Determinization of fuzzy automata by factorizations of fuzzy states and right invariant fuzzy quasi-orders

Stanimirović, Stefan; Ćirić, Miroslav; Ignjatović, Jelena

doi:10.1016/j.ins.2018.08.033

Cited by 15 publications

(15 citation statements)

References 33 publications

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“…Kirsten and Mäurer [23] show that their determinization algorithm of weighted automata is optimal using maximal factorizations and the zero-divisor-free condition (Theorem 3.3 in [23]). This behaviour has been corroborated in some determinization methods for fuzzy automata [15] [40]. The original Mohri's minimization algorithm for weighted automata over tropical semiring applies a maximal factorization [28].…”

Section: Let Nmentioning

confidence: 87%

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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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Section: Let Nmentioning

confidence: 87%

“…In fact, factorizations have allowed researchers to provide minimization algorithms [28][9] and determinization methods for weighted automata [23]. In the context of fuzzy automata, factorizations have been studied to obtain determinization methods [14][15] [40], and minimization algorithms for fuzzy automata [17][18] [41].…”

Section: Introductionmentioning

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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“…They have been used to model the indistinguishability of states of fuzzy finite automata, and have been applied in the state reduction and determinization of fuzzy automata (cf. above mentioned references and also [31,35,44]). The greatest right and left invariant fuzzy quasi-orders and equivalences were calculated in [14,15,43] by algorithms that approximate the greatest fixpoint by the means of the Kleene fixpoint theorem, and in [36] by partition refinement algorithms.…”

Section: Introductionmentioning

confidence: 88%

“…Further, we study weakly right and left invariant quasi-order and equivalence matrices, and give algorithms for their computation similar to those given for fuzzy automata in [43]. In the end, we show that right and left invariant matrices can be used in the determinization of weighted automata over additively idempotent, commutative and zero-divisor free semirings, as it was done for fuzzy automata in [44]. Determinization of automata is a well-elaborated problem with a long history, starting back from the paper of Rabin and Scott [41] in 1959.…”

Section: Introductionmentioning

confidence: 93%

Improved algorithms for computing the greatest right and left invariant Boolean matrices and their application

Stanimirović

Stamenković

Ćirić

2019

Filomat

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We define right and left invariant matrices as Boolean matrices that are solutions to certain systems of matrix equations and inequalities over additively idempotent semirings. We provide improved algorithms for computing the greatest right and left invariant equivalence and quasi-order matrices. The improvements are based on the usage of the well-known partition refinement technique. Afterwards, we present the application of right invariant matrices in the determinization of weighted automata over additively idempotent, commutative and zero-divisor free semirings. In particular, we provide improvements of the well-known determinization method of weighted automata over tropical semirings given by Mohri [Computational Linguistics 23 (2) (1997) 269-311].

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“…This model is widely used for modeling applications in hardware and software [5], and it is also essential for building compilers [4,6]. In recent years, several generalizations of the concept of finite automata have been presented, such as fuzzy automata [7,8,9,10,11], probabilistic automata [12,13,14], and quantum automata [15,16,17,18,19].…”

Section: Introductionmentioning

confidence: 99%

On typical hesitant fuzzy automata

Costa

Bedregal

2020

Soft Comput

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The idea of nondeterministic typical hesitant fuzzy automata is a generalization of the fuzzy automata presented by Costa and Bedregal. This paper, presents the sufficient and necessary conditions for a typical hesitant fuzzy language to be computed by nondeterministic typical hesitant fuzzy automata. Besides, the paper introduces a new class of Typical Hesitant Fuzzy Automata with crisp transitions, and we will show that this new class is equivalent to the original class introduced by Costa and Bedregal.

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Determinization of fuzzy automata by factorizations of fuzzy states and right invariant fuzzy quasi-orders

Cited by 15 publications

References 33 publications

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

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

Improved algorithms for computing the greatest right and left invariant Boolean matrices and their application

On typical hesitant fuzzy automata

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