Pub Date : 2021-09-06DOI: 10.1142/s0129054121500283
O. Finkel
We prove two new effective properties of rational functions over infinite words which are realized by finite state Büchi transducers. Firstly, for each such function [Formula: see text], one can construct a deterministic Büchi automaton [Formula: see text] accepting a dense [Formula: see text]-subset of [Formula: see text] such that the restriction of [Formula: see text] to [Formula: see text] is continuous. Secondly, we give a new proof of the decidability of the first Baire class for synchronous [Formula: see text]-rational functions from which we get an extension of this result involving the notion of Wadge classes of regular [Formula: see text]-languages.
{"title":"Two Effective Properties of ω-Rational Functions","authors":"O. Finkel","doi":"10.1142/s0129054121500283","DOIUrl":"https://doi.org/10.1142/s0129054121500283","url":null,"abstract":"We prove two new effective properties of rational functions over infinite words which are realized by finite state Büchi transducers. Firstly, for each such function [Formula: see text], one can construct a deterministic Büchi automaton [Formula: see text] accepting a dense [Formula: see text]-subset of [Formula: see text] such that the restriction of [Formula: see text] to [Formula: see text] is continuous. Secondly, we give a new proof of the decidability of the first Baire class for synchronous [Formula: see text]-rational functions from which we get an extension of this result involving the notion of Wadge classes of regular [Formula: see text]-languages.","PeriodicalId":192109,"journal":{"name":"Int. J. Found. Comput. Sci.","volume":"15 12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134290680","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 : 2021-09-06DOI: 10.1142/s0129054121500295
Bo Zhou, Zhenan Li, Haiyan Guo
Robustness of the network topology is a key aspect in the design of computer networks. Vertex (Link, respectively) residual closeness is a new graph-theoretic concept defined as a measure of network robustness due to the failure of individual vertices (links, respectively). In this paper, we identify the trees and unicyclic graphs with the first a few smallest vertex residual closeness, and determine the graphs that minimize or maximize the vertex (link, respectively) residual closeness over some classes of graphs.
{"title":"Extremal Results on Vertex and Link Residual Closeness","authors":"Bo Zhou, Zhenan Li, Haiyan Guo","doi":"10.1142/s0129054121500295","DOIUrl":"https://doi.org/10.1142/s0129054121500295","url":null,"abstract":"Robustness of the network topology is a key aspect in the design of computer networks. Vertex (Link, respectively) residual closeness is a new graph-theoretic concept defined as a measure of network robustness due to the failure of individual vertices (links, respectively). In this paper, we identify the trees and unicyclic graphs with the first a few smallest vertex residual closeness, and determine the graphs that minimize or maximize the vertex (link, respectively) residual closeness over some classes of graphs.","PeriodicalId":192109,"journal":{"name":"Int. J. Found. Comput. Sci.","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122614188","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 : 2021-09-01DOI: 10.1142/s0129054121420089
C. Bleak
Results in [Formula: see text] algebras, of Matte Bon and Le Boudec, and of Haagerup and Olesen, apply to the R. Thompson groups [Formula: see text]. These results together show that [Formula: see text] is non-amenable if and only if [Formula: see text] has a simple reduced [Formula: see text]-algebra. In further investigations into the structure of [Formula: see text]-algebras, Breuillard, Kalantar, Kennedy, and Ozawa introduce the notion of a normalish subgroup of a group [Formula: see text]. They show that if a group [Formula: see text] admits no non-trivial finite normal subgroups and no normalish amenable subgroups then it has a simple reduced [Formula: see text]-algebra. Our chief result concerns the R. Thompson groups [Formula: see text]; we show that there is an elementary amenable group [Formula: see text] [where here, [Formula: see text]] with [Formula: see text] normalish in [Formula: see text]. The proof given uses a natural partial action of the group [Formula: see text] on a regular language determined by a synchronising automaton in order to verify a certain stability condition: once again highlighting the existence of interesting intersections of the theory of [Formula: see text] with various forms of formal language theory.
