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. © 2012 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Malcher, A., Meckel, K., Mereghetti, C., & Palano, B. (2012). Descriptional complexity of pushdown store languages. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7386 LNCS, pp. 209–221). https://doi.org/10.1007/978-3-642-31623-4_16
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