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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| Vydáno v: | Fuzzy sets and systems Ročník 495-496; s. 109108 |
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| Jazyk: | angličtina |
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Elsevier B.V
01.11.2024
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| ISSN: | 0165-0114 |
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| Abstract | 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. |
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| AbstractList | 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. |
| ArticleNumber | 109108 |
| Author | de Mendívil Grau, Aitor González Fariña, Federico Stanimirović, Stefan Micić, Ivana de Mendívil, José Ramón González |
| Author_xml | – sequence: 1 givenname: Aitor González orcidid: 0000-0001-8961-8736 surname: de Mendívil Grau fullname: de Mendívil Grau, Aitor González email: mendivil.aitor@gmail.com organization: Departamento de Estadística, Informática y Matemáticas, Universidad Pública de Navarra, Arrosadía s/n, Pamplona, 31006, Spain – sequence: 2 givenname: Federico surname: Fariña fullname: Fariña, Federico email: fitxi@unavarra.es organization: Departamento de Estadística, Informática y Matemáticas, Universidad Pública de Navarra, Arrosadía s/n, Pamplona, 31006, Spain – sequence: 3 givenname: Stefan orcidid: 0000-0003-3126-1265 surname: Stanimirović fullname: Stanimirović, Stefan email: stefan.stanimirovic@pmf.edu.rs organization: University of Niš, Faculty of Sciences and Mathematics, Višegradska 33, Niš, 18000, Serbia – sequence: 4 givenname: Ivana orcidid: 0000-0002-3816-9464 surname: Micić fullname: Micić, Ivana email: ivana.micic@pmf.edu.rs organization: University of Niš, Faculty of Sciences and Mathematics, Višegradska 33, Niš, 18000, Serbia – sequence: 5 givenname: José Ramón González orcidid: 0000-0003-3150-6437 surname: de Mendívil fullname: de Mendívil, José Ramón González email: mendivil@unavarra.es organization: Departamento de Estadística, Informática y Matemáticas, Universidad Pública de Navarra, Arrosadía s/n, Pamplona, 31006, Spain |
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| Keywords | Deterministic fuzzy automaton Minimization algorithm Fuzzy átomaton Locally finite lattices Brzozowski's algorithm |
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| SubjectTerms | Brzozowski's algorithm Deterministic fuzzy automaton Fuzzy átomaton Locally finite lattices Minimization algorithm |
| Title | Polynomial crisp-minimization algorithm for fuzzy deterministic automata |
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