Right and left locally testable languages

Garcia, Pedro Castillo; Ruiz, José

doi:10.1016/s0304-3975(99)00108-5

Cited by 7 publications

(10 citation statements)

References 9 publications

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“…In [20], McNaughton and Papert define the class of locally testable languages as the set of languages that belong to the Boolean algebra generated by languages of the form uΣ * , Σ * u and Σ * uΣ * , where u ∈ Σ * . In [11], García and Ruiz define the classes of right and left locally testable languages as a generalization of the locally testable class. Figure 13 shows the inclusion relationship between these classes and the more restricted classes of finite and cofinite languages.…”

Section: Property 31mentioning

confidence: 99%

A sufficient condition to polynomially compute a minimum separating DFA

Parga

Garcia

López

2016

Information Sciences

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The computation of a minimal separating automaton (MSA) for regular languages has been studied from many different points of view, from synthesis of automata or Grammatical Inference to the minimization of incompletely specified machines or Compositional Verification. In the general case, the problem is NP-complete, but this drawback does not prevent the problem from having a real application in the above-mentioned fields. In this paper, we propose a sufficient condition that guarantees that the computation of the MSA can be carried out with polynomial time complexity.

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Section: Property 31mentioning

confidence: 99%

A sufficient condition to polynomially compute a minimum separating DFA

Parga

Garcia

López

2016

Information Sciences

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“…Thus the transition semigroup S is locally idempotent. If the identity xyx = xy [7] is not valid in eSe then for some node v ∈ Γ , some idempotent e and elements a, b ∈ S holds veaebe = veaebeae. So the node veaebe exists.…”

Section: Right Local Testabilitymentioning

confidence: 99%

“…Right [left] local testability was introduced and studied by König [9] and by Garcia and Ruiz [7]. These papers use different definitions of the conception and we follow [7] here Theorem 11 [7] A finite semigroup S is right [ For conception of local idempotency see, for instance, [6]. The varieties of semigroups defined by considered identities are located not far from atoms in the structure of idempotent varieties [4].…”

Section: Introductionmentioning

confidence: 99%

“…We present in this work necessary and sufficient condition for right [left] local testability for transition graph of the DFA and for the local idempotency of the transition semigroup on the corresponding transition graph. We improve necessary and sufficient condition for right [left] local testability from [7] for transition semigroup. On the base of these results, we introduced a polynomial time algorithm for the right [left] local testability problem for transition semigroup and transition graph of the deterministic finite automaton and for checking the transition graph of the automaton with locally idempotent semigroup.…”

Section: Introductionmentioning

confidence: 99%

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A Polynomial Time Algorithm for Left [Right] Local Testability

Trahtman¹

2003

Implementation and Application of Automata

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A right [left] locally testable language S is a language with the property that for some nonnegative integer k two words u and v in alphabet S are equal in the semigroup if (1) the prefix and suffix of the words of length k − 1 coincide, (2) the set of segments of length k of the words as well as 3) the order of the first appearance of these segments in prefixes [suffixes] coincide. We present necessary and sufficient condition for graph [semigroup] to be transition graph [semigroup] of the deterministic finite automaton that accepts right [left] locally testable language and necessary and sufficient condition for transition graph of the deterministic finite automaton with locally idempotent semigroup. We introduced polynomial time algorithms for the right [left] local testability problem for transition semigroup and transition graph of the deterministic finite automaton based on these conditions. Polynomial time algorithm verifies transition graph of automaton with locally idempotent transition semigroup.

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“…In 4 , t w o extensions of that family are de ned and c haracterized, the families of Right (RLT) and Left (LLT ) L oc ally T establelanguages. Informally, a language L is called k-R ightT estable (k-RT) (resp.…”

Section: Introductionmentioning

confidence: 99%