Pub Date : 2023-03-22DOI: 10.1142/s0129054123460012
Xiaofei Liu, Weidong Li
Given a graph [Formula: see text], a set of [Formula: see text] source-sink pairs [Formula: see text] [Formula: see text] and a profit bound [Formula: see text], every edge [Formula: see text] has a cost [Formula: see text], and every source-sink pair [Formula: see text] has a profit [Formula: see text] and a penalty [Formula: see text]. The [Formula: see text]-prize-collecting multicut problem ([Formula: see text]-PCMP) is to find a multicut [Formula: see text] such that the objective cost, which consists of the total cost of the edges in [Formula: see text] and the total penalty of the pairs still connected after removing [Formula: see text], is minimized and the total profit of the disconnected pairs by removing [Formula: see text] is at least [Formula: see text]. In this paper, we firstly consider the [Formula: see text]-PCMP in paths, and prove that it is [Formula: see text]-hard even when [Formula: see text] for any [Formula: see text]. Then, we present a fully polynomial time approximation scheme (FPTAS) whose running time is [Formula: see text] for the [Formula: see text]-PCMP in paths. Based on this algorithm, we present an FPTAS whose running time is [Formula: see text] for the [Formula: see text]-PCMP in spider graphs, and an FPTAS whose running time is [Formula: see text] for the [Formula: see text]-PCMP in rings, respectively, where [Formula: see text] is the number of leaves of spider graph.
给定一个图[公式:见文]，一组[公式:见文]源汇对[公式:见文][公式:见文]和一个利润界限[公式:见文]，每条边[公式:见文]都有一个成本[公式:见文]，每个源汇对[公式:见文]都有一个利润[公式:见文]和一个损失[公式:见文]。[公式:见文]-计奖多切口问题([公式:见文]-PCMP)是寻找一个多切口[公式:见文]，使[公式:见文]中边缘的总成本和去除[公式:见文]后仍然连接的对的总惩罚的客观成本最小，并且通过去除[公式:见文]而断开的对的总利润至少为[公式:见文]。本文首先考虑路径中的[Formula: see text]-PCMP，并证明对于任何[Formula: see text]，即使[Formula: see text]是[Formula: see text]-hard。然后，我们提出了一个完全多项式时间近似方案(FPTAS)，其运行时间为[公式:见文本]-路径中的pcmp。在此算法的基础上，我们提出了一个运行时间为[公式:见文]的蜘蛛图-PCMP的FPTAS，以及一个运行时间为[公式:见文]的[公式:见文]的[圆环]-PCMP的FPTAS，其中[公式:见文]为蜘蛛图的叶子数。
{"title":"The B-Prize-Collecting Multicut Problem in Paths, Spider Graphs and Rings","authors":"Xiaofei Liu, Weidong Li","doi":"10.1142/s0129054123460012","DOIUrl":"https://doi.org/10.1142/s0129054123460012","url":null,"abstract":"Given a graph [Formula: see text], a set of [Formula: see text] source-sink pairs [Formula: see text] [Formula: see text] and a profit bound [Formula: see text], every edge [Formula: see text] has a cost [Formula: see text], and every source-sink pair [Formula: see text] has a profit [Formula: see text] and a penalty [Formula: see text]. The [Formula: see text]-prize-collecting multicut problem ([Formula: see text]-PCMP) is to find a multicut [Formula: see text] such that the objective cost, which consists of the total cost of the edges in [Formula: see text] and the total penalty of the pairs still connected after removing [Formula: see text], is minimized and the total profit of the disconnected pairs by removing [Formula: see text] is at least [Formula: see text]. In this paper, we firstly consider the [Formula: see text]-PCMP in paths, and prove that it is [Formula: see text]-hard even when [Formula: see text] for any [Formula: see text]. Then, we present a fully polynomial time approximation scheme (FPTAS) whose running time is [Formula: see text] for the [Formula: see text]-PCMP in paths. Based on this algorithm, we present an FPTAS whose running time is [Formula: see text] for the [Formula: see text]-PCMP in spider graphs, and an FPTAS whose running time is [Formula: see text] for the [Formula: see text]-PCMP in rings, respectively, where [Formula: see text] is the number of leaves of spider graph.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45350162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-21DOI: 10.1142/s0129054123500077
Zeynep Nihan Berberler, A. Aytaç
Networks are known to be prone to node or link failures. A central issue in the analysis of networks is the assessment of their stability and reliability. A central concept that is used to assess stability and robustness of the performance of a network under failures is that of vulnerability. Node and link residual closeness are novel sensitive graph based characteristics for network vulnerability analysis. Node and link residual closeness measure the vulnerability even when the removal of nodes or links does not disconnect the network. Node and link residual closeness are of great theoretical and practical significance to network design and optimization. In this paper, vulnerabilities of multipartite network type topologies to the failure of individual nodes and links are computed via node and link residual closeness which provides a much fuller characterization of the network. Then, how multipartite network type topologies perform when they suffer a node or a link failure is analyzed.
