Converting two-way nondeterministic unary automata into simpler automata

Authors:
Viliam Geffert;Carlo Mereghetti;Giovanni Pighizzini
Affiliations:
Department of Computer Science, P.J. Safárik University, Jesenná 5, 04154 Kosice, Slovakia;Dipartimento di Informatica, Sistemistica e Comunicazione, Università degli Studi di Milano, Bicocca, via Bicocca degli Arcimboldi 8, 20126 Milano, Italy;Dipartimento di Scienze dell'Informazione, Università degli Studi di Milano, via Comelico 39, I-20135, Milano, Italy
Venue:
Theoretical Computer Science - Mathematical foundations of computer science
Year:
2003

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Abstract

We show that, on inputs of length exceeding 5n2, any n-state unary two-way nondeterministic finite automaton (2nfa) can be simulated by a (2n + 2)-state quasi-sweeping 2nfa. Such a result, besides providing a "normal form" for 2nfa's, enables us to get a subexponential simulation of unary 2nfa's by two-way deterministic finite automata (2dfa's). In fact, we prove that any n-state unary 2nfa can be simulated by a sweeping 2dfa with O(n ⌈log2(n+1)+3⌉) states.