Pub Date : 2021-05-25DOI: 10.1142/S0129054121500374
Hongbin Zhuang, Wenzhong Guo, Xiaoyan Li, Ximeng Liu, Cheng-Kuan Lin
The processor failures in a multiprocessor system have a negative impact on its distributed computing efficiency. Because of the rapid expansion of multiprocessor systems, the importance of fault diagnosis is becoming increasingly prominent. The [Formula: see text]-component diagnosability of [Formula: see text], denoted by [Formula: see text], is the maximum number of nodes of the faulty set [Formula: see text] that is correctly identified in a system, and the number of components in [Formula: see text] is at least [Formula: see text]. In this paper, we determine the [Formula: see text]-component diagnosability of general networks under the PMC model and MM[Formula: see text] model. As applications, the component diagnosability is explored for some well-known networks, including complete cubic networks, hierarchical cubic networks, generalized exchanged hypercubes, dual-cube-like networks, hierarchical hypercubes, Cayley graphs generated by transposition trees (except star graphs), and DQcube as well. Furthermore, we provide some comparison results between the component diagnosability and other fault diagnosabilities.
{"title":"The Component Diagnosability of General Networks","authors":"Hongbin Zhuang, Wenzhong Guo, Xiaoyan Li, Ximeng Liu, Cheng-Kuan Lin","doi":"10.1142/S0129054121500374","DOIUrl":"https://doi.org/10.1142/S0129054121500374","url":null,"abstract":"The processor failures in a multiprocessor system have a negative impact on its distributed computing efficiency. Because of the rapid expansion of multiprocessor systems, the importance of fault diagnosis is becoming increasingly prominent. The [Formula: see text]-component diagnosability of [Formula: see text], denoted by [Formula: see text], is the maximum number of nodes of the faulty set [Formula: see text] that is correctly identified in a system, and the number of components in [Formula: see text] is at least [Formula: see text]. In this paper, we determine the [Formula: see text]-component diagnosability of general networks under the PMC model and MM[Formula: see text] model. As applications, the component diagnosability is explored for some well-known networks, including complete cubic networks, hierarchical cubic networks, generalized exchanged hypercubes, dual-cube-like networks, hierarchical hypercubes, Cayley graphs generated by transposition trees (except star graphs), and DQcube as well. Furthermore, we provide some comparison results between the component diagnosability and other fault diagnosabilities.","PeriodicalId":192109,"journal":{"name":"Int. J. Found. Comput. Sci.","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116746601","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 : 2021-05-24DOI: 10.1142/S0129054121500258
Mengyu Cao, Tongtong Ding, Min Xu
In this paper, we present a new interconnection topology, called the[Formula: see text]-modified-bubble-sort graph, which is a generalization of the modified-bubble-sort graph. Additionally, we show many of its properties, such as its hierarchical structure, vertex transitivity, connectivity, edge-connectivity, super connectivity and super edge-connectivity. The [Formula: see text]-modified-bubble-sort graph presents more flexibility than the modified-bubble-sort graph in terms of its major design properties.
{"title":"The (n, k)-Modified-Bubble-Sort Graph: A Generalized Modified-Bubble-Sort Graph","authors":"Mengyu Cao, Tongtong Ding, Min Xu","doi":"10.1142/S0129054121500258","DOIUrl":"https://doi.org/10.1142/S0129054121500258","url":null,"abstract":"In this paper, we present a new interconnection topology, called the[Formula: see text]-modified-bubble-sort graph, which is a generalization of the modified-bubble-sort graph. Additionally, we show many of its properties, such as its hierarchical structure, vertex transitivity, connectivity, edge-connectivity, super connectivity and super edge-connectivity. The [Formula: see text]-modified-bubble-sort graph presents more flexibility than the modified-bubble-sort graph in terms of its major design properties.","PeriodicalId":192109,"journal":{"name":"Int. J. Found. Comput. Sci.","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115918354","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 : 2021-05-07DOI: 10.1142/S012905412142003X
Johan Kopra
We consider the range of possible dynamics of cellular automata (CA) on two-sided beta-shifts [Formula: see text] and its relation to direct topological factorizations. We show that any reversible CA [Formula: see text] has an almost equicontinuous direction whenever [Formula: see text] is not sofic. This has the corollary that non-sofic beta-shifts are topologically direct prime, i.e. they are not conjugate to direct topological factorizations [Formula: see text] of two nontrivial subshifts [Formula: see text] and [Formula: see text]. We also give a simple criterion to determine whether [Formula: see text] is conjugate to [Formula: see text] for a given integer [Formula: see text] and a given real [Formula: see text] when [Formula: see text] is a subshift of finite type. When [Formula: see text] is strictly sofic, we show that such a conjugacy is not possible at least when [Formula: see text] is a quadratic Pisot number of degree [Formula: see text]. We conclude by using direct factorizations to give a new proof for the classification of reversible multiplication automata on beta-shifts with integral base and ask whether nontrivial multiplication automata exist when the base is not an integer.
