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Descriptional Complexity of Pushdown Store Languages

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Descriptional Complexity of Formal Systems (DCFS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7386))

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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.

Partially supported by CRUI/DAAD under the project “Programma Vigoni: Descriptional Complexity of Non-Classical Computational Models.”

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Author information

Authors and Affiliations

  1. Institut für Informatik, Universität Giessen, Arndtstr. 2, 35392, Giessen, Germany

    Andreas Malcher & Katja Meckel

  2. Dipartimento di Informatica, Università degli Studi di Milano, via Comelico 39, 20135, Milano, Italy

    Carlo Mereghetti & Beatrice Palano

Authors
  1. Andreas Malcher
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  2. Katja Meckel
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  3. Carlo Mereghetti
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  4. Beatrice Palano
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Universität Giessen, Arndtstraße 2, 35392, Giessen, Germany

    Martin Kutrib

  2. Departamento de Ciência de Computadores, Universidade do Porto, Faculdade de Ciências, Rua do Campo Alegre 1021-1055, 4169-007, Porto, Portugal

    Nelma Moreira  & Rogério Reis  & 

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Malcher, A., Meckel, K., Mereghetti, C., Palano, B. (2012). Descriptional Complexity of Pushdown Store Languages. In: Kutrib, M., Moreira, N., Reis, R. (eds) Descriptional Complexity of Formal Systems. DCFS 2012. Lecture Notes in Computer Science, vol 7386. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31623-4_16

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  • DOI: https://doi.org/10.1007/978-3-642-31623-4_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31622-7

  • Online ISBN: 978-3-642-31623-4

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