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":" ","pages":""},"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":" ","pages":""},"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":"27 1","pages":"0"},"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":" ","pages":""},"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":" ","pages":""},"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":" ","pages":""},"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":" ","pages":""},"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":" ","pages":""},"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}
Pub Date : 2023-02-03DOI: 10.1142/s012905412246008x
Ao Zhao, Yang Zhou, Qian Liu
Both matroid means and knapsack means are variations of the classic [Formula: see text]-means problem in which we replace the cardinality constraint by matroid constraint or knapsack constraint respectively. In this paper, we give a 64-approximation algorithm for the matroid means problem and a [Formula: see text]-approximation algorithm for the knapsack means problem by using a simpler and more efficient rounding method. We improve previous 304 approximate ratio for the former and 20016 approximate ratio for the latter. In the rounding process, the application of integrality of the intersection of submodular (or matroid) polyhedra provides strong theoretical support. Moreover, we extend this method to matroid means problem with penalties, and give 64 and 880-approximate algorithms for uniform penalties and nonuniform penalties problem.
{"title":"Improved Approximation Algorithms for Matroid and Knapsack Means Problems","authors":"Ao Zhao, Yang Zhou, Qian Liu","doi":"10.1142/s012905412246008x","DOIUrl":"https://doi.org/10.1142/s012905412246008x","url":null,"abstract":"Both matroid means and knapsack means are variations of the classic [Formula: see text]-means problem in which we replace the cardinality constraint by matroid constraint or knapsack constraint respectively. In this paper, we give a 64-approximation algorithm for the matroid means problem and a [Formula: see text]-approximation algorithm for the knapsack means problem by using a simpler and more efficient rounding method. We improve previous 304 approximate ratio for the former and 20016 approximate ratio for the latter. In the rounding process, the application of integrality of the intersection of submodular (or matroid) polyhedra provides strong theoretical support. Moreover, we extend this method to matroid means problem with penalties, and give 64 and 880-approximate algorithms for uniform penalties and nonuniform penalties problem.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47347263","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 : 2023-02-01DOI: 10.1142/s012905412344001x
Mikhail Mrykhin, Alexander Okhotin
This paper establishes an analogue of Greibach’s hardest language theorem (“The hardest context-free language”, SIAM J. Comp., 1973, http://dx.doi.org/10.1137/0202025 ) for the classical family of LL([Formula: see text]) languages. The first result is that there is a language [Formula: see text] defined by an LL(1) grammar in the Greibach normal form, to which every language [Formula: see text] defined by an LL(1) grammar in the Greibach normal form can be reduced by a homomorphism, that is, [Formula: see text] if and only if [Formula: see text]. Then it is shown that this statement does not hold for the full class of LL([Formula: see text]) languages. The other hardest language theorem is then established in the following form: there is a language [Formula: see text] defined by an LL(1) grammar in the Greibach normal form, such that, for every language [Formula: see text] defined by an LL([Formula: see text]) grammar, with [Formula: see text], there exists a homomorphism [Formula: see text], for which [Formula: see text] if and only if [Formula: see text] [Formula: see text] [Formula: see text], where [Formula: see text] is a new symbol. The results lead to two robust language families: the closures of the languages defined by LL(1) grammars in the Greibach normal form under inverse homomorphisms and under inverse finite transductions.
本文建立了一个类似于Greibach最难语言定理(“最难上下文无关语言”，SIAM J. Comp.， 1973, http://dx.doi.org/10.1137/0202025)的经典LL(公式:见文本)语言族。第一个结果是存在一种由Greibach范式的LL(1)语法定义的语言[公式:见文]，而每一种由Greibach范式的LL(1)语法定义的语言[公式:见文]都可以被同态约简，即当且仅当[公式:见文]。然后证明，这一说法并不适用于LL([公式:见文本])语言的整个类。然后其他困难的语言定理是成立于以下形式:有一个语言(公式:看到文本)定义为一种LL(1)文法Greibach范式,这样,每一个语言(公式:看到文本)定义为一个会([公式:看到文本])语法,(公式:看到文本),存在一个同态(公式:看到文本),因为(公式:看到文本)当且仅当[公式:看到文本][公式:看到文本][公式:看到文本],在[公式:看到文本]是一个新的象征。这些结果导致了两个鲁棒语系:在逆同态和逆有限转导下，由LL(1)语法在Greibach范式下定义的语言闭包。
{"title":"The Hardest LL(k) Language","authors":"Mikhail Mrykhin, Alexander Okhotin","doi":"10.1142/s012905412344001x","DOIUrl":"https://doi.org/10.1142/s012905412344001x","url":null,"abstract":"This paper establishes an analogue of Greibach’s hardest language theorem (“The hardest context-free language”, SIAM J. Comp., 1973, http://dx.doi.org/10.1137/0202025 ) for the classical family of LL([Formula: see text]) languages. The first result is that there is a language [Formula: see text] defined by an LL(1) grammar in the Greibach normal form, to which every language [Formula: see text] defined by an LL(1) grammar in the Greibach normal form can be reduced by a homomorphism, that is, [Formula: see text] if and only if [Formula: see text]. Then it is shown that this statement does not hold for the full class of LL([Formula: see text]) languages. The other hardest language theorem is then established in the following form: there is a language [Formula: see text] defined by an LL(1) grammar in the Greibach normal form, such that, for every language [Formula: see text] defined by an LL([Formula: see text]) grammar, with [Formula: see text], there exists a homomorphism [Formula: see text], for which [Formula: see text] if and only if [Formula: see text] [Formula: see text] [Formula: see text], where [Formula: see text] is a new symbol. The results lead to two robust language families: the closures of the languages defined by LL(1) grammars in the Greibach normal form under inverse homomorphisms and under inverse finite transductions.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136019615","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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