Simulating finite automata with context-free grammars

Authors:
Michael Domaratzki;Giovanni Pighizzini;Jeffrey Shallit
Affiliations:
Department of Computer Science, Queen's University Kingston, Kingston, ON, Canada K7L 3N6;Dipartimento di Scienze dell'Informazione, Università degli Studi di Milano, via Comelico 39, 20135 Milano, Italy;Department of Computer Science, University of Waterloo, Waterloo, ON, Canada N2L 3G1
Venue:
Information Processing Letters
Year:
2002

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Abstract

We consider simulating finite automata (both deterministic and nondeterministic) with context-free grammars in Chomsky normal form (CNF). We show that any unary DFA with n states can be simulated by a CNF grammar with O(n1/3) variables, and this bound is tight. We show that any unary NFA with n states can be simulated by a CNF grammar with O(n2/3) variables. Finally, for larger alphabets we show that there exist languages which can be accepted by an n-state DFA, but which require Ω(n/log n) variables in any equivalent CNF grammar.