State complexity and the monoid of transformations of a finite set

Authors:
Bryan Krawetz;John Lawrence;Jeffrey Shallit
Affiliations:
School of Computer Science, University of Waterloo;School of Computer Science, University of Waterloo;Department of Pure Mathematics, University of Waterloo
Venue:
CIAA'04 Proceedings of the 9th international conference on Implementation and Application of Automata
Year:
2004

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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.