Minimization of lattice finite automata and its application to the decomposition of lattice languages

Li, Yongming; Pedrycz, Witold

doi:10.1016/j.fss.2007.03.003

Cited by 72 publications

(44 citation statements)

References 25 publications

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“…Note that the traversal value of a run r of a simple LDFA is either ⊥ or ⊤, thus the value of r is induced by F . Simple LDFAs have been studied in the context of fuzzy logic and automata [18,23].…”

Section: Consider a Latticementioning

confidence: 99%

Minimizing Deterministic Lattice Automata

Halamish

Kupferman

2015

ACM Trans. Comput. Logic

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Abstract. Traditional automata accept or reject their input, and are therefore Boolean. In contrast, weighted automata map each word to a value from a semiring over a large domain. The special case of lattice automata, in which the semiring is a finite lattice, has interesting theoretical properties as well as applications in formal methods. A minimal deterministic automaton captures the combinatorial nature and complexity of a formal language. Deterministic automata are used in run-time monitoring, pattern recognition, and modeling systems. Thus, the minimization problem for deterministic automata is of great interest, both theoretically and in practice. For deterministic traditional automata on finite words, a minimization algorithm, based on the Myhill-Nerode right congruence on the set of words, generates in polynomial time a canonical minimal deterministic automaton. A polynomial algorithm is known also for deterministic weighted automata over the tropical semiring. For general deterministic weighted automata, the problem of minimization is open. In this paper we study minimization of deterministic lattice automata. We show that it is impossible to define a right congruence in the context of lattices, and that no canonical minimal automaton exists. Consequently, the minimization problem is much more complicated, and we prove that it is NP-complete. As good news, we show that while right congruence fails already for finite lattices that are fully ordered, for this setting we are able to combine a finite number of right congruences and generate a minimal deterministic automaton in polynomial time.

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Section: Consider a Latticementioning

confidence: 99%

Minimizing Deterministic Lattice Automata

Halamish

Kupferman

2015

ACM Trans. Comput. Logic

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“…Note that the traversal value of a run r of a simple LDFA is either ⊥ or , thus the value of r is induced by F . Simple LDFAs have been studied in the context of fuzzy logic and automata [17,22].…”

Section: Lattices and Lattice Automatamentioning

confidence: 99%

“…In fact, for the case of simple LDFA, the plan proceeds smoothly (see [17,22], where the problem is discussed by means of fuzzy automata) 3 …”

Section: Minimizing Ldfasmentioning

confidence: 99%

Minimizing Deterministic Lattice Automata

Halamish

Kupferman

2011

Foundations of Software Science and Computational Structures

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Abstract. Traditional automata accept or reject their input, and are therefore Boolean. In contrast, weighted automata map each word to a value from a semiring over a large domain. The special case of lattice automata, in which the semiring is a finite lattice, has interesting theoretical properties as well as applications in formal methods. A minimal deterministic automaton captures the combinatoric nature and complexity of a formal language. Deterministic automata are used in run-time monitoring, pattern recognition, and modeling systems. Thus, the minimization problem for deterministic automata is of great interest, both theoretically and in practice.For traditional automata on finite words, a minimization algorithm, based on the Myhill-Nerode right congruence on the set of words, generates in polynomial time a canonical minimal deterministic automaton. A polynomial algorithm is known also for weighted automata over the tropical semiring. For general deterministic weighted automata, the problem of minimization is open. In this paper we study minimization of lattice automata. We show that it is impossible to define a right congruence in the context of lattices, and that no canonical minimal automaton exists. Consequently, the minimization problem is much more complicated, and we prove that it is NP-complete. As good news, we show that while right congruence fails already for finite lattices that are fully ordered, for this setting we are able to combine a finite number of right congruences and generate a minimal deterministic automaton in polynomial time.

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“…Recently, there has been tremendous growth in research on fuzzy automata theory, theoretically [8][9][10]12] as well as practically [5,7,10,13]. Fuzzy Mealy machine is a kind of fuzzy automaton with outputs capabilities based on both the current state and the current input on similar lines to fuzzy automaton, fuzzy Mealy machine generalize classical Mealy machines, in the sense of partial (degree of) transition of states and outputs.This makes possible to tackled uncertainty in transition as well output.…”

Section: Introductionmentioning

confidence: 99%

On Properties of Fuzzy Mealy Machines

Morye¹,

Chaudhari²

2013

IJCA

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It has been shown that the problem of equivalent and minimization of fuzzy Mealy machines can be resolved via their algebraic study. However, no attention has paid to study fuzzy Mealy machines topologically. This paper introduces topology on the state set of a fuzzy Mealy machine and study of various kinds of fuzzy Mealy machines viz. cyclic, retrievable, strongly connected, with exchange property and connected through this topology. In addition, various products of fuzzy Mealy machines and their relationship in regards to aforementioned kinds of fuzzy Mealy machines are also studied.

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Minimization of lattice finite automata and its application to the decomposition of lattice languages

Cited by 72 publications

References 25 publications

Minimizing Deterministic Lattice Automata

Minimizing Deterministic Lattice Automata

Minimizing Deterministic Lattice Automata

On Properties of Fuzzy Mealy Machines

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