Finite automata with undirected state graphs

IF 0.4 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Acta Informatica Pub Date : 2021-05-24 DOI:10.1007/s00236-021-00402-0

Martin Kutrib, Andreas Malcher, Christian Schneider

引用次数: 0

Abstract

We investigate finite automata whose state graphs are undirected. This means that for any transition from state p to q consuming some letter a from the input there exists a symmetric transition from state q to p consuming a letter a as well. So, the corresponding language families are subregular, and in particular in the deterministic case, subreversible. In detail, we study the operational descriptional complexity of deterministic and nondeterministic undirected finite automata. To this end, the different types of automata on alphabets with few letters are characterized. Then, the operational state complexity of the Boolean operations as well as the operations concatenation and iteration is investigated, where tight upper and lower bounds are derived for unary as well as arbitrary alphabets under the condition that the corresponding language classes are closed under the operation considered.

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具有无向状态图的有限自动机

研究状态图无向的有限自动机。这意味着对于任何从状态p到q的转换，从输入消耗一个字母a，存在一个从状态q到p的对称转换，也消耗一个字母a。因此，相应的语系是次规则的，特别是在确定性的情况下，是次可逆的。详细地研究了确定性和非确定性无向有限自动机的操作描述复杂性。为此，对具有少量字母的字母表上不同类型的自动机进行了表征。然后，研究了布尔运算的运算状态复杂度以及运算的连接和迭代，在相应的语言类在所考虑的运算下关闭的条件下，推导了一元和任意字母的紧上界和下界。

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

Acta Informatica 工程技术-计算机：信息系统

CiteScore

2.40

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： Acta Informatica provides international dissemination of articles on formal methods for the design and analysis of programs, computing systems and information structures, as well as related fields of Theoretical Computer Science such as Automata Theory, Logic in Computer Science, and Algorithmics. Topics of interest include: • semantics of programming languages • models and modeling languages for concurrent, distributed, reactive and mobile systems • models and modeling languages for timed, hybrid and probabilistic systems • specification, program analysis and verification • model checking and theorem proving • modal, temporal, first- and higher-order logics, and their variants • constraint logic, SAT/SMT-solving techniques • theoretical aspects of databases, semi-structured data and finite model theory • theoretical aspects of artificial intelligence, knowledge representation, description logic • automata theory, formal languages, term and graph rewriting • game-based models, synthesis • type theory, typed calculi • algebraic, coalgebraic and categorical methods • formal aspects of performance, dependability and reliability analysis • foundations of information and network security • parallel, distributed and randomized algorithms • design and analysis of algorithms • foundations of network and communication protocols.