Ambrus, Mónika Csikós, Gergely Kiss, János Pach, Gábor Somlai

引用次数: 0