State complexity of multiple Boolean and catenation operations April 2008 1 (original) (raw)

2008

Abstract

In the last decade, many new results in the area of state complexity have been obtained. Some are about Boolean operations, e.g. intersection, union and catenation and most of them focused on the cases of these operations on two languages. But in the practical applications, these operations are often required to be performed multiple times on three or more languages. The state complexity of these operations on k languages may not necessarily equal to the k-1 times direct combination of their state complexities on two languages. Thus, it is important to study the state complexities of multiple Boolean operations. Several results about the state complexities of intersection and union on k regular languages are given and proved here. The state complexities are also obtained in the cases of the catenations of three and four languages.

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