The g-extra connectivity and diagonalisability are two important metrics to fault-tolerance and robustness of a multiprocessor system whose network structure is modelled by a graph. In this work, we explore the reliability of a newly proposed network called hyper bijective connection networks (HBC, for short), which is an extension of the family of the well-known interconnection networks, such as hypercube and its variants. We prove that 2-extra vertex connectivity and 3-extra vertex connectivity of n-dimensional HBC are 3n + m−6 for and and 4n + m−8 for and , respectively. Using its desirable fault-tolerance, we show that the conditional diagonalizabilities of n-dimensional HBC under the PMC model are m + 4n−7 (resp., 4n−5) for and (resp., m = 3 and ) and its conditional diagonalizability under MM model is m + 3n−6 for and .
{"title":"Reliability and conditional diagnosability of hyper bijective connection networks","authors":"Guanqin Lian, Shuming Zhou, E. Cheng, Jiafei Liu, Gaolin Chen, Zhendong Gu","doi":"10.1080/23799927.2020.1720825","DOIUrl":"https://doi.org/10.1080/23799927.2020.1720825","url":null,"abstract":"The g-extra connectivity and diagonalisability are two important metrics to fault-tolerance and robustness of a multiprocessor system whose network structure is modelled by a graph. In this work, we explore the reliability of a newly proposed network called hyper bijective connection networks (HBC, for short), which is an extension of the family of the well-known interconnection networks, such as hypercube and its variants. We prove that 2-extra vertex connectivity and 3-extra vertex connectivity of n-dimensional HBC are 3n + m−6 for and and 4n + m−8 for and , respectively. Using its desirable fault-tolerance, we show that the conditional diagonalizabilities of n-dimensional HBC under the PMC model are m + 4n−7 (resp., 4n−5) for and (resp., m = 3 and ) and its conditional diagonalizability under MM model is m + 3n−6 for and .","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"11 1","pages":"25 - 47"},"PeriodicalIF":0.8,"publicationDate":"2020-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75207419","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 : 2019-12-05DOI: 10.1080/23799927.2020.1755367
M. Harada
An s-extremal optimal unimodular lattice in dimension 52 is constructed for the first time. This lattice is constructed from a certain self-dual -code by Construction A. In addition, as neighbours of the lattice, two more s-extremal optimal unimodular lattices are constructed.
{"title":"Construction of s-extremal optimal unimodular lattices in dimension 52","authors":"M. Harada","doi":"10.1080/23799927.2020.1755367","DOIUrl":"https://doi.org/10.1080/23799927.2020.1755367","url":null,"abstract":"An s-extremal optimal unimodular lattice in dimension 52 is constructed for the first time. This lattice is constructed from a certain self-dual -code by Construction A. In addition, as neighbours of the lattice, two more s-extremal optimal unimodular lattices are constructed.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"1962 1","pages":"87 - 91"},"PeriodicalIF":0.8,"publicationDate":"2019-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91315785","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 : 2019-10-02DOI: 10.1080/23799927.2019.1671903
Albert Guan
ABSTRACT Computationally lightweight and unconditionally secure key agreement protocols are very useful for secure communication in public networks, especially for sensors with limited computing resources. In 2017, Guan and Tseng proposed a key agreement protocol which is computationally lightweight and unconditionally secure. In their protocol, it was assumed that the two communicating nodes can receive random bit string from a beacon node. Random bit string plays an important role in the generation of secret keys. With the advancement of hardware and software technologies, sensors may be able to generate good random strings. In this paper, we consider the case that the sensor nodes can generate random bit strings for secret keys. Therefore, no beacon nodes are required. The results of this study show that a key agreement protocol can be much more effective and efficient in the case that the communicating nodes can generate good random bit strings.
