Lattice minimal automata and lattice reduced automata

Yang Wang

Zhi-wen Mo

pp. 251-257

in: Bing-yuan Cao, Cheng-yi Zhang, Tai-fu Li (eds), Fuzzy information and Engineering I, Berlin, Springer, 2009

Abstract

We apply lattice ordered monoids in the study of lattice finite automata, and obtain some results similar to the ones of fuzzy finite automata. In this paper, the concepts of lattice minimal automata and lattice reduced automata are put forward, and the relationship of them associated with an L-language is discussed. Moreover, the L-fuzzy equivalence relation on states is defined, and an algorithm to minimize the lattice finite automata is presented based on clustering states.