Polynomial crisp-minimization algorithm for fuzzy deterministic automata

Designing automata minimization algorithms is a significant topic in Automata Theory and Languages with practical applications. In this paper, we develop an efficient minimization algorithm for deterministic fuzzy finite automata over locally finite lattices. More precisely, the algorithm outputs an...

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Bibliographic Details
Published in:Fuzzy sets and systems Vol. 495-496; p. 109108
Main Authors: de Mendívil Grau, Aitor González, Fariña, Federico, Stanimirović, Stefan, Micić, Ivana, de Mendívil, José Ramón González
Format: Journal Article
Language:English
Published: Elsevier B.V 01.11.2024
Subjects:
Brzozowski's algorithm
Deterministic fuzzy automaton
Fuzzy átomaton
Locally finite lattices
Minimization algorithm
Deterministic fuzzy automaton
Minimization algorithm
Fuzzy átomaton
Locally finite lattices
Brzozowski's algorithm
ISSN:0165-0114
Online Access:Get full text
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Summary:Designing automata minimization algorithms is a significant topic in Automata Theory and Languages with practical applications. In this paper, we develop an efficient minimization algorithm for deterministic fuzzy finite automata over locally finite lattices. More precisely, the algorithm outputs an equivalent minimal crisp-deterministic fuzzy finite automaton for an input fuzzy deterministic finite automaton (FDfA). The running time of the proposed algorithm is polynomial for particular types of locally finite lattices, specifically for max-min-based complete residuated lattices. The intuition behind the proposed algorithm relies on the polynomial minimization algorithm's intuition for ordinary deterministic automata developed by Vazquez de Parga, Garcia, and Lopez (2013) [35]. The motivation for this study comes from the fact that the original algorithm's notions and meanings are lost in the context of fuzzy automata. Thus, we establish a new theoretical foundation that provides the correctness and the polynomial-time nature of this new crisp-minimization algorithm for FDfAs.
ISSN:0165-0114
DOI:10.1016/j.fss.2024.109108