Book Chapter10.1007/978-3-642-25929-6_9
Basic operations on binary suffix-free languages
Roland Cmorik,Galina Jir,skov +2 more
- 14 Oct 2011
- pp 94-102
33
TL;DR: It is proved that the bound for reversal cannot be met by binary languages, and the upper bounds on the state complexity of all the boolean operations as well as of Kleene star are tight in the binary case.
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Abstract: We give a characterization of nondeterministic automata accepting suffix-free languages, and a sufficient condition on deterministic automata to accept suffix-free languages. Then we investigate the state complexity of basic operations on binary suffix-free regular languages. In particular, we show that the upper bounds on the state complexity of all the boolean operations as well as of Kleene star are tight in the binary case. On the other hand, we prove that the bound for reversal cannot be met by binary languages. This solves several open questions stated by Han and Salomaa (Theoret. Comput. Sci. 410, 2537-2548, 2009).
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Citations
•Posted Content
Quotient Complexity of Bifix-, Factor-, and Subword-Free Regular Languages
TL;DR: In this paper, the quotient complexity of intersection, union, difference, symmetric difference, concatenation, star, and reversal operations in the classes of bifix-, factor-, and subword-free regular languages was studied.
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Quotient Complexity of Bifix-, Factor-, and Subword-Free Regular Languages.
Janusz A. Brzozowski,Galina Jirásková,Baiyu Li,Joshua Smith +3 more
- 01 Jan 2011
TL;DR: In this article, the quotient complexity of intersection, union, difference, symmetric difference, concatenation, star, and reversal operations in the classes of bifix-, factor-, and subword-free regular languages was studied.
Quotient Complexity of Bifix-, Factor-, and Subword-free Regular Language
TL;DR: Tight upper bounds are found on the quotient complexity of intersection, union, difference, symmetric difference, concatenation, star, and reversal in these three classes of languages.
•Posted Content
Complexity of Suffix-Free Regular Languages
TL;DR: It is proved that there does not exist a most complex stream in the class of suffix-free regular languages, but one ternary suffix- free stream is exhibited that meets the bound for product and whose restrictions to binary alphabets meet the bounds for star and boolean operations.
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State Complexity of k-Union and k-Intersection for Prefix-Free Regular Languages
Hae Sung Eom,Yo-Sub Han,Kai Salomaa +2 more
- 22 Jul 2013
TL;DR: It is proved that the state complexity upper bound for k-union cannot be reached by languages over an alphabet with less than k symbols, and a tighter lower bound construction is presented using an alphabet of size k + 1 and a binary alphabet.
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TL;DR: This first handbook of formal languages gives a comprehensive up-to-date coverage of all important aspects and subareas of the field.
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Regular languages
Sheng Yu
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TL;DR: The class of regular sets is the smallest class of sets containing the finite sets which is closed under union, concatenation, and Kleene closure as discussed by the authors, and it is shown that any finite set can be easily generated by a regular grammar.
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