{"title":"Node and Link Vulnerability in Complete Multipartite Networks","authors":"Zeynep Nihan Berberler, A. Aytaç","doi":"10.1142/s0129054123500077","DOIUrl":"https://doi.org/10.1142/s0129054123500077","url":null,"abstract":"Networks are known to be prone to node or link failures. A central issue in the analysis of networks is the assessment of their stability and reliability. A central concept that is used to assess stability and robustness of the performance of a network under failures is that of vulnerability. Node and link residual closeness are novel sensitive graph based characteristics for network vulnerability analysis. Node and link residual closeness measure the vulnerability even when the removal of nodes or links does not disconnect the network. Node and link residual closeness are of great theoretical and practical significance to network design and optimization. In this paper, vulnerabilities of multipartite network type topologies to the failure of individual nodes and links are computed via node and link residual closeness which provides a much fuller characterization of the network. Then, how multipartite network type topologies perform when they suffer a node or a link failure is analyzed.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41565969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-18DOI: 10.1142/s0129054123430049
M. Holzer, C. Rauch
We investigate the state complexity of languages resulting from the cascade product of two minimal deterministic finite automata with [Formula: see text] and [Formula: see text] states, respectively. More precisely we study the magic number problem of the cascade product operation and show what range of complexities can be produced in case the left automaton is unary, that is, has only a singleton letter alphabet. Here we distinguish the cases when the involved automata are reset automata, permutation automata, permutation-reset automata, or do not have any restriction on their structure. It turns out that the picture on the obtained state complexities of the cascade product is diverse, and for all cases, except where the left automaton is a unary permutation(-reset) or a deterministic finite automaton without structural restrictions, and the right one is a reset automaton or a deterministic finite automaton without structural restrictions, we are able to identify state sizes that cannot be reached — these numbers are called “magic.”
{"title":"The Range of State Complexities of Languages Resulting from the Cascade Product — The Unary Case","authors":"M. Holzer, C. Rauch","doi":"10.1142/s0129054123430049","DOIUrl":"https://doi.org/10.1142/s0129054123430049","url":null,"abstract":"We investigate the state complexity of languages resulting from the cascade product of two minimal deterministic finite automata with [Formula: see text] and [Formula: see text] states, respectively. More precisely we study the magic number problem of the cascade product operation and show what range of complexities can be produced in case the left automaton is unary, that is, has only a singleton letter alphabet. Here we distinguish the cases when the involved automata are reset automata, permutation automata, permutation-reset automata, or do not have any restriction on their structure. It turns out that the picture on the obtained state complexities of the cascade product is diverse, and for all cases, except where the left automaton is a unary permutation(-reset) or a deterministic finite automaton without structural restrictions, and the right one is a reset automaton or a deterministic finite automaton without structural restrictions, we are able to identify state sizes that cannot be reached — these numbers are called “magic.”","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42807655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-14DOI: 10.1142/s012905412350003x
Xiangdong Cheng, X. Cao, Liqin Qian
Let [Formula: see text] be an odd prime number, [Formula: see text] for a positive integer [Formula: see text], let [Formula: see text] be the finite field with [Formula: see text] elements and [Formula: see text] be a primitive element of [Formula: see text]. We first give an orthogonal decomposition of the ring [Formula: see text], where [Formula: see text] and [Formula: see text] for a fixed integer [Formula: see text]. In addition, Galois dual of a linear code over [Formula: see text] is discussed. Meanwhile, constacyclic codes and cyclic codes over the ring [Formula: see text] are investigated as well. Remarkably, we obtain that if linear codes [Formula: see text] and [Formula: see text] are a complementary pair, then the code [Formula: see text] and the dual code [Formula: see text] of [Formula: see text] are equivalent to each other.
