{"title":"Forbidden Patterns for FO2 Alternation Over Finite and Infinite Words","authors":"Viktoria Henriksson, Manfred Kufleitner","doi":"10.1142/s0129054123440021","DOIUrl":"https://doi.org/10.1142/s0129054123440021","url":null,"abstract":"We consider two-variable first-order logic FO2 and its quantifier alternation hierarchies over both finite and infinite words. Our main results are forbidden patterns for deterministic automata (finite words) and for Carton-Michel automata (infinite words). In order to give concise patterns, we allow the use of subwords on paths in finite graphs. This concept is formalized as subword-patterns. For certain types of subword-patterns there exists a non-deterministic logspace algorithm to decide their presence or absence in a given automaton. In particular, this leads to NL algorithms for deciding the levels of the FO2 quantifier alternation hierarchies. This applies to both full and half levels, each over finite and infinite words. Moreover, we show that these problems are NL-hard and, hence, NL-complete.","PeriodicalId":192109,"journal":{"name":"Int. J. Found. Comput. Sci.","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125326884","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}
{"title":"Special Issue: 25th International Conference on Developments in Language Theory (DLT 2021) - Preface","authors":"Nelma Moreira, Rogério Reis","doi":"10.1142/s012905412302001x","DOIUrl":"https://doi.org/10.1142/s012905412302001x","url":null,"abstract":"","PeriodicalId":192109,"journal":{"name":"Int. J. Found. Comput. Sci.","volume":"601 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133466552","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}
{"title":"Transportation Problem Allowing Sending and Bringing Back","authors":"T. Asano","doi":"10.1142/s0129054122500289","DOIUrl":"https://doi.org/10.1142/s0129054122500289","url":null,"abstract":"This paper considers a transportation problem on a weighted graph. The weights specify the amounts of commodities at nodes, which are positive if the amounts are stored at nodes and negative if the amounts are needed at nodes. To meet all demands we use vehicles, one at each node, with some loading capacity to and from neighbors. In a trip using a vehicle we can send commodities from a node to a neighbor along an edge and also bring back some other commodities from the neighbor. In this paper we are interested in feasibility problem, which is to decide whether there is a single round of trips that meet all demands. We prove the feasibility problem is NP-complete even in the easiest case of a one-commodity transportation problem with unbounded capacity. We also present several different polynomial-time algorithms for other cases.","PeriodicalId":192109,"journal":{"name":"Int. J. Found. Comput. Sci.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123875164","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}
{"title":"Online and Approximate Network Construction from Bounded Connectivity Constraints","authors":"Jesper Jansson, C. Levcopoulos, A. Lingas","doi":"10.1142/s0129054122500265","DOIUrl":"https://doi.org/10.1142/s0129054122500265","url":null,"abstract":"The Network Construction problem, studied by Angluin et al., Hosoda et al., and others, asks for a minimum-cost network satisfying a set of connectivity constraints which specify subsets of the vertices in the network that have to form connected subgraphs. More formally, given a set [Formula: see text] of vertices, construction costs for all possible edges between pairs of vertices from [Formula: see text], and a sequence [Formula: see text] of connectivity constraints, the objective is to find a set [Formula: see text] of edges such that each [Formula: see text] induces a connected subgraph of the graph [Formula: see text] and the total cost of [Formula: see text] is minimized. First, we study the online version where every constraint must be satisfied immediately after its arrival and edges that have already been added can never be removed. We give an [Formula: see text]-competitive and [Formula: see text]-competitive polynomial-time algorithms, where [Formula: see text] is an upper bound on the size of constraints, while [Formula: see text] denote the number of constraints and the number of vertices, respectively. On the other hand, we observe that an [Formula: see text]-competitive lower bound as well as an [Formula: see text]-competitive lower bound in the cost-uniform case are implied by the known lower bounds for unbounded constraints. For the cost-uniform case with unbounded constraints, we provide an [Formula: see text]-competitive upper bound with high probability. The latter bound is against an oblivious adversary while our other randomized competitive bounds are against an adaptive adversary. Next, we discuss a hybrid approximation method for the (offline) Network Construction problem combining an approximation algorithm of Hosoda et al. with one of Angluin et al. and an application of the hybrid method to bioinformatics. Finally, we consider a natural strengthening of the connectivity requirements in the Network Construction problem, where each constraint has to induce a subgraph (of the constructed graph) of diameter at most [Formula: see text]. Among other things, we provide a polynomial-time [Formula: see text]-approximation algorithm for the Network Construction problem with the [Formula: see text]-diameter requirements, when each constraint has at most [Formula: see text] vertices, and show the APX-completeness of this variant.","PeriodicalId":192109,"journal":{"name":"Int. J. Found. Comput. Sci.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127885984","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}
