State Complexity of Combined Operations with Union, Intersection, Star and Reversal

Authors:
Yuan Gao;Sheng Yu
Affiliations:
(Correspd.) Department of Computer Science, The University of Western Ontario, London, Ontario, Canada N6A 5B7, ygao72@csd.uwo.ca;Department of Computer Science, The University of Western Ontario, London, Ontario, Canada N6A 5B7, syu@csd.uwo.ca
Venue:
Fundamenta Informaticae - Words, Graphs, Automata, and Languages; Special Issue Honoring the 60th Birthday of Professor Tero Harju
Year:
2012

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Abstract

In this paper, we study the state complexities of four combined operations: L*1 ∪ L2, L*1 ∩ L2, LR1 ∪ L2, and LR1 ∩ L2. The tight bounds for all these combined operations on regular languages are obtained and proved. We show that, as usual, they are different from the mathematical compositions of the state complexities of their individual participating operations.