{"title":"On the Interplay of Direct Topological Factorizations and Cellular Automata Dynamics on Beta-Shifts","authors":"Johan Kopra","doi":"10.1142/S012905412142003X","DOIUrl":"https://doi.org/10.1142/S012905412142003X","url":null,"abstract":"We consider the range of possible dynamics of cellular automata (CA) on two-sided beta-shifts [Formula: see text] and its relation to direct topological factorizations. We show that any reversible CA [Formula: see text] has an almost equicontinuous direction whenever [Formula: see text] is not sofic. This has the corollary that non-sofic beta-shifts are topologically direct prime, i.e. they are not conjugate to direct topological factorizations [Formula: see text] of two nontrivial subshifts [Formula: see text] and [Formula: see text]. We also give a simple criterion to determine whether [Formula: see text] is conjugate to [Formula: see text] for a given integer [Formula: see text] and a given real [Formula: see text] when [Formula: see text] is a subshift of finite type. When [Formula: see text] is strictly sofic, we show that such a conjugacy is not possible at least when [Formula: see text] is a quadratic Pisot number of degree [Formula: see text]. We conclude by using direct factorizations to give a new proof for the classification of reversible multiplication automata on beta-shifts with integral base and ask whether nontrivial multiplication automata exist when the base is not an integer.","PeriodicalId":192109,"journal":{"name":"Int. J. Found. Comput. Sci.","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130484803","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 : 2021-04-23DOI: 10.1142/S0129054121410082
S. Fazekas, Hwee Kim, Ryuichi Matsuoka, R. Morita, S. Seki
Oritatami is a computational model of RNA cotranscriptional folding, in which an RNA transcript is folding upon itself while being synthesized from its template DNA. This model is known to be Turin...
{"title":"Linear Bounds on the Size of Conformations in Greedy Deterministic Oritatami","authors":"S. Fazekas, Hwee Kim, Ryuichi Matsuoka, R. Morita, S. Seki","doi":"10.1142/S0129054121410082","DOIUrl":"https://doi.org/10.1142/S0129054121410082","url":null,"abstract":"Oritatami is a computational model of RNA cotranscriptional folding, in which an RNA transcript is folding upon itself while being synthesized from its template DNA. This model is known to be Turin...","PeriodicalId":192109,"journal":{"name":"Int. J. Found. Comput. Sci.","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123101281","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 : 2021-04-23DOI: 10.1142/S0129054121410070
B. Nagy
Union-free expressions are regular expressions without using the union operation. Consequently, (nondeterministic) union-free languages are described by regular expressions using only concatenation...
{"title":"Union-Freeness Revisited - Between Deterministic and Nondeterministic Union-Free Languages","authors":"B. Nagy","doi":"10.1142/S0129054121410070","DOIUrl":"https://doi.org/10.1142/S0129054121410070","url":null,"abstract":"Union-free expressions are regular expressions without using the union operation. Consequently, (nondeterministic) union-free languages are described by regular expressions using only concatenation...","PeriodicalId":192109,"journal":{"name":"Int. J. Found. Comput. Sci.","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129700832","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 : 2021-03-16DOI: 10.1142/S0129054121500222
Albert Guan
Computationally lightweight and unconditionally secure key agreement protocols are very useful for secure communication in public networks. Recently, Guan et al. proposed a key agreement protocol w...
