It is well known that the pushdown store language P(M) of a pushdown automaton (PDA) M — i.e., the language consisting of words occurring on the pushdown along accepting computations of M — is a regular language. Here, we design succinct nondeterministic finite automata (NFA) accepting P(M). In detail, an upper bound on the size of an NFA for P(M) is obtained, which is quadratic in the number of states and linear in the number of pushdown symbols of M. Moreover, this upper bound is shown to be asymptotically optimal. Then, several restricted variants of PDA are considered, leading to improved constructions. In all cases, we prove the asymptotical optimality of the size of the resulting NFA. Finally, we apply our results to decidability questions related to PDA, and obtain solutions in deterministic polynomial time.
Descriptional complexity of pushdown store languages / A. Malcher, K. Meckel, C. Mereghetti, B. Palano (LECTURE NOTES IN COMPUTER SCIENCE). - In: Descriptional Complexity of Formal Systems / [a cura di] M. Kutrib, N. Moreira, R. Reis. - Berlin : Springer, 2012. - ISBN 9783642316227. - pp. 209-221 (( Intervento presentato al 14. convegno International Workshop on Descriptional Complexity of Formal Systems tenutosi a Braga nel 2012 [10.1007/978-3-642-31623-4_16].
Descriptional complexity of pushdown store languages
C. MereghettiPenultimo
;B. PalanoUltimo
2012
Abstract
It is well known that the pushdown store language P(M) of a pushdown automaton (PDA) M — i.e., the language consisting of words occurring on the pushdown along accepting computations of M — is a regular language. Here, we design succinct nondeterministic finite automata (NFA) accepting P(M). In detail, an upper bound on the size of an NFA for P(M) is obtained, which is quadratic in the number of states and linear in the number of pushdown symbols of M. Moreover, this upper bound is shown to be asymptotically optimal. Then, several restricted variants of PDA are considered, leading to improved constructions. In all cases, we prove the asymptotical optimality of the size of the resulting NFA. Finally, we apply our results to decidability questions related to PDA, and obtain solutions in deterministic polynomial time.File | Dimensione | Formato | |
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