Descriptional complexity of pushdown store languages

  • Authors:

  • Andreas Malcher;Katja Meckel;Carlo Mereghetti;Beatrice Palano

  • Affiliations:

  • Institut für Informatik, Universität Giessen, Giessen, Germany;Institut für Informatik, Universität Giessen, Giessen, Germany;Dipartimento di Informatica, Università degli Studi di Milano, Milano, Italy;Dipartimento di Informatica, Università degli Studi di Milano, Milano, Italy

  • Venue:
  • DCFS'12 Proceedings of the 14th international conference on Descriptional Complexity of Formal Systems
  • Year:
  • 2012

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Abstract

It is well known that the pushdown store languageP(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.