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1. Finite Automata Theory with Membership Values in Lattices | |||
Li Yongming | |||
Computer Science and Technology 05 February 2010 | |||
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Abstract:In this paper, we study finite automata with membership values in a lattice, which are called lattice-valued finite automata. The extended subset construction of lattice-valued finite automata is introduced, then the equivalences between lattice-valued finite automata, lattice-valued deterministic finite automata and lattice-valued finite automata with varepsilon$-moves are proved. We give a simple characterization of lattice-valued languages recognized by lattice-valued finite automata, then we prove that the Kleene theorem holds in the frame of lattice-setting. A minimization algorithm of lattice-valued deterministic finite automata is presented. In particular, the role of the distributive law for the truth valued domain of finite automata is analyzed: the distributive law is not necessary to many constructions of lattice-valued finite automata, but it indeed provides some convenience in simply processing lattice-valued finite automata. | |||
TO cite this article:Li Yongming. Finite Automata Theory with Membership Values in Lattices[J]. |
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