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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Vydané v:	Fuzzy sets and systems Ročník 495-496; s. 109108
Hlavní autori:	de Mendívil Grau, Aitor González, Fariña, Federico, Stanimirović, Stefan, Micić, Ivana, de Mendívil, José Ramón González
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier B.V 01.11.2024
Predmet:	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
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Popis
Shrnutí:	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