2009/05/08 by Giovanni Pighizzini, Pighizzini, Giovanni
Biochemistry, Genetics and Molecular Biology · Computer Science · #DNA and Biological Computing #F.1.1 #F.4.3 #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #Logic, programming, and type systems #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.0905.1248
openalex publication_date 2009/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.