A Kleene-Schützenberger Theorem for Trace Series over Bounded Lattices

IF 0.4 4区计算机科学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Fundamenta Informaticae Pub Date : 2011-04-01 DOI:10.3233/FI-2011-586

Martin Huschenbett

引用次数: 1

Abstract

We study weighted trace automata with weights in strong bimonoids. Traces form a generalization of words that allow to model concurrency; strong bimonoids are algebraic structures that can be regarded as “semirings without distributivity”. A very important example for the latter are bounded lattices, especially non-distributive ones. We show that if both operations of the bimonoid are locally finite, then the classes of recognizable and mc-rational trace series coincide and, in general, are properly contained in the class of c-rational series. Moreover, if, in addition, in the bimonoid the addition is idempotent and the multiplication is commutative, then all three classes coincide.

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有界格上迹级数的kleene - sch岑伯格定理

我们研究了强双峰中带权的加权迹自动机。跟踪形成了允许对并发性建模的单词的泛化;强双峰是一种代数结构，可以看作是“无分布的半环”。后者的一个非常重要的例子是有界格，特别是非分配格。我们证明了如果双模的两个运算都是局部有限的，那么可识别的轨迹级数和mc-有理的轨迹级数的类重合，并且一般地包含在c-有理的轨迹级数的类中。此外，如果在双模中加法是幂等的，乘法是交换的，那么这三个类是重合的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Fundamenta Informaticae 工程技术-计算机：软件工程

CiteScore

2.00

自引率

0.00%

发文量

审稿时长

9.8 months

期刊介绍： Fundamenta Informaticae is an international journal publishing original research results in all areas of theoretical computer science. Papers are encouraged contributing: solutions by mathematical methods of problems emerging in computer science solutions of mathematical problems inspired by computer science. Topics of interest include (but are not restricted to): theory of computing, complexity theory, algorithms and data structures, computational aspects of combinatorics and graph theory, programming language theory, theoretical aspects of programming languages, computer-aided verification, computer science logic, database theory, logic programming, automated deduction, formal languages and automata theory, concurrency and distributed computing, cryptography and security, theoretical issues in artificial intelligence, machine learning, pattern recognition, algorithmic game theory, bioinformatics and computational biology, quantum computing, probabilistic methods, algebraic and categorical methods.