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DOI: 10.4230/LIPIcs.MFCS.2023.78

Probabilistic Input-Driven Pushdown Automata

Authors: Alex Rose and Alexander Okhotin

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract

A probabilistic variant of input-driven pushdown automata (IDPDA), also known as visibly pushdown automata, is introduced. It is proved that these automata can be determinized: an n-state probabilistic IDPDA that accepts each string with probability at least λ+δ or at most λ-δ is transformed to a deterministic IDPDA with at most (1 + 1/δ)^(n² - n) states recognizing the same language. An asymptotically close lower bound is provided: for infinitely many n, there is a probabilistic IDPDA with 4n + 1 states and δ = 1/(270n), such that every equivalent deterministic IDPDA needs at least 7^(n²/14) states. A few special cases of automata with reduced determinization complexity are identified.

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Alex Rose and Alexander Okhotin. Probabilistic Input-Driven Pushdown Automata. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 78:1-78:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{rose_et_al:LIPIcs.MFCS.2023.78,
  author =	{Rose, Alex and Okhotin, Alexander},
  title =	{{Probabilistic Input-Driven Pushdown Automata}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{78:1--78:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.78},
  URN =		{urn:nbn:de:0030-drops-186120},
  doi =		{10.4230/LIPIcs.MFCS.2023.78},
  annote =	{Keywords: Finite automata, probabilistic automata, input-driven automata, visibly pushdown automata, state complexity}
}

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Probabilistic Input-Driven Pushdown Automata

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