STATE COMPLEXITY AND THE MONOID OF TRANSFORMATIONS OF A FINITE SET

Author:

KRAWETZ BRYAN1,LAWRENCE JOHN2,SHALLIT JEFFREY1

Affiliation:

1. School of Computer Science, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada

2. Department of Pure Mathematics, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada

Abstract

In this paper we consider the state complexity of an operation on formal languages, root(L). This naturally entails the discussion of the monoid of transformations of a finite set. We obtain good upper and lower bounds on the state complexity of root(L) over alphabets of all sizes. As well, we present an application of these results to the problem of 2DFA-DFA conversion.

Publisher

World Scientific Pub Co Pte Lt

Subject

Computer Science (miscellaneous)

Reference17 articles.

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3. J. Dénes, Permutations: Actes du Colloque sur Les Permutations, (1972) (Gauthier-Villars, 1972) pp. 117–120.

4. M. Holzer and B. König, Proc. DLT 2002, LNCS 2450 (Springer-Verlag, 2003) pp. 258–269.

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