Pub Date : 2023-02-22DOI: 10.1142/s0129054123440021
Viktoria Henriksson, Manfred Kufleitner
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.
{"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}
Pub Date : 2023-02-22DOI: 10.1142/s012905412302001x
Nelma Moreira, Rogério Reis
{"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}
Pub Date : 2023-01-19DOI: 10.1142/s0129054122500289
T. Asano
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.
{"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}
Pub Date : 2023-01-06DOI: 10.1142/s0129054122500265
Jesper Jansson, C. Levcopoulos, A. Lingas
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.
Angluin等人、Hosoda等人研究的网络构造问题(Network Construction problem)要求一个最小代价的网络满足一组连接约束，这些连接约束规定了网络中必须形成连通子图的顶点子集。更正式地说，给定一组[公式:见文]的顶点，在[公式:见文]的顶点对之间的所有可能的边的构建成本，以及连接约束的序列[公式:见文]，目标是找到一组[公式:见文]的边，这样每个[公式:见文]都能引出图[公式:见文]的连通子图，并且[公式:见文]的总成本最小。首先，我们研究了在线版本，其中每个约束必须在到达后立即得到满足，并且已经添加的边永远不能删除。我们给出了[公式:见文]-竞争和[公式:见文]-竞争多项式时间算法，其中[公式:见文]是约束大小的上界，而[公式:见文]分别表示约束的数量和顶点的数量。另一方面，我们观察到[公式:见文]竞争下界和[公式:见文]成本均匀情况下的竞争下界是由无界约束的已知下界隐含的。对于具有无界约束的成本一致情况，我们提供了一个[公式:见文本]-高概率竞争上界。后一个界限是针对无意识对手的，而另一个随机竞争界限是针对适应性对手的。接下来，我们将Hosoda等人的近似算法与Angluin等人的近似算法相结合，讨论了(离线)网络构建问题的混合近似方法，以及该混合方法在生物信息学中的应用。最后，我们考虑网络构造问题中连通性要求的自然强化，其中每个约束必须诱导(构造图的)最大直径的子图[公式:见文本]。在其他方面，我们提供了一个多项式时间[公式:见文本]的网络建设问题的近似算法[公式:见文本]-直径要求，当每个约束有最多[公式:见文本]顶点时，并显示了这种变体的apx -完备性。
{"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}
Pub Date : 2023-01-04DOI: 10.1142/s0129054122500277
Hong Zhang, Shuming Zhou, Baohua Niu
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.
{"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}
Pub Date : 2022-11-22DOI: 10.1142/s0129054122440026
L. Edixhoven, S. Jongmans
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.
{"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}
Pub Date : 2022-11-22DOI: 10.1142/s0129054122500253
Meijie Ma, Chaoming Guo, Xiang-Jun Li
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].
互联网络中的menger型问题近年来受到广泛关注。一个连通图[公式:见文]是强门格尔(边)连通的，如果在[公式:见文]中存在[公式:见文]顶点(边)不相交的路径连接任意两个不同的顶点[公式:见文]和[公式:见文]。容错性是互连网络设计的一个重要标准。折叠超立方体[公式:见文]是超立方体[公式:见文]的一个重要变体，它保留了超立方体的许多理想性质。我们考虑了当网络部分故障时折叠超立方体的强门格连通性。我们证明了[Formula: see text] [Formula: see text]是强门格尔(edge)连通的。这意味着当一个子立方体[公式:见文]有缺陷时，幸存的图[公式:见文]是强门格尔(边)连通的。这推广了[J]中的[公式:见文本]的结果。Distrib平行。计算机学报，138(2020):190-198。
{"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}
Pub Date : 2022-11-22DOI: 10.1142/s0129054122440075
Julian Pape-Lange
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.
{"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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