{"title":"Linear Codes and Linear Complementary Pairs of Codes Over a Non-Chain Ring","authors":"Xiangdong Cheng, X. Cao, Liqin Qian","doi":"10.1142/s012905412350003x","DOIUrl":"https://doi.org/10.1142/s012905412350003x","url":null,"abstract":"Let [Formula: see text] be an odd prime number, [Formula: see text] for a positive integer [Formula: see text], let [Formula: see text] be the finite field with [Formula: see text] elements and [Formula: see text] be a primitive element of [Formula: see text]. We first give an orthogonal decomposition of the ring [Formula: see text], where [Formula: see text] and [Formula: see text] for a fixed integer [Formula: see text]. In addition, Galois dual of a linear code over [Formula: see text] is discussed. Meanwhile, constacyclic codes and cyclic codes over the ring [Formula: see text] are investigated as well. Remarkably, we obtain that if linear codes [Formula: see text] and [Formula: see text] are a complementary pair, then the code [Formula: see text] and the dual code [Formula: see text] of [Formula: see text] are equivalent to each other.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47356782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-02DOI: 10.1142/s0129054123430013
Andreas Maletti, Teodora Nasz, Kevin Stier, Markus Ulbricht
Weighted tree automata (WTA) extend classical weighted automata (WA) to the non-linear structure of trees. The expressive power of WA with varying degrees of ambiguity has been extensively studied. Unambiguous, finitely ambiguous, and polynomially ambiguous WA over the tropical (as well as the arctic) semiring strictly increase in expressive power. The recently developed pumping results of Mazowiecki and Riveros (STACS 2018) are lifted to trees in order to achieve the same strict hierarchy for WTA over the tropical (as well as the arctic) semiring.
加权树自动机(Weighted tree automata, WTA)是将经典加权自动机扩展到树的非线性结构。不同程度歧义的WA的表达能力已被广泛研究。在热带(以及北极)半环上，无模糊、有限模糊和多项式模糊的WA在表达能力上严格增加。Mazowiecki和Riveros最近开发的泵送结果(STACS 2018)被提升到树木上，以便在热带(以及北极)半采油中实现同样严格的WTA等级。
{"title":"Ambiguity Hierarchies for Weighted Tree Automata","authors":"Andreas Maletti, Teodora Nasz, Kevin Stier, Markus Ulbricht","doi":"10.1142/s0129054123430013","DOIUrl":"https://doi.org/10.1142/s0129054123430013","url":null,"abstract":"Weighted tree automata (WTA) extend classical weighted automata (WA) to the non-linear structure of trees. The expressive power of WA with varying degrees of ambiguity has been extensively studied. Unambiguous, finitely ambiguous, and polynomially ambiguous WA over the tropical (as well as the arctic) semiring strictly increase in expressive power. The recently developed pumping results of Mazowiecki and Riveros (STACS 2018) are lifted to trees in order to achieve the same strict hierarchy for WTA over the tropical (as well as the arctic) semiring.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135423678","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-23DOI: 10.1142/s0129054123020021
Sebastian Maneth
{"title":"Preface","authors":"Sebastian Maneth","doi":"10.1142/s0129054123020021","DOIUrl":"https://doi.org/10.1142/s0129054123020021","url":null,"abstract":"","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44140166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-16DOI: 10.1142/s0129054122460108
Hao Sun, Longkun Guo, Xiaoyan Zhang
Neighbor diffusion effect (NDE) is a crucial aspect in advanced technology node that is well-known for its infamous consequence of significant performance decrement of the circuit. In this paper, we observe that NDE is caused by different diffusion heights (the number of fins) between two adjacent cells, and consider reducing the number of height differences in single row to reduce NDE violations. Ignoring the movement of the cells, we first propose a Hamiltonian-completion-based algorithm that reorders the cells in the row such that the number of NDE violations is reduced to a near-optimal value. Then, for a given fixed integer [Formula: see text], we devise an algorithm to compute the new positions of cells, such that the number of NDE violations is bounded by [Formula: see text] and the maximum displacement is minimized. Moreover, we extend our algorithm for legalization in multiple rows against mixed-height cells. Experimental results show that our algorithm reduces the NDE violations to a near-optimal minimum without any area overheads while achieving a better practical running time compared to baselines conforming with the theoretical analysis.