{"title":"An efficient secret key agreement protocol based on random noise without beacons","authors":"Albert Guan","doi":"10.1080/23799927.2019.1671903","DOIUrl":"https://doi.org/10.1080/23799927.2019.1671903","url":null,"abstract":"ABSTRACT Computationally lightweight and unconditionally secure key agreement protocols are very useful for secure communication in public networks, especially for sensors with limited computing resources. In 2017, Guan and Tseng proposed a key agreement protocol which is computationally lightweight and unconditionally secure. In their protocol, it was assumed that the two communicating nodes can receive random bit string from a beacon node. Random bit string plays an important role in the generation of secret keys. With the advancement of hardware and software technologies, sensors may be able to generate good random strings. In this paper, we consider the case that the sensor nodes can generate random bit strings for secret keys. Therefore, no beacon nodes are required. The results of this study show that a key agreement protocol can be much more effective and efficient in the case that the communicating nodes can generate good random bit strings.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"37 2","pages":"171 - 184"},"PeriodicalIF":0.8,"publicationDate":"2019-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23799927.2019.1671903","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72475759","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 : 2019-10-02DOI: 10.1080/23799927.2019.1694997
Mohamad Abdallah
ABSTRACT Jwo et al. introduced the alternating group graph as an interconnection network topology for computing systems. A graph is pancyclic if it contains cycles of all possible lengths. P-Y Tsai et al. showed that the alternating group graph is pancyclic, and remains pancyclic after the deletion of 2n−6 edges. In this paper we consider a class of Cayley graphs introduced by Cheng et al. that are generated by certain 3-cycles on the alternating group . These graphs are generalizations of the alternating group graph . We look at the case when the 3-cycles form a ‘tree-like structure’, and analyse the pancyclicity of these graphs. We prove that this family of Cayley graphs is -edge-fault-tolerant pancyclic.
{"title":"Edge-fault-tolerant pancyclicity of 2-tree-generated networks","authors":"Mohamad Abdallah","doi":"10.1080/23799927.2019.1694997","DOIUrl":"https://doi.org/10.1080/23799927.2019.1694997","url":null,"abstract":"ABSTRACT Jwo et al. introduced the alternating group graph as an interconnection network topology for computing systems. A graph is pancyclic if it contains cycles of all possible lengths. P-Y Tsai et al. showed that the alternating group graph is pancyclic, and remains pancyclic after the deletion of 2n−6 edges. In this paper we consider a class of Cayley graphs introduced by Cheng et al. that are generated by certain 3-cycles on the alternating group . These graphs are generalizations of the alternating group graph . We look at the case when the 3-cycles form a ‘tree-like structure’, and analyse the pancyclicity of these graphs. We prove that this family of Cayley graphs is -edge-fault-tolerant pancyclic.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"115 1","pages":"140 - 150"},"PeriodicalIF":0.8,"publicationDate":"2019-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80315169","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 : 2019-10-02DOI: 10.1080/23799927.2019.1700396
A. Balamesh, A. Rushdi
ABSTRACT This paper considers the problem of solving a system of Boolean equations over a finite (atomic) Boolean algebra other than the two-valued one, referred to herein as a ‘big’ Boolean algebra. The paper suggests the replacement of this system of equations by a single Boolean equation, and then proposes a novel method for solving this equation by using its atomic decomposition into several independent switching equations. This method has many advantages including the efficient derivation of a complete compact listing of all particular solutions in a form similar to the recently developed permutative additive form, but obtained in a more direct fashion without using parameters. Many detailed examples are used to illustrate the proposed new method. The examples demonstrate how the consistency condition might force a collapse of the underlying Boolean algebra into a subalgebra, and also how to list a huge number of particular solutions in a very small space.
