Complexity of Bifix-Free Regular Languages

Ferens, Robert; Szykuła, Marek

doi:10.1007/978-3-319-60134-2_7

Cited by 4 publications

(4 citation statements)

References 19 publications

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“…Since every bifix-free language has an empty quotient, the restricted and unrestricted cases for binary operations coincide. The results below were found recently [41]. Even though bifix-free languages are a subclass of suffix-free languages and there does not exist a most complex suffix-free stream, we do have a most complex bifix-free stream.…”

Section: Bifix-free Languagessupporting

confidence: 65%

“…Even though bifix-free languages are a subclass of suffix-free languages and there does not exist a most complex suffix-free stream, we do have a most complex bifix-free stream. This stream has an alphabet of size (n − 2) n−3 + (n − 3)2 n−3 − 1 [41], and the alphabet size cannot be reduced. The syntactic semigroup of this language is of size (n − 1)…”

Section: Bifix-free Languagesmentioning

confidence: 99%

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Towards a Theory of Complexity of Regular Languages

Brzozowski¹

2017

Preprint

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We survey recent results concerning the complexity of regular languages represented by their minimal deterministic finite automata. In addition to the quotient complexity of the language -which is the number of its (left) quotients, and is the same as its state complexity -we also consider the size of its syntactic semigroup and the quotient complexity of its atoms -basic components of every regular language. We then turn to the study of the quotient/state complexity of common operations on regular languages: reversal, (Kleene) star, product (concatenation) and boolean operations. We examine relations among these complexity measures. We discuss several subclasses of regular languages defined by convexity. In many, but not all, cases there exist "most complex" languages, languages satisfying all these complexity measures.

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Section: Bifix-free Languagessupporting

confidence: 65%

Section: Bifix-free Languagesmentioning

confidence: 99%

Towards a Theory of Complexity of Regular Languages

Brzozowski¹

2017

Preprint

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“…Finally, our results enabled establishing the existence of most complex bifix-free languages ( [12,13]).…”

Section: Discussionmentioning

confidence: 56%

“…These are languages that meet all the upper bounds on the state complexities of Boolean operations, product, star, and reversal, and also have maximal syntactic semigroups and most complex atoms [10]. In particular, the results from this paper enabled the study of most complex bifix-free languages [12].…”

Section: Introductionmentioning

confidence: 92%

Syntactic complexity of bifix-free regular languages

Szykuła

Wittnebel

2019

Theoretical Computer Science

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Syntactic Complexity of Bifix-Free Languages

Szykuła

Wittnebel

2017

Implementation and Application of Automata

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Abstract. We study the properties of syntactic monoids of bifix-free regular languages. In particular, we solve an open problem concerning syntactic complexity: We prove that the cardinality of the syntactic semigroup of a bifix-free language with state complexity n is at most (n−1) n−3 +(n−2) n−3 +(n−3)2 n−3 for n 6. The main proof uses a large construction with the method of injective function. Since this bound is known to be reachable, and the values for n 5 are known, this completely settles the problem. We also prove that (n − 2) n−3 + (n − 3)2 n−3 − 1 is the minimal size of the alphabet required to meet the bound for n 6. Finally, we show that the largest transition semigroups of minimal DFAs which recognize bifix-free languages are unique up to renaming the states.

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Complexity of Bifix-Free Regular Languages

Cited by 4 publications

References 19 publications

Towards a Theory of Complexity of Regular Languages

Towards a Theory of Complexity of Regular Languages

Syntactic complexity of bifix-free regular languages

Syntactic Complexity of Bifix-Free Languages

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