Automata theory based on complete residuated lattice-valued logic: Reduction and minimization

  • Authors:

  • Lihua Wu;Daowen Qiu

  • Affiliations:

  • Department of Computer Science, Zhongshan University, Guangzhou 510275, People's Republic of China;Department of Computer Science, Zhongshan University, Guangzhou 510275, People's Republic of China and SQIG--Instituto de Telecomunicaçöes, IST, TULisbon, Av. Rovisco Pais 1049-001, Lisb ...

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2010

Quantified Score

Hi-index 0.20

Visualization

Abstract

Automata theory based on complete residuated lattice-valued logic, called L-valued finite automata (L-VFAs), has been established by Qiu recently. In this paper, we define a kind of Mealy type of L-VFAs (MLFAs), a generalization of L-VFAs. Two kinds of statewise equivalence relations are introduced, and a minimal form is defined. We study the existence of the minimal form of an MLFA. Then, we show that any two states can be distinguished by some word with finite length. Also, a minimization algorithm of the MLFAs is presented. In addition, we obtain a minimization algorithm for L-VFAs as well. Finally, we define L-valued languages (L-VLs) and L-valued regular languages (L-VRLs) recognized by L-VFAs, and provide some properties of L-VRLs.