{"title":"Normalish Amenable Subgroups of the R. Thompson Groups","authors":"C. Bleak","doi":"10.1142/s0129054121420089","DOIUrl":"https://doi.org/10.1142/s0129054121420089","url":null,"abstract":"Results in [Formula: see text] algebras, of Matte Bon and Le Boudec, and of Haagerup and Olesen, apply to the R. Thompson groups [Formula: see text]. These results together show that [Formula: see text] is non-amenable if and only if [Formula: see text] has a simple reduced [Formula: see text]-algebra. In further investigations into the structure of [Formula: see text]-algebras, Breuillard, Kalantar, Kennedy, and Ozawa introduce the notion of a normalish subgroup of a group [Formula: see text]. They show that if a group [Formula: see text] admits no non-trivial finite normal subgroups and no normalish amenable subgroups then it has a simple reduced [Formula: see text]-algebra. Our chief result concerns the R. Thompson groups [Formula: see text]; we show that there is an elementary amenable group [Formula: see text] [where here, [Formula: see text]] with [Formula: see text] normalish in [Formula: see text]. The proof given uses a natural partial action of the group [Formula: see text] on a regular language determined by a synchronising automaton in order to verify a certain stability condition: once again highlighting the existence of interesting intersections of the theory of [Formula: see text] with various forms of formal language theory.","PeriodicalId":192109,"journal":{"name":"Int. J. Found. Comput. Sci.","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115704015","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 : 2021-08-25DOI: 10.1142/S0129054122440038
Stijn Cambie, M. Bondt, H. Don
The largest known reset thresholds for DFAs are equal to [Formula: see text], where [Formula: see text] is the number of states. This is conjectured to be the maximum possible. PFAs (with partial transition function) can have exponentially large reset thresholds. This is still true if we restrict to binary PFAs. However, asymptotics do not give conclusions for fixed [Formula: see text]. We prove that the maximal reset threshold for binary PFAs is strictly greater than [Formula: see text] if and only if [Formula: see text]. These results are mostly based on the analysis of synchronizing word lengths for a certain family of binary PFAs. This family has the following properties: it contains the well-known Černý automata; for [Formula: see text] it contains a binary PFA with maximal possible reset threshold; for all [Formula: see text] it contains a PFA with reset threshold larger than the maximum known for DFAs. Analysis of this family reveals remarkable patterns involving the Fibonacci numbers and related sequences such as the Padovan sequence. We derive explicit formulas for the reset thresholds in terms of these recurrent sequences. Asymptotically the Černý family gives reset thresholds of polynomial order. We prove that PFAs in the family are not extremal for [Formula: see text]. For that purpose, we present an improvement of Martyugin’s prime number construction of binary PFAs.
已知最大的dfa重置阈值等于[Formula: see text]，其中[Formula: see text]是状态数。据推测这是可能的最大值。PFAs(具有部分转移函数)可以具有指数级大的重置阈值。如果我们限制为二进制pfa，这仍然是正确的。然而，对于固定的情况，渐近性不能给出结论[公式:见文本]。我们证明了二元PFAs的最大复位阈值严格大于[公式:见文]当且仅当[公式:见文]。这些结果主要是基于对某些二进制PFAs族的同步字长的分析。这个系列具有以下性质:它包含众所周知的Černý自动机;对于[公式:见文本]，它包含一个具有最大可能复位阈值的二进制PFA;对于所有[公式:见文本]，它包含一个重置阈值大于dfa已知最大值的PFA。对这个家族的分析揭示了涉及斐波那契数列和相关序列(如帕多万序列)的显著模式。我们根据这些循环序列推导出复位阈值的显式公式。渐近的Černý族给出了多项式阶的重置阈值。我们证明了家庭中的PFAs不是极端的[公式:见文本]。为此，我们提出了一种改进的martyyugin二元pfa素数构造方法。
{"title":"Extremal Binary PFAs with Small Number of States","authors":"Stijn Cambie, M. Bondt, H. Don","doi":"10.1142/S0129054122440038","DOIUrl":"https://doi.org/10.1142/S0129054122440038","url":null,"abstract":"The largest known reset thresholds for DFAs are equal to [Formula: see text], where [Formula: see text] is the number of states. This is conjectured to be the maximum possible. PFAs (with partial transition function) can have exponentially large reset thresholds. This is still true if we restrict to binary PFAs. However, asymptotics do not give conclusions for fixed [Formula: see text]. We prove that the maximal reset threshold for binary PFAs is strictly greater than [Formula: see text] if and only if [Formula: see text]. These results are mostly based on the analysis of synchronizing word lengths for a certain family of binary PFAs. This family has the following properties: it contains the well-known Černý automata; for [Formula: see text] it contains a binary PFA with maximal possible reset threshold; for all [Formula: see text] it contains a PFA with reset threshold larger than the maximum known for DFAs. Analysis of this family reveals remarkable patterns involving the Fibonacci numbers and related sequences such as the Padovan sequence. We derive explicit formulas for the reset thresholds in terms of these recurrent sequences. Asymptotically the Černý family gives reset thresholds of polynomial order. We prove that PFAs in the family are not extremal for [Formula: see text]. For that purpose, we present an improvement of Martyugin’s prime number construction of binary PFAs.","PeriodicalId":192109,"journal":{"name":"Int. J. Found. Comput. Sci.","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129324899","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 : 2021-08-04DOI: 10.1142/s0129054121500271
Ö. Eğecioğlu, Elif Saygı, Zülfükar Saygı
We introduce alternate Lucas cubes, a new family of graphs designed as an alternative for the well known Lucas cubes. These interconnection networks are subgraphs of Fibonacci cubes and have a useful fundamental decomposition similar to the one for Fibonacci cubes. The vertices of alternate Lucas cubes are constructed from binary strings that are encodings of Lucas representation of integers. As well as ordinary hypercubes, Fibonacci cubes and Lucas cubes, alternate Lucas cubes have several interesting structural and enumerative properties. In this paper we study some of these properties. Specifically, we give the fundamental decomposition giving the recursive structure, determine the number of edges, number of vertices by weight, the distribution of the degrees; as well as the properties of induced hypercubes, [Formula: see text]-cube polynomials and maximal hypercube polynomials. We also obtain the irregularity polynomials of this family of graphs, determine the conditions for Hamiltonicity, and calculate metric properties such as the radius, diameter, and the center.