{"title":"Solution of Boolean equations via atomic decomposition into independent switching equations","authors":"A. Balamesh, A. Rushdi","doi":"10.1080/23799927.2019.1700396","DOIUrl":"https://doi.org/10.1080/23799927.2019.1700396","url":null,"abstract":"ABSTRACT This paper considers the problem of solving a system of Boolean equations over a finite (atomic) Boolean algebra other than the two-valued one, referred to herein as a ‘big’ Boolean algebra. The paper suggests the replacement of this system of equations by a single Boolean equation, and then proposes a novel method for solving this equation by using its atomic decomposition into several independent switching equations. This method has many advantages including the efficient derivation of a complete compact listing of all particular solutions in a form similar to the recently developed permutative additive form, but obtained in a more direct fashion without using parameters. Many detailed examples are used to illustrate the proposed new method. The examples demonstrate how the consistency condition might force a collapse of the underlying Boolean algebra into a subalgebra, and also how to list a huge number of particular solutions in a very small space.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"71 1","pages":"185 - 203"},"PeriodicalIF":0.8,"publicationDate":"2019-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83613407","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 : 2019-10-02DOI: 10.1080/23799927.2019.1685006
C. Aouiti, El Abed Assali
ABSTRACT In this paper, without transforming the original inertial neural networks into the first-order differential equation by some variable substitutions, fuzziness, time-varying and distributed delays are introduced into inertial networks and the existence, the uniqueness and the asymptotic stability for the neural networks are investigated. The existence of a unique equilibrium point is proved by using inequality techniques, and the properties of an M-matrix. By finding a new Lyapunov–Krasovskii functional, some sufficient conditions are derived ensuring the asymptotic stability. Finally, three numerical examples with simulation are presented to show the effectiveness of our theoretical results.
{"title":"Effect of fuzziness on the stability of inertial neural networks with mixed delay via non-reduced-order method","authors":"C. Aouiti, El Abed Assali","doi":"10.1080/23799927.2019.1685006","DOIUrl":"https://doi.org/10.1080/23799927.2019.1685006","url":null,"abstract":"ABSTRACT In this paper, without transforming the original inertial neural networks into the first-order differential equation by some variable substitutions, fuzziness, time-varying and distributed delays are introduced into inertial networks and the existence, the uniqueness and the asymptotic stability for the neural networks are investigated. The existence of a unique equilibrium point is proved by using inequality techniques, and the properties of an M-matrix. By finding a new Lyapunov–Krasovskii functional, some sufficient conditions are derived ensuring the asymptotic stability. Finally, three numerical examples with simulation are presented to show the effectiveness of our theoretical results.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"79 10","pages":"151 - 170"},"PeriodicalIF":0.8,"publicationDate":"2019-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23799927.2019.1685006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72487743","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 : 2019-08-09DOI: 10.1080/23799927.2020.1716074
Ramón Flores, Delaram Kahrobaei, T. Koberda
We discuss some applications of 3-manifold topology to cryptography. In particular, we propose a public-key and a symmetric-key cryptographic scheme based on the Thurston norm on the first cohomology of hyperbolic manifolds.
{"title":"A cryptographic application of the Thurston norm","authors":"Ramón Flores, Delaram Kahrobaei, T. Koberda","doi":"10.1080/23799927.2020.1716074","DOIUrl":"https://doi.org/10.1080/23799927.2020.1716074","url":null,"abstract":"We discuss some applications of 3-manifold topology to cryptography. In particular, we propose a public-key and a symmetric-key cryptographic scheme based on the Thurston norm on the first cohomology of hyperbolic manifolds.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"73 6","pages":"15 - 24"},"PeriodicalIF":0.8,"publicationDate":"2019-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23799927.2020.1716074","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72371343","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 : 2019-07-25DOI: 10.1080/23799927.2019.1645210
S. Alhassan, M. M. Iddrisu, M. I. Daabo
ABSTRACT In this paper, the properties of rotation matrices are employed to construct special orthogonal matrices that are used to encrypt and decrypt video with varying perceptibility. Square orthogonal matrices of varying sides are formulated as cipher key matrices. The encryption algorithm uses these matrices to encrypt plain video into cipher video and transmit while the decryption algorithm uses the transpose of the cipher key matrices to recover the original video at the other end of the communication channel. Degradation in visual quality is controlled by varying cipher key dimension and the number of repetitions. Barring any noise in the communication channel, the proposed method retrieves the original video free of any error. Analysis of results show that the proposed method is key sensitive and resistant to chosen/known plain-text attacks.
