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1.
Shan Zhao 《Information Sciences》2010,180(24):5115-5124
This paper deals with invertible matrices and semilinear spaces over commutative semirings. Some necessary and sufficient conditions for matrices to be invertible over commutative semirings are obtained. The condition under which the cardinality of each basis of semilinear space of n-dimensional vectors is n is given. In the end, the factor rank of matrices over semirings is investigated.  相似文献   
2.
研究一类特殊反环-加法幂等的除半环上的正则上三角矩阵.得到了正则上三角矩阵的一些性质,以及一类特殊的正则上三角矩阵.  相似文献   
3.
引入了半环上矩阵Moore-Penrose逆的概念.通过矩阵的T-序关系探讨半环上矩阵的Moore-Penrose逆,得到了矩阵满足T-序条件的若干性质,并且得到Moore-Penrose逆是其他广义逆的最大元或最小元.研究了幂等的非负偏序半环上的矩阵,得到了一个很有用的结论.  相似文献   
4.
Rong Su  Gerhard Woeginger 《Automatica》2011,47(10):2326-2329
In performance evaluation or supervisory control, we often encounter problems of determining the maximum or minimum string execution time for a finite language when estimating the worst-case or best-case performance. It has been shown in the literature that the time complexity for computing the maximum string execution time for a finite language is polynomial with respect to the size of an automaton recognizer of that language and the dimension of the corresponding resource matrices. In this paper we provide a more efficient algorithm to compute such maximum string execution time. Then we show that it is NP-complete to determine the minimum string execution time.  相似文献   
5.
Kleene代数在计算机科学中具有基础而特殊的重要性。在计算机工程应用中,Kleene代数及相关*-半环已被成功应用于基础安全分析、底层程序变换以及并行控制等许多领域。本文定义了几类具有Kleene*-运算的半环,给出了相关的等价刻画,并研究了这些*-半环之间的关系。  相似文献   
6.
设F是半域,在F上定义一类矩阵半环FN,讨论了FN的一些重要性质。  相似文献   
7.
Automata are the prime example of general systems over discrete spaces, and yet the theory of automata is fragmentary and it is not clear what makes a general structure an automaton. This paper investigates the logical foundations of automata relating it to the semantics of our notions of uncertainty, state and state-determined. A single framework is established for the conventional spectrum of automata: deterministic, probabilistic, fuzzy, and non-deterministic, which shows this set to be, in some sense, complete. Counter-examples are then developed to show that this spectrum alone is inadequate to describe the behaviour of certain forms of uncertain system. Finally a general formulation is developed based on the fundamental semantics of our notion of a state that shows that the logical Structure of an automaton must be at least a positive ordered semiring. The role of probability logic, its relationship to fuzzy logic, the rotes of topological models of automata, and the symmetry between inputs and outputs in hyperstate/hyperinput-determinedsystems are also discussed.  相似文献   
8.
Automata are the prime example of general systems over discrete spaces, and yet the theory of automata is fragmentary and it is not clear what makes a general structure an automaton. This paper investigates the logical foundations of automata relating it to the semantics of our notions of uncertainty, state and state-determined. A single framework is established for the conventional spectrum of automata: deterministic, probabilistic, fuzzy, and non-deterministic, which shows this set to be, in some sense, complete. Counter-examples are then developed to show that this spectrum alone is inadequate to describe the behaviour of certain forms of uncertain system. Finally a general formulation is developed based on the fundamental semantics of our notion of a state that shows that the logical structure of an automaton must be at least a positive ordered semiring. The role of probability logic, its relationship to fuzzy logic, the roles of topological models of automata, and the symmetry between inputs and outputs in hyperstate/hyperinput-determined systems are also discussed.  相似文献   
9.
对加法幂等半环上矩阵幂收敛的条件,以及加法幂等半环和坡代数赋权图路径优化问题与伴随矩阵幂的关系进行了研究,优化问题是在加法诱导的偏序≤下考虑的.特别,证明了对于选择的加法幂等半环E上的n阶赋权图G,如果其伴随矩阵A满足aij=e,且对G的任一基本回路p,权w(p)≤e,e是E的乘法幺元,则An-1的(i,j)分量表示从顶点i到j的所有路径的权在偏序≤下的最大元,且最大元一定在某一基本路径上取得.坡代数赋权图的结果作为特例得到.最后给出了几个应用的实例.说明加法幂等半环赋权图的这类广义路径优化问题仍可用矩阵幂的方法来解.  相似文献   
10.
引入并研究了D-Clifford半群.刻画了其上的Domain算子.给出了"任意Domain半环S中的Domain格d(S)是否都是(co)-Heyting代数"这一公开问题的否定回答.证明了有限布尔格上仅能赋予惟一的Domain算子.  相似文献   
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