{"title":"Alternate Lucas Cubes","authors":"Ö. Eğecioğlu, Elif Saygı, Zülfükar Saygı","doi":"10.1142/s0129054121500271","DOIUrl":"https://doi.org/10.1142/s0129054121500271","url":null,"abstract":"We introduce alternate Lucas cubes, a new family of graphs designed as an alternative for the well known Lucas cubes. These interconnection networks are subgraphs of Fibonacci cubes and have a useful fundamental decomposition similar to the one for Fibonacci cubes. The vertices of alternate Lucas cubes are constructed from binary strings that are encodings of Lucas representation of integers. As well as ordinary hypercubes, Fibonacci cubes and Lucas cubes, alternate Lucas cubes have several interesting structural and enumerative properties. In this paper we study some of these properties. Specifically, we give the fundamental decomposition giving the recursive structure, determine the number of edges, number of vertices by weight, the distribution of the degrees; as well as the properties of induced hypercubes, [Formula: see text]-cube polynomials and maximal hypercube polynomials. We also obtain the irregularity polynomials of this family of graphs, determine the conditions for Hamiltonicity, and calculate metric properties such as the radius, diameter, and the center.","PeriodicalId":192109,"journal":{"name":"Int. J. Found. Comput. Sci.","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115046044","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 : 2021-08-04DOI: 10.1142/s012905412150026x
Jiejing Wen, Fang-Wei Fu
Multiply constant-weight codes (MCWCs) were introduced recently to improve the reliability of certain physically unclonable function response. In this paper, two methods of constructing MCWCs are presented following the concatenation methodology. In other words, MCWCs are constructed by concatenating approximate outer codes and inner codes. Besides, several classes of optimal MCWCs are derived from these methods. In the first method, the outer codes are [Formula: see text]-ary codes and the inner codes are constant-weight codes over [Formula: see text]. Furthermore, if the outer code achieves the Plotkin bound and the inner code achieves Johnson bound, then the resulting MCWC is optimal. In the second method, the outer codes are [Formula: see text]-ary codes and the inner codes are MCWCs. Furthermore, if the outer code achieves the Plotkin bound and the inner code achieves the Johnson bound, then the resulting MCWC is optimal.
{"title":"On the Construction of Multiply Constant-Weight Codes","authors":"Jiejing Wen, Fang-Wei Fu","doi":"10.1142/s012905412150026x","DOIUrl":"https://doi.org/10.1142/s012905412150026x","url":null,"abstract":"Multiply constant-weight codes (MCWCs) were introduced recently to improve the reliability of certain physically unclonable function response. In this paper, two methods of constructing MCWCs are presented following the concatenation methodology. In other words, MCWCs are constructed by concatenating approximate outer codes and inner codes. Besides, several classes of optimal MCWCs are derived from these methods. In the first method, the outer codes are [Formula: see text]-ary codes and the inner codes are constant-weight codes over [Formula: see text]. Furthermore, if the outer code achieves the Plotkin bound and the inner code achieves Johnson bound, then the resulting MCWC is optimal. In the second method, the outer codes are [Formula: see text]-ary codes and the inner codes are MCWCs. Furthermore, if the outer code achieves the Plotkin bound and the inner code achieves the Johnson bound, then the resulting MCWC is optimal.","PeriodicalId":192109,"journal":{"name":"Int. J. Found. Comput. Sci.","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127203752","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 : 2021-07-14DOI: 10.1142/S0129054121420065
F. Koechlin, C. Nicaud, P. Rotondo
In this article, we study the impact of applying simple reduction rules to random syntactic formulas encoded as trees. We assume that there is an operator that has an absorbing pattern and prove that if we use this property to simplify a uniform random expression with [Formula: see text] nodes, then the expected size of the result is bounded by a constant. The same holds for higher moments, establishing the lack of expressivity of uniform random expressions. Our framework is quite general as we consider expressions defined by systems of combinatorial equations. For our proofs, we rely on Drmota’s multidimensional theorem for systems of generating functions.
