Minimization of lattice finite automata and its application to the decomposition of lattice languages

  • Authors:

  • Yongming Li;Witold Pedrycz

  • Affiliations:

  • College of Computer Science, Shaanxi Normal University, Xi'an 710062, China;Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Canada T6G2V4

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2007

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Abstract

In this paper, we study the minimization of lattice-valued finite automata with membership values in a distributive lattice and its relationships to the decomposition of lattice-valued regular languages. First, we establish the equivalence of (nondeterministic) lattice finite automata (LA) and deterministic lattice finite automata (DLA). Furthermore, we provide some characterization of lattice-valued regular languages and regular operations on family of lattice-valued regular languages. In the sequel, we introduce some notions that help clarify the concept of minimal DLAs and present an effective algorithm to obtain a minimal DLA from a given LA. Using the construction of minimal DLA, we introduce some simple classes of lattice-valued regular languages such as L-unitary and L-prefix ones. We demonstrate that any lattice-valued regular language can be decomposed as disjoint joins of such kinds of simple languages.