Prefix-Free regular languages: closure properties, difference, and left quotient

Authors:
Monika Krausov$#225/
Affiliations:
Institute of Computer Science, P.J. Š/af$#225/rik University, Ko$#353/ice, Slovakia
Venue:
MEMICS'11 Proceedings of the 7th international conference on Mathematical and Engineering Methods in Computer Science
Year:
2011

Citing 4
Cited 0

The state complexities of some basic operations on regular languages

Theoretical Computer Science
Introduction to the Theory of Computation

Introduction to the Theory of Computation
Nondeterministic State Complexity of Basic Operations for Prefix-Free Regular Languages

Fundamenta Informaticae
State Complexity of Combined Operations for Prefix-Free Regular Languages

LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications

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Abstract

We show that the class of prefix-free languages is closed under intersection, difference, concatenation, square, and the k-th power and is not closed under complement, union, symmetric difference, Kleene star, reversal, cyclic shift, shuffle, and left quotient. Then, we study the state complexity of difference and left quotient of prefix-free regular languages. In both cases we get tight bounds. In the case of difference, the tight bound is mn−m−2n+4 and is met by binary languages. In the case of left quotient, the tight bound is 2n−1. The bound is met by languages over (n−1)-letter alphabet and cannot be met using smaller alphabets.