{"title":"Simplifications of Uniform Expressions Specified by Systems","authors":"F. Koechlin, C. Nicaud, P. Rotondo","doi":"10.1142/S0129054121420065","DOIUrl":"https://doi.org/10.1142/S0129054121420065","url":null,"abstract":"In this article, we study the impact of applying simple reduction rules to random syntactic formulas encoded as trees. We assume that there is an operator that has an absorbing pattern and prove that if we use this property to simplify a uniform random expression with [Formula: see text] nodes, then the expected size of the result is bounded by a constant. The same holds for higher moments, establishing the lack of expressivity of uniform random expressions. Our framework is quite general as we consider expressions defined by systems of combinatorial equations. For our proofs, we rely on Drmota’s multidimensional theorem for systems of generating functions.","PeriodicalId":192109,"journal":{"name":"Int. J. Found. Comput. Sci.","volume":"60 11","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114040530","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 : 2021-06-05DOI: 10.1142/S0129054121420028
Lukas Fleischer, J. Shallit
For a formal language [Formula: see text], the problem of language enumeration asks to compute the length-lexicographically smallest word in [Formula: see text] larger than a given input [Formula: see text] (henceforth called the [Formula: see text]-successor of [Formula: see text]). We investigate this problem for regular languages from a computational complexity and state complexity perspective. We first show that if [Formula: see text] is recognized by a DFA with [Formula: see text] states, then [Formula: see text] states are (in general) necessary and sufficient for an unambiguous finite-state transducer to compute [Formula: see text]-successors. As a byproduct, we obtain that if [Formula: see text] is recognized by a DFA with [Formula: see text] states, then [Formula: see text] states are sufficient for a DFA to recognize the subset [Formula: see text] of [Formula: see text] composed of its lexicographically smallest words. We give a matching lower bound that holds even if [Formula: see text] is represented as an NFA. It has been known that [Formula: see text]-successors can be computed in polynomial time, even if the regular language is given as part of the input (assuming a suitable representation of the language, such as a DFA). In this paper, we refine this result in multiple directions. We show that if the regular language is given as part of the input and encoded as a DFA, the problem is in [Formula: see text]. If the regular language [Formula: see text] is fixed, we prove that the enumeration problem of the language is reducible to deciding membership to the Myhill-Nerode equivalence classes of [Formula: see text] under [Formula: see text]-uniform [Formula: see text] reductions. In particular, this implies that fixed star-free languages can be enumerated in [Formula: see text], arbitrary fixed regular languages can be enumerated in [Formula: see text] and that there exist regular languages for which the problem is [Formula: see text]-complete.