{"title":"Fault-Tolerance of Star Graph Based on Subgraph Fault Pattern","authors":"Hong Zhang, Shuming Zhou, Baohua Niu","doi":"10.1142/s0129054122500277","DOIUrl":"https://doi.org/10.1142/s0129054122500277","url":null,"abstract":"Traditional fault tolerability is regularly measured by classical vertex or edge connectivity. Menger’s theorem shows that the number of (edge)-disjoint paths is closely related to (edge) connectivity. Clearly, disjoint paths not only provide alternative routings to tolerate faulty vertices but also avoid communication bottlenecks. Furthermore, disjoint paths can speed up the transmission time by distributing data among disjoint paths. In order to assess the fault tolerance of the network objectively, we aim to extend vertex or edge failures to substructure malfunction. In this paper, we show the maximum number of vertex (edge)-disjoint paths in star graph in the case of genetic substructure faults. Let [Formula: see text] ([Formula: see text]) be a [Formula: see text]-dimensional substar of [Formula: see text]. We show that there exist [Formula: see text] vertex (edge)-disjoint paths to connect any two vertices [Formula: see text] and [Formula: see text] in [Formula: see text], where [Formula: see text] is the degree of vertex [Formula: see text] in [Formula: see text]. In addition, we show that (edge) connectivity and [Formula: see text]-extra connectivity of [Formula: see text] are [Formula: see text], [Formula: see text], respectively.","PeriodicalId":192109,"journal":{"name":"Int. J. Found. Comput. Sci.","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116206036","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}
{"title":"Balanced-by-Construction Regular and ω-Regular Languages","authors":"L. Edixhoven, S. Jongmans","doi":"10.1142/s0129054122440026","DOIUrl":"https://doi.org/10.1142/s0129054122440026","url":null,"abstract":"Parenn is the typical generalization of the Dyck language to multiple types of parentheses. We generalize its notion of balancedness to allow parentheses of different types to freely commute. We show that balanced regular and [Formula: see text]-regular languages can be characterized by syntactic constraints on regular and [Formula: see text]-regular expressions and, using the shuffle on trajectories operator, we define grammars for balanced-by-construction expressions with which one can express every balanced regular and [Formula: see text]-regular language.","PeriodicalId":192109,"journal":{"name":"Int. J. Found. Comput. Sci.","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122142508","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}
{"title":"Strong Menger Connectivity of Folded Hypercubes with Faulty Subcube","authors":"Meijie Ma, Chaoming Guo, Xiang-Jun Li","doi":"10.1142/s0129054122500253","DOIUrl":"https://doi.org/10.1142/s0129054122500253","url":null,"abstract":"Menger-type problems in interconnection networks have received many attentions in recent years. A connected graph [Formula: see text] is strong Menger (edge) connected if there are [Formula: see text] vertex (edge)-disjoint paths joining any two distinct vertices [Formula: see text] and [Formula: see text] in [Formula: see text]. Fault tolerance is an important criterion in the design of interconnection networks. The folded hypercube [Formula: see text] is an important variant of hypercube [Formula: see text] which remains many desirable properties of hypercube. We consider the strong Menger connectivity of folded hypercubes when part of the network is faulty. We show that [Formula: see text] [Formula: see text] is strong Menger (edge) connected. Which means that when a subcube [Formula: see text] is faulty, the surviving graph [Formula: see text] is strong Menger (edge) connected. This generalizes the result of [Formula: see text] in [J. Parallel Distrib. Comput. 138 (2020) 190–198].","PeriodicalId":192109,"journal":{"name":"Int. J. Found. Comput. Sci.","volume":"250 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122914231","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}
{"title":"Tight Upper Bounds on Distinct Maximal (Sub-)Repetitions in Highly Compressible Strings","authors":"Julian Pape-Lange","doi":"10.1142/s0129054122440075","DOIUrl":"https://doi.org/10.1142/s0129054122440075","url":null,"abstract":"For [Formula: see text], maximal [Formula: see text]-repetitions ([Formula: see text]-subrepetitions) are fractional powers in strings with exponent of at least [Formula: see text] (and [Formula: see text], respectively) which are non-extendable with respect to their minimum period. In this paper, we show that in a string [Formula: see text] with string attractor [Formula: see text] there are at most [Formula: see text] distinct (unpositioned) extended maximal [Formula: see text]-repetitions. Also for any natural number [Formula: see text] the string contains at most [Formula: see text] distinct extended maximal [Formula: see text]-subrepetitions without [Formula: see text]th powers. We further prove that for fixed [Formula: see text] and [Formula: see text], both upper bounds are tight up to a constant factor.","PeriodicalId":192109,"journal":{"name":"Int. J. Found. Comput. Sci.","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114279480","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}
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