Determinization of fuzzy automata via factorization of fuzzy states

Mendívil, José Ramón González de; Garitagoitia, José Ramón

doi:10.1016/j.ins.2014.06.033

Cited by 27 publications

(22 citation statements)

References 27 publications

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“…A generalized concept of a deterministic fuzzy automaton is recently introduced in [7]. In future, we will try to study the categorical concepts for such automaton.…”

Section: Resultsmentioning

confidence: 99%

On a category of deterministic fuzzy automata

Tiwari

Pal

2019

Proceedings of the 2019 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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The purpose of the present work is to use the concepts of reachability and observability maps to provide a solution of a wellknown characterization of fuzzy regular languages. In between, we associate two deterministic fuzzy automata for a given deterministic fuzzy automaton and show that the reachability and observability maps of the given deterministic fuzzy automaton turn out to be morphisms in the category of deterministic fuzzy automata.

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“…A generalized concept of a deterministic fuzzy automaton is recently introduced in [7]. In future, we will try to study the categorical concepts for such automaton.…”

Section: Resultsmentioning

confidence: 99%

On a category of deterministic fuzzy automata

Tiwari

Pal

2019

Proceedings of the 2019 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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“…In addition, the k-th symbol in α is denoted by α(k) where, by convention, α(k) = ε when k < 1 or k > |α|. Taken into account such a notation, by (15), we can expand w * (q, α) as follows:…”

Section: Deterministic Finite Automata With Values On a Monoidmentioning

confidence: 99%

“…where w * () and ρ() are the extended monoid-transition function and final function provided in (15) and Definition 4. Following a similar reasoning as in the proof of Lemma 3, we have that w…”

Section: Asmentioning

confidence: 99%

Recognizability of languages via deterministic finite automata with values on a monoid: General Myhill-Nerode Theorem

de Mendívil,

Fariña

2021

Preprint

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This paper deals with the problem of recognizability of functions ℓ : Σ * → M that map words to values in the support set M of a monoid (M, •, 1). These functions are called M -languages. M -languages are studied from the aspect of their recognition by deterministic finite automata whose components take values on M (M -DFAs). The characterization of an M -language ℓ is based on providing a right congruence on Σ * that is defined through ℓ and a factorization on the set of all M -languages, L(Σ * , M ) (in short L). A factorization on L is a pair of functions (g, f ) such that, for each ℓ ∈ L, g(ℓ) • f (ℓ) = ℓ, where g(ℓ) ∈ M and f (ℓ) ∈ L. In essence, a factorization is a form of common factor extraction. In this way, a general Myhill-Nerode theorem, which is valid for any L(Σ * , M ), is provided. Basically, ℓ ∈ L is recognized by an M -DFA if and only if there exists a factorization on L, (g, f ), such that the right congruence on Σ * induced by the factorization (g, f ) and f (ℓ) ∈ L, has finite index. This paper shows that the existence of M -DFAs guarantees the existence of natural non-trivial factorizations on L without taking account any additional property on the monoid. In addition, the composition of factorizations is also a new factorization, and the composition of natural factorizations preserves the recognition capability of each individual natural factorization.

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“…In this section, we recall the concepts related to residuated lattices [5,39]; L-fuzzy relations [24,39]; L-fuzzy automata [7,23,36]; L-fuzzy languages [7,39], and Lfuzzy objects [23,24].…”

Section: Preliminariesmentioning

confidence: 99%

On L-fuzzy partitioned automata

Tiwari

Singh

2019

Proceedings of the 2019 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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This paper is towards the study of theory of fuzzy automata with fuzzy partitions. Specifically, we study the concept of the L-fuzzy partitioned automaton corresponding to a given L-fuzzy automaton. Further, we introduce the concept of a crisp-deterministic L-fuzzy automaton corresponding to the Lfuzzy partitioned automaton such that both accept the same L-fuzzy language. Finally, the notion of the fuzzified L-fuzzy partitioned automaton corresponding to a given L-fuzzy partitioned automaton is introduced and a characterization of its L-fuzzy language is given.

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Determinization of fuzzy automata via factorization of fuzzy states

Cited by 27 publications

References 27 publications

On a category of deterministic fuzzy automata

On a category of deterministic fuzzy automata

Recognizability of languages via deterministic finite automata with values on a monoid: General Myhill-Nerode Theorem

On L-fuzzy partitioned automata

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