Equivalence in automata theory based on complete residuated lattice-valued logic

doi:10.1016/j.fss.2007.01.008

Fuzzy Sets and Systems

Volume 158, Issue 13, 1 July 2007, Pages 1407-1422

https://doi.org/10.1016/j.fss.2007.01.008 Get rights and content

Abstract

Automata theory based on complete residuated lattice-valued logic, called $L$ -valued finite automata (abbr. $L$ -VFAs), was introduced by the second author in 2001. In this paper we deal with the problems of equivalence between $L$ -valued sequential machines (abbr. $L$ -VSMs) and $L$ -VFAs. We define $L$ -VSMs, and particularly present a method for deciding the equivalence between $L$ -VSMs as well. An algorithm procedure for deciding the equivalence between $L$ -VSMs is constructed. We analyze the complexity and efficiency of the algorithm procedure and obtain the relative results to $L$ -VFAs. Moreover, the definitions of $L$ -valued languages (abbr. $L$ -VLs), and $L$ -valued regular languages (abbr. $L$ -VRLs) recognized by $L$ -VFAs are given, and some related properties are also discussed. We show an equivalent relation between $L$ -VRLs and conventional regular languages. By using $L$ -valued pumping lemma, we get a necessary and sufficient condition for an $L$ -VL to be nonconstant.

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^☆: This research is supported in part by the National Natural Science Foundation (Nos. 90303024, 60573006), the Higher School Doctoral Subject Foundation of Ministry of Education (No. 20050558015), and the Natural Science Foundation of Guangdong Province (Nos. 020146, 031541) of China.

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Equivalence in automata theory based on complete residuated lattice-valued logic☆

Abstract

J. Math. Anal. Appl.

Fuzzy Sets and Systems

Inform. Sci.

Inform. Sci.

Theoret. Comput. Sci.

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Inform. and Control

Inform. and Control

J. Math. Anal. Appl.

Inform. Sci.

Inform. Sci.

J. Math. Anal. Appl.

Sequential Machines and Automata Theory

Comments on the minimization of stochastic machines

IEEE Trans. Electron. Comput.

Introduction to Automata Theory, Languages and Computation