Complementing two-way finite automata

Authors:
Viliam Geffert;Carlo Mereghetti;Giovanni Pighizzini
Affiliations:
Department of Computer Science, P. J. Šafárik University, Košice, Slovakia;Dipartimento di Scienze dell'Informazione, Università degli Studi di Milano, Milano, Italy;Dipartimento di Informatica e Comunicazione, Università degli Studi di Milano, Milano, Italy
Venue:
DLT'05 Proceedings of the 9th international conference on Developments in Language Theory
Year:
2005

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Abstract

We study the relationship between the sizes of two-way finite automata accepting a language and its complement. In the deterministic case, by adapting Sipser's method, for a given automaton (2dfa) with n states we build an automaton accepting the complement with at most 4n states, independently of the size of the input alphabet. Actually, we show a stronger result, by presenting an equivalent 4n–state 2dfa that always halts. For the nondeterministic case, using a variant of inductive counting, we show that the complement of a unary language, accepted by an n–state two-way automaton (2nfa), can be accepted by an O(n8)–state 2nfa. Here we also make the 2nfa halting. This allows the simulation of unary 2nfa's by probabilistic Las Vegas two-way automata with O(n8) states.