DMTCS Proceedings, Fifth Colloquium on Mathematics and Computer Science

Font Size:  Small  Medium  Large

Hopcroft's automaton minimization algorithm and Sturmian words

Jean Berstel, Luc Boasson, Olivier Carton


This paper is concerned with the analysis of the worst case behavior of Hopcroft's algorithm for minimizing deterministic finite state automata. We extend a result of Castiglione, Restivo and Sciortino. They show that Hopcroft's algorithm has a worst case behavior for the automata recognizing Fibonacci words. We prove that the same holds for all standard Sturmian words having an ultimately periodic directive sequence (the directive sequence for Fibonacci words is (1,1,…)).

Full Text: GZIP Compressed PostScript PostScript PDF

Valid XHTML 1.0 Transitional