{"title":"Hamiltonian-Based Efficient Algorithms for Legalization with Neighbor Diffusion Effect","authors":"Hao Sun, Longkun Guo, Xiaoyan Zhang","doi":"10.1142/s0129054122460108","DOIUrl":"https://doi.org/10.1142/s0129054122460108","url":null,"abstract":"Neighbor diffusion effect (NDE) is a crucial aspect in advanced technology node that is well-known for its infamous consequence of significant performance decrement of the circuit. In this paper, we observe that NDE is caused by different diffusion heights (the number of fins) between two adjacent cells, and consider reducing the number of height differences in single row to reduce NDE violations. Ignoring the movement of the cells, we first propose a Hamiltonian-completion-based algorithm that reorders the cells in the row such that the number of NDE violations is reduced to a near-optimal value. Then, for a given fixed integer [Formula: see text], we devise an algorithm to compute the new positions of cells, such that the number of NDE violations is bounded by [Formula: see text] and the maximum displacement is minimized. Moreover, we extend our algorithm for legalization in multiple rows against mixed-height cells. Experimental results show that our algorithm reduces the NDE violations to a near-optimal minimum without any area overheads while achieving a better practical running time compared to baselines conforming with the theoretical analysis.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44766452","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-08DOI: 10.1142/s0129054122460017
Lin Li, Feng Zhang, Jiashuai Zhang, Qiang Hua, Chun-Ru Dong, C. Lim
Unsupervised image clustering is a challenging task in computer vision. Recently, various deep clustering algorithms based on contrastive learning have achieved promising performance and some distinguishable features representation were obtained only by taking different augmented views of same image as positive pairs and maximizing their similarities, whereas taking other images’ augmentations in the same batch as negative pairs and minimizing their similarities. However, due to the fact that there is more than one image in a batch belong to the same class, simply pushing the negative instances apart will result in inter-class conflictions and lead to the clustering performance degradation. In order to solve this problem, we propose a deep clustering algorithm based on supported nearest neighbors (SNDC), which constructs positive pairs of current images by maintaining a support set and find its k nearest neighbors from the support set. By going beyond single instance positive, SNDC can learn more generalized features representation with inherent semantic meaning and therefore alleviating inter-class conflictions. Experimental results on multiple benchmark datasets show that the performance of SNDC is superior to the state-of-the-art clustering models, with accuracy improvement of 6.2% and 20.5% on CIFAR-10 and ImageNet-Dogs respectively.
{"title":"A Novel Image Clustering Algorithm Based on Supported Nearest Neighbors","authors":"Lin Li, Feng Zhang, Jiashuai Zhang, Qiang Hua, Chun-Ru Dong, C. Lim","doi":"10.1142/s0129054122460017","DOIUrl":"https://doi.org/10.1142/s0129054122460017","url":null,"abstract":"Unsupervised image clustering is a challenging task in computer vision. Recently, various deep clustering algorithms based on contrastive learning have achieved promising performance and some distinguishable features representation were obtained only by taking different augmented views of same image as positive pairs and maximizing their similarities, whereas taking other images’ augmentations in the same batch as negative pairs and minimizing their similarities. However, due to the fact that there is more than one image in a batch belong to the same class, simply pushing the negative instances apart will result in inter-class conflictions and lead to the clustering performance degradation. In order to solve this problem, we propose a deep clustering algorithm based on supported nearest neighbors (SNDC), which constructs positive pairs of current images by maintaining a support set and find its k nearest neighbors from the support set. By going beyond single instance positive, SNDC can learn more generalized features representation with inherent semantic meaning and therefore alleviating inter-class conflictions. Experimental results on multiple benchmark datasets show that the performance of SNDC is superior to the state-of-the-art clustering models, with accuracy improvement of 6.2% and 20.5% on CIFAR-10 and ImageNet-Dogs respectively.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48434727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-08DOI: 10.1142/s0129054123500028
Baohua Niu, Shuming Zhou, Hong Zhang
Networks with distinct topological structures varies in the ability to resist different kinds of attacks. Node protection in terms of node importance is an effective way to ensure the reliable communication of networks. Thus, the protection of influential node detected by node importance evaluation is beneficial to strengthen the invulnerability and robustness of networks. In this work, the network agglomeration method based on node contraction is utilized to evaluate the influence of nodes and identify important nodes in five kinds of interconnection networks. We show that the agglomeration method, which takes both the degree and position into account, is valid and feasible for these five interconnection networks.