对于一种形式语言[Formula: see text]，语言枚举问题要求计算[Formula: see text]中比给定输入[Formula: see text](今后称为[Formula: see text]- [Formula: see text]的后继者)大的按字典顺序排列的最小单词的长度。我们从计算复杂性和状态复杂性的角度来研究正则语言的这个问题。我们首先表明，如果[Formula: see text]被具有[Formula: see text]状态的DFA识别，那么[Formula: see text]状态(通常)对于一个明确的有限状态传感器计算[Formula: see text]-后继器是必要和充分的。作为一个副产品，我们得到，如果[Formula: see text]被具有[Formula: see text]状态的DFA识别，那么[Formula: see text]状态就足以让DFA识别由字典上最小的单词组成的[Formula: see text]子集[Formula: see text]。我们给出了一个匹配的下界，即使[公式:见文本]被表示为NFA。众所周知，[公式:见文本]-继承者可以在多项式时间内计算，即使正则语言作为输入的一部分给出(假设语言的合适表示，例如DFA)。在本文中，我们从多个方向对这一结果进行了改进。我们表明，如果正则语言作为输入的一部分给出并编码为DFA，问题就在[公式:见文本]中。如果正则语言[公式:见文]是固定的，我们证明了该语言的枚举问题可约简为在[公式:见文]-一致[公式:见文]约简下决定[公式:见文]的Myhill-Nerode等价类的隶属关系。特别地，这意味着固定的无星型语言可以在[公式:见文本]中枚举，任意固定的正则语言可以在[公式:见文本]中枚举，并且存在问题为[公式:见文本]-complete的正则语言。
{"title":"Recognizing Lexicographically Smallest Words and Computing Successors in Regular Languages","authors":"Lukas Fleischer, J. Shallit","doi":"10.1142/S0129054121420028","DOIUrl":"https://doi.org/10.1142/S0129054121420028","url":null,"abstract":"For a formal language [Formula: see text], the problem of language enumeration asks to compute the length-lexicographically smallest word in [Formula: see text] larger than a given input [Formula: see text] (henceforth called the [Formula: see text]-successor of [Formula: see text]). We investigate this problem for regular languages from a computational complexity and state complexity perspective. We first show that if [Formula: see text] is recognized by a DFA with [Formula: see text] states, then [Formula: see text] states are (in general) necessary and sufficient for an unambiguous finite-state transducer to compute [Formula: see text]-successors. As a byproduct, we obtain that if [Formula: see text] is recognized by a DFA with [Formula: see text] states, then [Formula: see text] states are sufficient for a DFA to recognize the subset [Formula: see text] of [Formula: see text] composed of its lexicographically smallest words. We give a matching lower bound that holds even if [Formula: see text] is represented as an NFA. It has been known that [Formula: see text]-successors can be computed in polynomial time, even if the regular language is given as part of the input (assuming a suitable representation of the language, such as a DFA). In this paper, we refine this result in multiple directions. We show that if the regular language is given as part of the input and encoded as a DFA, the problem is in [Formula: see text]. If the regular language [Formula: see text] is fixed, we prove that the enumeration problem of the language is reducible to deciding membership to the Myhill-Nerode equivalence classes of [Formula: see text] under [Formula: see text]-uniform [Formula: see text] reductions. In particular, this implies that fixed star-free languages can be enumerated in [Formula: see text], arbitrary fixed regular languages can be enumerated in [Formula: see text] and that there exist regular languages for which the problem is [Formula: see text]-complete.","PeriodicalId":192109,"journal":{"name":"Int. J. Found. Comput. Sci.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123548413","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 : 2021-06-01DOI: 10.1142/S0129054121500234
Shiying Wang
The diagnosability of a multiprocessor system or an interconnection network plays an important role in measuring the fault tolerance of the network. In 2016, Zhang et al. proposed a new measure for fault diagnosis of the system, namely, the [Formula: see text]-extra diagnosability, which restrains that every fault-free component has at least [Formula: see text] fault-free nodes. As a famous topology structure of interconnection networks, the hyper Petersen graph [Formula: see text] has many good properties. It is difficult to prove the [Formula: see text]-extra diagnosability of an interconnection network. In this paper, we show that the [Formula: see text]-extra diagnosability of [Formula: see text] is [Formula: see text] for [Formula: see text] and [Formula: see text] in the PMC model and for [Formula: see text] and [Formula: see text] in the MM[Formula: see text] model.
{"title":"The r-Extra Diagnosability of Hyper Petersen Graphs","authors":"Shiying Wang","doi":"10.1142/S0129054121500234","DOIUrl":"https://doi.org/10.1142/S0129054121500234","url":null,"abstract":"The diagnosability of a multiprocessor system or an interconnection network plays an important role in measuring the fault tolerance of the network. In 2016, Zhang et al. proposed a new measure for fault diagnosis of the system, namely, the [Formula: see text]-extra diagnosability, which restrains that every fault-free component has at least [Formula: see text] fault-free nodes. As a famous topology structure of interconnection networks, the hyper Petersen graph [Formula: see text] has many good properties. It is difficult to prove the [Formula: see text]-extra diagnosability of an interconnection network. In this paper, we show that the [Formula: see text]-extra diagnosability of [Formula: see text] is [Formula: see text] for [Formula: see text] and [Formula: see text] in the PMC model and for [Formula: see text] and [Formula: see text] in the MM[Formula: see text] model.","PeriodicalId":192109,"journal":{"name":"Int. J. Found. Comput. Sci.","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124719046","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 : 2021-05-31DOI: 10.1007/978-3-030-81508-0_24
S. Maneth, H. Seidl, Martin Vu
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