Embargo
Finite determinization of fuzzy automata using a parametric product-based t-norm
(Elsevier, 2024) Micic, Ivana; Stanimirovic, Stefan; González de Mendívil Moreno, José Ramón; Ciric, Miroslav; Jancic, Zorana; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC
This paper presents a novel approach for the approximate determinization of fuzzy automata over the product structure. We introduce the parametric modification of the product t-norm in the pre-determinization setting. On the one hand, the behavior of a fuzzy automaton over the parametric t-norm differs from the behavior of the fuzzy automaton over the product t-norm only in words with a degree of acceptance below the given parameter. However, using the parametric t-norm, we obtain an algorithm that outputs a finite minimal deterministic fuzzy automaton whose behavior differs from the starting fuzzy automaton described above. By setting the parameter to a sufficiently small value, the proposed algorithm provides a deterministic fuzzy automaton with behavior that differs insignificantly from the starting fuzzy automaton, as the difference is achieved only for words accepted by the starting fuzzy automaton with an insignificant value. As a tradeoff, the proposed approach provides finite determinization, even when all other determinization methods would result in an infinite deterministic automaton. We support this fact with an illustrative example.
Embargo
Polynomial crisp-minimization algorithm for fuzzy deterministic automata
(Elsevier, 2024-11-01) González de Mendívil Grau, Aitor; Fariña Figueredo, Federico; Stanimirovic, Stefan; Micic, Ivana; González de Mendívil Moreno, José Ramón; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC
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.
Open Access
Finite Nerode construction for fuzzy automata over the product algebra
(Springer, 2023) Jancic, Zorana; Micic, Ivana; Stanimirovic, Stefan; González de Mendívil Moreno, José Ramón; Ciric, Miroslav; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
The Nerode's automaton of a given fuzzy automaton A is a crisp-deterministic fuzzy automaton obtained by determinization of A using the well-known accessible fuzzy subset construction. This celebrated construction of a crisp-deterministic fuzzy automaton has served as a basis for various determinization procedures for fuzzy automata. However, the drawback of this construction is that it may not be feasible when the underlying structure for fuzzy automata is the product algebra because it is not locally finite. This paper provides an alternative way to construct a Nerode-like fuzzy automaton when the input fuzzy automaton is defined over the product algebra. This construction is always finite, since the fuzzy language recognized by this fuzzy automaton has a finite domain. However, this new construction does not accept the same fuzzy language as the initial fuzzy automaton. Nonetheless, it differs only in words accepted to some very small degree, which we treat as irrelevant. Therefore, our construction is an excellent finite approximation of Nerode's automaton.
Open Access
Conditions for the existence of maximal factorizations
(Elsevier, 2020) Gerdjikov, Stefan; González de Mendívil Moreno, José Ramón; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Extending classical algorithms for ordinary weighted or string-to-string automata to automata with underlying more general algebraic structures is of significant practical and theoretical interest. However, the generalization of classical algorithms sets certain assumptions on the underlying structure. In this respect the maximal factorization turns out to be a sufficient condition for many practical problems, e.g. minimization and canonization. Recently, an axiomatic approach on monoid structures suggested that monoids with most general equalizer (mge-monoids) provide an alternative framework to achieve similar results. In this paper, we study the fundamental relation between monoids admitting a maximal factorization and mge-monoids. We describe necessary conditions for the existence of a maximal factorization and provide sufficient conditions for an mge-monoid to admit a maximal factorization.

González de Mendívil Moreno, José Ramón

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