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Most Complex Regular Right-Ideal Languages
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TL;DR: In this paper, it was shown that there exists a stream (sequence) (R_n : n \ge 3) of regular right ideal languages, where R_n has n left quotients and is most complex under the following measures of complexity.
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Abstract: A right ideal is a language L over an alphabet A that satisfies L = LA*. We show that there exists a stream (sequence) (R_n : n \ge 3) of regular right ideal languages, where R_n has n left quotients and is most complex under the following measures of complexity: the state complexities of the left quotients, the number of atoms (intersections of complemented and uncomplemented left quotients), the state complexities of the atoms, the size of the syntactic semigroup, the state complexities of the operations of reversal, star, and product, and the state complexities of all binary boolean operations. In that sense, this stream of right ideals is a universal witness.
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Citations
•Posted Content
A Survey on Operational State Complexity
TL;DR: In this paper, a survey of state complexity of individual regularity preserving language operations on regular and some subregular languages is presented, along with methods of estimation and approximation of more complex combined operations.
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Symmetric Groups and Quotient Complexity of Boolean Operations
Jason P. Bell,Janusz A. Brzozowski,Nelma Moreira,Rogério Reis +3 more
- 08 Jul 2014
TL;DR: The notion of uniform minimality to direct products of automata is generalized and the non-trivial connection between complexity of boolean operations and group theory is established.
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Complexity of Suffix-Free Regular Languages
Janusz A. Brzozowski,Marek Szykuła +1 more
- 01 Nov 2017
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 that meets the bound for product and whose restrictions to binary alphabets meet the bounds for star and boolean operations is exhibited.
Asymptotic Approximation for the Quotient Complexities of Atoms
Volker Diekert,Tobias Walter +1 more
TL;DR: The result for G was shown independently by Luke Schaeffer and the first author soon after the paper of Brzozowski and Tamm appeared in 2012; and the results here are valid for all five classes above.
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References
•Book
Syntactic semigroups
Jean-Eric Pin
- 01 Apr 1997
TL;DR: HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not, for teaching and research institutions in France or abroad, or from public or private research centers.
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Theory of átomata
Janusz A. Brzozowski,Hellis Tamm +1 more
- 19 Jul 2011
TL;DR: It is shown that every regular language defines a unique nondeterministic finite automaton (NFA), which is called "atomaton", whose states are the "atoms" of the language, that is, non-empty intersections of complemented or uncomplemented left quotients of thelanguage.
86
•Journal Article
Quotient Complexity of Regular Languages.
TL;DR: In this article, the problem of finding the quotient complexity of a language f(K,L) is considered, where K and L are regular languages and f is a regular operation.
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Syntactic complexity of ideal and closed languages
Janusz A. Brzozowski,Yuli Ye +1 more
- 19 Jul 2011
TL;DR: In this article, it was shown that nn-1 is a tight upper bound on the complexity of right ideals and prefix-closed regular languages, and that there exist left ideals and suffix-closed languages of syntactic complexity n n-1 + n - 1, and two-sided ideals and factor-closeness of syntactically complex regular languages with state complexity nn -2 + (n - 2)2n-2 + 1.
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