The simulation of deterministic pushdown automata defined over a one-letter alphabet by finite state automata is investigated from a descriptional complexity point of view. We show that each unary deterministic pushdown automaton of size s can be simulated by a deterministic finite automaton with a number of states that is exponential in s. We prove that this simulation is tight. Furthermore, its cost cannot be reduced even if it is performed by a two-way nondeterministic automaton. We also prove that there are unary languages for which deterministic pushdown automata cannot be exponentially more succinct than finite automata. In order to state this result, we investigate the conversion of deterministic pushdown automata into context-free grammars. We prove that in the unary case the number of variables in the resulting grammar is strictly smaller than the number of variables needed in the case of nonunary alphabets.

Deterministic Pushdown Automata and Unary Languages / G. Pighizzini. - In: INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE. - ISSN 0129-0541. - 20:4(2009 Aug), pp. 629-645. [10.1142/S0129054109006784]

Deterministic Pushdown Automata and Unary Languages

G. Pighizzini
Primo
2009

Abstract

The simulation of deterministic pushdown automata defined over a one-letter alphabet by finite state automata is investigated from a descriptional complexity point of view. We show that each unary deterministic pushdown automaton of size s can be simulated by a deterministic finite automaton with a number of states that is exponential in s. We prove that this simulation is tight. Furthermore, its cost cannot be reduced even if it is performed by a two-way nondeterministic automaton. We also prove that there are unary languages for which deterministic pushdown automata cannot be exponentially more succinct than finite automata. In order to state this result, we investigate the conversion of deterministic pushdown automata into context-free grammars. We prove that in the unary case the number of variables in the resulting grammar is strictly smaller than the number of variables needed in the case of nonunary alphabets.
Descriptional complexity; Deterministic pushdown automata; Formal languages; Unary languages
Settore INF/01 - Informatica
ago-2009
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/67439
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