{"title":"A Lightweight Key Agreement Protocol with Authentication Capability","authors":"Albert Guan","doi":"10.1142/S0129054121500222","DOIUrl":"https://doi.org/10.1142/S0129054121500222","url":null,"abstract":"Computationally lightweight and unconditionally secure key agreement protocols are very useful for secure communication in public networks. Recently, Guan et al. proposed a key agreement protocol w...","PeriodicalId":192109,"journal":{"name":"Int. J. Found. Comput. Sci.","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122725938","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 : 2021-03-01DOI: 10.1142/s0129054122500046
Hongyu Zhou, Xinmin Hou
Given a simple undirected graph [Formula: see text], an orientation of [Formula: see text] is to assign every edge of [Formula: see text] a direction. Borradaile et al gave a greedy algorithm SC-Path-Reversal (in polynomial time) which finds a strongly connected orientation that minimizes the maximum indegree, and conjectured that SC-Path-Reversal is indeed optimal for the ”minimizing the lexicographic order” objective as well. In this note, we give a positive answer to the conjecture, which is that we show that the algorithm SC-PATH-REVERSAL finds a strongly connected orientation that minimizes the lexicographic order of indegrees.
{"title":"Strongly Connected Orientation with Minimum Lexicographic Order of Indegrees","authors":"Hongyu Zhou, Xinmin Hou","doi":"10.1142/s0129054122500046","DOIUrl":"https://doi.org/10.1142/s0129054122500046","url":null,"abstract":"Given a simple undirected graph [Formula: see text], an orientation of [Formula: see text] is to assign every edge of [Formula: see text] a direction. Borradaile et al gave a greedy algorithm SC-Path-Reversal (in polynomial time) which finds a strongly connected orientation that minimizes the maximum indegree, and conjectured that SC-Path-Reversal is indeed optimal for the ”minimizing the lexicographic order” objective as well. In this note, we give a positive answer to the conjecture, which is that we show that the algorithm SC-PATH-REVERSAL finds a strongly connected orientation that minimizes the lexicographic order of indegrees.","PeriodicalId":192109,"journal":{"name":"Int. J. Found. Comput. Sci.","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121164062","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 : 2021-02-06DOI: 10.1142/S0129054121410033
S. Konstantinidis, M. Mastnak, Juraj Sebej
We consider the problem of partitioning effectively a given irreflexive (and possibly symmetric) rational relation [Formula: see text] into two asymmetric rational relations. This problem is motivated by a recent method of embedding an [Formula: see text]-independent language into one that is maximal [Formula: see text]-independent, where the method requires to use an asymmetric partition of [Formula: see text]. We solve the problem when [Formula: see text] is length-separable, which means that the following two subsets of [Formula: see text] are rational: the subset of word pairs [Formula: see text] where [Formula: see text]; and the subset of word pairs [Formula: see text] where [Formula: see text]. This property is satisfied by all recognizable, all left synchronous, and all right synchronous relations. We leave it as an open problem when [Formula: see text] is not length-separable. We also define zero-avoiding transducers for length-separable relations, which makes our partitioning solution constructive.
我们考虑将一个给定的非自反性(可能是对称的)有理关系(公式:见文本)有效地划分为两个非对称有理关系的问题。这个问题是由最近的一种方法引起的，该方法将一个[公式:见文本]独立的语言嵌入到一个最大的[公式:见文本]独立的语言中，该方法需要使用[公式:见文本]的不对称分割。当[Formula: see text]是长度可分的时候，我们解决了这个问题，这意味着[Formula: see text]的以下两个子集是有理的:词对的子集[Formula: see text]，其中[Formula: see text];以及单词对的子集[公式:见文本]，其中[公式:见文本]。所有可识别的、所有左同步和所有右同步关系都满足此属性。当[公式:见文本]不可分长度时，我们把它作为一个开放的问题。我们还定义了长度可分关系的避零换能器，这使得我们的分划解具有建设性。
{"title":"Zero-Avoiding Transducers, Length Separable Relations, and the Rational Asymmetric Partition Problem","authors":"S. Konstantinidis, M. Mastnak, Juraj Sebej","doi":"10.1142/S0129054121410033","DOIUrl":"https://doi.org/10.1142/S0129054121410033","url":null,"abstract":"We consider the problem of partitioning effectively a given irreflexive (and possibly symmetric) rational relation [Formula: see text] into two asymmetric rational relations. This problem is motivated by a recent method of embedding an [Formula: see text]-independent language into one that is maximal [Formula: see text]-independent, where the method requires to use an asymmetric partition of [Formula: see text]. We solve the problem when [Formula: see text] is length-separable, which means that the following two subsets of [Formula: see text] are rational: the subset of word pairs [Formula: see text] where [Formula: see text]; and the subset of word pairs [Formula: see text] where [Formula: see text]. This property is satisfied by all recognizable, all left synchronous, and all right synchronous relations. We leave it as an open problem when [Formula: see text] is not length-separable. We also define zero-avoiding transducers for length-separable relations, which makes our partitioning solution constructive.","PeriodicalId":192109,"journal":{"name":"Int. J. Found. Comput. Sci.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127075511","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 : 2021-02-06DOI: 10.1142/S012905412141001X
C. Nicaud, P. Rotondo
In this article, we study some properties of random regular expressions of size [Formula: see text], when the cardinality of the alphabet also depends on [Formula: see text]. For this, we revisit and improve the classical Transfer Theorem from the field of analytic combinatorics. This provides precise estimations for the number of regular expressions, the probability of recognizing the empty word and the expected number of Kleene stars in a random expression. For all these statistics, we show that there is a threshold when the size of the alphabet approaches [Formula: see text], at which point the leading term in the asymptotics starts oscillating.
