Quotient complexities of atoms in regular ideal languages

Brzozowski, Janusz and Davies, Sylvie: Quotient complexities of atoms in regular ideal languages. Acta cybernetica, (22) 2. pp. 293-311. (2015)

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Abstract

A (left) quotient of a language L by a word w is the language w −1L = {x | wx ϵ L}. The quotient complexity of a regular language L is the number of quotients of L; it is equal to the state complexity of L, which is the number of states in a minimal deterministic finite automaton accepting L. An atom of L is an equivalence class of the relation in which two words are equivalent if for each quotient, they either are both in the quotient or both not in it; hence it is a non-empty intersection of complemented and uncomplemented quotients of L. A right (respectively, left and two-sided) ideal is a language L over an alphabet Σ that satisfies L = LΣ* (respectively, L = Σ*L and L = Σ*LΣ*). We compute the maximal number of atoms and the maximal quotient complexities of atoms of right, left and two-sided regular ideals.

Item Type: Article
Journal or Publication Title: Acta cybernetica
Date: 2015
Volume: 22
Number: 2
Page Range: pp. 293-311
ISSN: 0324-721X
Language: angol
DOI: https://doi.org/10.14232/actacyb.22.2.2015.4
Uncontrolled Keywords: Reakcióképesség kémiai
Additional Information: Bibliogr.: p. 309-311.
Date Deposited: 2016. Oct. 17. 10:36
Last Modified: 2018. Jun. 06. 18:38
URI: http://acta.bibl.u-szeged.hu/id/eprint/36234

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