Tight lower bounds in the length of word chains
Information Processing Letters
Two Families of Languages Related to ALGOL
Journal of the ACM (JACM)
Regularity and Related Problems for Deterministic Pushdown Automata
Journal of the ACM (JACM)
Two-way automata simulations and unary languages
Journal of Automata, Languages and Combinatorics
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Introduction to Formal Language Theory
Introduction to Formal Language Theory
Optimal Simulations between Unary Automata
SIAM Journal on Computing
Simulating finite automata with context-free grammars
Information Processing Letters
The Equivalence Problem for Deterministic Pushdown Automata is Decidable
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Economy of description by automata, grammars, and formal systems
SWAT '71 Proceedings of the 12th Annual Symposium on Switching and Automata Theory (swat 1971)
On the complexity of hopcroft’s state minimization algorithm
CIAA'04 Proceedings of the 9th international conference on Implementation and Application of Automata
Descriptional complexity of (un)ambiguous finite state machines and pushdown automata
RP'10 Proceedings of the 4th international conference on Reachability problems
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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 scan be simulated by a deterministic finite automaton with a number of states which 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 lower than the number of variables needed in the case of nonunary alphabets.