Quotient Complexity Of Star-Free Languages
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Date
2012-09-01
Authors
Brzozowski, Janusz
Liu, Bo
Journal Title
Journal ISSN
Volume Title
Publisher
World Scientific Publishing
Abstract
The quotient complexity, also known as state complexity, of a regular language is the number of distinct left quotients of the language. The quotient complexity of an operation is the maximal quotient complexity of the language resulting from the operation, as a function of the quotient complexities of the operands. The class of star free languages is the smallest class containing the finite languages and closed under boolean operations and concatenation. We prove that the tight bounds on the quotient complexities of union, intersection, difference, symmetric difference, concatenation and star for star-free languages are the same as those for regular languages, with some small exceptions, whereas 2(n) - 1 is a lower bound for reversal.
Description
Electronic version of an article published as International Journal of Foundations of Computer Science, 23(06), 2012, 1261–1276. http://dx.doi.org/10.1142/S0129054112400515 © World Scientific Publishing Company http://www.worldscientific.com/
Keywords
Aperiodic, automaton, complexity, language, operation, quotient, regular, star-free, state complexity