{"title":"Influential Node Identification of Network Based on Agglomeration Operation","authors":"Baohua Niu, Shuming Zhou, Hong Zhang","doi":"10.1142/s0129054123500028","DOIUrl":"https://doi.org/10.1142/s0129054123500028","url":null,"abstract":"Networks with distinct topological structures varies in the ability to resist different kinds of attacks. Node protection in terms of node importance is an effective way to ensure the reliable communication of networks. Thus, the protection of influential node detected by node importance evaluation is beneficial to strengthen the invulnerability and robustness of networks. In this work, the network agglomeration method based on node contraction is utilized to evaluate the influence of nodes and identify important nodes in five kinds of interconnection networks. We show that the agglomeration method, which takes both the degree and position into account, is valid and feasible for these five interconnection networks.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42435034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-06DOI: 10.1142/s0129054123500016
Fei Guo, Zilong Wang
Rotation symmetric Boolean functions are good candidates for stream ciphers because they have such advantages as simple structure, high operational speed and low implement cost. Recently, Mesnager et al. proposed for the first time an efficient method to construct balanced rotation symmetric Boolean functions with optimal algebraic immunity and good nonlinearity for an arbitrary even number of variables. However, the algebraic degree of their constructed [Formula: see text]-variable ([Formula: see text]) function is always less than the maximum value [Formula: see text]. In this paper, by modifying the support of Boolean functions from Mesnager et al.’s construction, we present two new constructions of balanced even-variable rotation symmetric Boolean functions with optimal algebraic immunity as well as higher algebraic degree and nonlinearity. The algebraic degree of Boolean functions in the first construction reaches the maximum value [Formula: see text] if [Formula: see text] is odd and [Formula: see text] or [Formula: see text] for integer [Formula: see text], while that of the second construction reaches the maximum value for all [Formula: see text]. Moreover, the nonlinearities of Boolean functions in both two constructions are higher than that of Mesnager et al.’s construction.
旋转对称布尔函数具有结构简单、运算速度快、实现成本低等优点，是流密码的理想选择。最近，Mesnager等人首次提出了一种构造对任意偶数变量具有最优代数免疫和良好非线性的平衡旋转对称布尔函数的有效方法。然而，它们构造的[公式:见文]-变量([公式:见文])函数的代数度总是小于最大值[公式:见文]。本文通过对Mesnager等构造的布尔函数的支持进行修正，给出了两种具有最优代数免疫、较高代数度和非线性的平衡偶变旋转对称布尔函数的新构造。当[Formula: see text]为奇数，[Formula: see text]或[Formula: see text]为整数[Formula: see text]时，第一种结构中的布尔函数的代数度达到最大值[公式:见文]，而第二种结构中的布尔函数的代数度达到所有[公式:见文]的最大值。而且，这两种构造的布尔函数的非线性程度都高于Mesnager等人的构造。
{"title":"Balanced Even-Variable Rotation Symmetric Boolean Functions with Optimal Algebraic Immunity, Maximum Algebraic Degree and Higher Nonlinearity","authors":"Fei Guo, Zilong Wang","doi":"10.1142/s0129054123500016","DOIUrl":"https://doi.org/10.1142/s0129054123500016","url":null,"abstract":"Rotation symmetric Boolean functions are good candidates for stream ciphers because they have such advantages as simple structure, high operational speed and low implement cost. Recently, Mesnager et al. proposed for the first time an efficient method to construct balanced rotation symmetric Boolean functions with optimal algebraic immunity and good nonlinearity for an arbitrary even number of variables. However, the algebraic degree of their constructed [Formula: see text]-variable ([Formula: see text]) function is always less than the maximum value [Formula: see text]. In this paper, by modifying the support of Boolean functions from Mesnager et al.’s construction, we present two new constructions of balanced even-variable rotation symmetric Boolean functions with optimal algebraic immunity as well as higher algebraic degree and nonlinearity. The algebraic degree of Boolean functions in the first construction reaches the maximum value [Formula: see text] if [Formula: see text] is odd and [Formula: see text] or [Formula: see text] for integer [Formula: see text], while that of the second construction reaches the maximum value for all [Formula: see text]. Moreover, the nonlinearities of Boolean functions in both two constructions are higher than that of Mesnager et al.’s construction.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47867507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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