{"title":"Random Regular Expression Over Huge Alphabets","authors":"C. Nicaud, P. Rotondo","doi":"10.1142/S012905412141001X","DOIUrl":"https://doi.org/10.1142/S012905412141001X","url":null,"abstract":"In this article, we study some properties of random regular expressions of size [Formula: see text], when the cardinality of the alphabet also depends on [Formula: see text]. For this, we revisit and improve the classical Transfer Theorem from the field of analytic combinatorics. This provides precise estimations for the number of regular expressions, the probability of recognizing the empty word and the expected number of Kleene stars in a random expression. For all these statistics, we show that there is a threshold when the size of the alphabet approaches [Formula: see text], at which point the leading term in the asymptotics starts oscillating.","PeriodicalId":192109,"journal":{"name":"Int. J. Found. Comput. Sci.","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124730476","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 : 2021-01-30DOI: 10.1142/S0129054121410021
J. Dassow
For a regular language [Formula: see text], let [Formula: see text] be the minimal number of nonterminals necessary to generate [Formula: see text] by right linear grammars. Moreover, for natural numbers [Formula: see text] and an [Formula: see text]-ary regularity preserving operation [Formula: see text], let the range [Formula: see text] be the set of all numbers [Formula: see text] such that there are regular languages [Formula: see text] with [Formula: see text] for [Formula: see text] and [Formula: see text]. We show that, for the circular shift operation [Formula: see text], [Formula: see text] is infinite for all [Formula: see text], and we completely determine the set [Formula: see text]. Moreover, we give a precise range for the left right quotient and a partial result for the left quotient. Furthermore, we add some values to the range for the operation intersection which improves the result of [ 2 ].
对于正则语言[Formula: see text]，设[Formula: see text]为通过右线性语法生成[Formula: see text]所需的最小非终结符数。此外，对于自然数[公式:见文]和一个[公式:见文]-任何正则性保持运算[公式:见文]，设范围[公式:见文]是所有数字[公式:见文]的集合，使得对于[公式:见文]和[公式:见文]存在正则语言[公式:见文]和[公式:见文]。我们证明，对于圆移位运算[公式:见文]，[公式:见文]对于所有[公式:见文]都是无限的，并且我们完全确定了集合[公式:见文]。并给出了左商的精确取值范围和左商的部分结果。进一步，我们在操作交集的范围内增加了一些值，改进了[2]的结果。
{"title":"Further Remarks on the Operational Nonterminal Complexity","authors":"J. Dassow","doi":"10.1142/S0129054121410021","DOIUrl":"https://doi.org/10.1142/S0129054121410021","url":null,"abstract":"For a regular language [Formula: see text], let [Formula: see text] be the minimal number of nonterminals necessary to generate [Formula: see text] by right linear grammars. Moreover, for natural numbers [Formula: see text] and an [Formula: see text]-ary regularity preserving operation [Formula: see text], let the range [Formula: see text] be the set of all numbers [Formula: see text] such that there are regular languages [Formula: see text] with [Formula: see text] for [Formula: see text] and [Formula: see text]. We show that, for the circular shift operation [Formula: see text], [Formula: see text] is infinite for all [Formula: see text], and we completely determine the set [Formula: see text]. Moreover, we give a precise range for the left right quotient and a partial result for the left quotient. Furthermore, we add some values to the range for the operation intersection which improves the result of [ 2 ].","PeriodicalId":192109,"journal":{"name":"Int. J. Found. Comput. Sci.","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126968618","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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