Equivalence in automata theory based on complete residuated lattice-valued logic

Xing, Hongyan; Qiu, Daowen; Liu, Fuchun; Fan, Zhixiang

doi:10.1016/j.fss.2007.01.008

Cited by 43 publications

(20 citation statements)

References 25 publications

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“…Note that the obtained results also hold for fuzzy languages and automata over a complete residuated lattice, which have been intensively studied in recent papers [7,8,10,11,21,[24][25][26][27]. Let us also note that fuzzy languages over a quantale L have a natural interpretation as power series on the underlying free monoid X Ã , with coefficients in the semiring reduct of L, but this approach completely differs than the approach proposed here.…”

Section: Introductionmentioning

confidence: 66%

Formal power series and regular operations on fuzzy languages

Ignjatović

Ćirić

2010

Information Sciences

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Section: Introductionmentioning

confidence: 66%

Formal power series and regular operations on fuzzy languages

Ignjatović

Ćirić

2010

Information Sciences

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“…[17,26,27,[54][55][56][63][64][65][66]). For undefined notions and notation we refer to [2,3,15,16,26,27,50,67].…”

Section: Preliminariesmentioning

confidence: 99%

Fuzzy relation equations and reduction of fuzzy automata

Ćirić

Stamenković

Ignjatović

et al. 2010

Journal of Computer and System Sciences

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We show that the state reduction problem for fuzzy automata is related to the problem of finding a solution to a particular system of fuzzy relation equations in the set of all fuzzy equivalences on its set of states. This system may consist of infinitely many equations, and finding its non-trivial solutions may be a very difficult task. For that reason we aim our attention to some instances of this system which consist of finitely many equations and are easier to solve. First, we study right invariant fuzzy equivalences, and their duals, the left invariant ones. We prove that each fuzzy automaton possesses the greatest right (resp. left) invariant fuzzy equivalence, which provides the best reduction by means of fuzzy equivalences of this type, and we give an effective procedure for computing this fuzzy equivalence, which works if the underlying structure of truth values is a locally finite residuated lattice. Moreover, we show that even better reductions can be achieved alternating reductions by means of right and left invariant fuzzy equivalences. We also study strongly right and left invariant fuzzy equivalences, which give worse reductions than right and left invariant ones, but whose computing is much easier. We give an effective procedure for computing the greatest strongly right (resp. left) invariant fuzzy equivalence, which is applicable to fuzzy automata over an arbitrary complete residuated lattice.

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“…Determinization of FFAs over a complete residuated lattice (introduced by Qiu [28,29,34,35]) was also considered by Ignjatović et al [16]. They study another determinization procedure, called the accessible fuzzy subset construction, which is an analogue of the well-known accessible subset construction.…”

Section: Related Workmentioning

confidence: 99%