{"title":"Perceptual video encryption using orthogonal matrix","authors":"S. Alhassan, M. M. Iddrisu, M. I. Daabo","doi":"10.1080/23799927.2019.1645210","DOIUrl":"https://doi.org/10.1080/23799927.2019.1645210","url":null,"abstract":"ABSTRACT In this paper, the properties of rotation matrices are employed to construct special orthogonal matrices that are used to encrypt and decrypt video with varying perceptibility. Square orthogonal matrices of varying sides are formulated as cipher key matrices. The encryption algorithm uses these matrices to encrypt plain video into cipher video and transmit while the decryption algorithm uses the transpose of the cipher key matrices to recover the original video at the other end of the communication channel. Degradation in visual quality is controlled by varying cipher key dimension and the number of repetitions. Barring any noise in the communication channel, the proposed method retrieves the original video free of any error. Analysis of results show that the proposed method is key sensitive and resistant to chosen/known plain-text attacks.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"66 1","pages":"129 - 139"},"PeriodicalIF":0.8,"publicationDate":"2019-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89279981","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 : 2019-05-17DOI: 10.1080/23799927.2020.1861104
Osman Asif Malik, Stephen Becker
ABSTRACT We present a method for randomizing formulas for bilinear computation of matrix products which does not increase the leading order complexity of the computation. We consider the implications of such randomization when there are two sources of error. The first source is due to the computation formula itself only being approximately correct. Such formulas come up when numerically searching for faster matrix multiplication algorithms. The second source is due to using floating point arithmetic. This kind of error is especially important when computing on low precision hardware like GPUs. Our theoretical results and numerical experiments indicate that our method can improve performance when the two kinds of error are present individually, as well as when they are present at the same time.
{"title":"Randomization of approximate bilinear computation for matrix multiplication","authors":"Osman Asif Malik, Stephen Becker","doi":"10.1080/23799927.2020.1861104","DOIUrl":"https://doi.org/10.1080/23799927.2020.1861104","url":null,"abstract":"ABSTRACT We present a method for randomizing formulas for bilinear computation of matrix products which does not increase the leading order complexity of the computation. We consider the implications of such randomization when there are two sources of error. The first source is due to the computation formula itself only being approximately correct. Such formulas come up when numerically searching for faster matrix multiplication algorithms. The second source is due to using floating point arithmetic. This kind of error is especially important when computing on low precision hardware like GPUs. Our theoretical results and numerical experiments indicate that our method can improve performance when the two kinds of error are present individually, as well as when they are present at the same time.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"1 1","pages":"54 - 93"},"PeriodicalIF":0.8,"publicationDate":"2019-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78539308","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}
ABSTRACT System-level diagnosis aims to identify faulty processors in a multiprocessor system by analysing the test results among the processors. The -diagnosis requires to identify and repair at least k faulty processors in each iteration until that all t faulty processors are found where . It is one of the most important system-level diagnosis strategies. Meanwhile, shuffle-cube , a variant of hypercube for multiprocessor systems, has some good combinatorial properties and fault-tolerant properties. In this paper, we propose a -diagnosis algorithm for n-dimensional shuffle-cube , and then we show that is -diagnosable. Moreover, we prove that the proposed algorithm can identify at most faulty nodes under the condition that it can identify at least n faulty nodes in each iteration.
{"title":"The (t, k)-diagnosability of shuffle-cubes under PMC model","authors":"Jin'e Li, Limei Lin, Yanze Huang, Hui Yu, Riqing Chen","doi":"10.1080/23799927.2019.1625949","DOIUrl":"https://doi.org/10.1080/23799927.2019.1625949","url":null,"abstract":"ABSTRACT System-level diagnosis aims to identify faulty processors in a multiprocessor system by analysing the test results among the processors. The -diagnosis requires to identify and repair at least k faulty processors in each iteration until that all t faulty processors are found where . It is one of the most important system-level diagnosis strategies. Meanwhile, shuffle-cube , a variant of hypercube for multiprocessor systems, has some good combinatorial properties and fault-tolerant properties. In this paper, we propose a -diagnosis algorithm for n-dimensional shuffle-cube , and then we show that is -diagnosable. Moreover, we prove that the proposed algorithm can identify at most faulty nodes under the condition that it can identify at least n faulty nodes in each iteration.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"58 1","pages":"111 - 126"},"PeriodicalIF":0.8,"publicationDate":"2019-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82290736","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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