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Probabilistic Input-Driven Pushdown Automata

Authors Alex Rose , Alexander Okhotin

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Author Details

Alex Rose
  • Department of Mathematics and Computer Science, Saint Petersburg State University, Russia
Alexander Okhotin
  • Department of Mathematics and Computer Science, Saint Petersburg State University, Russia

Funding

This work was supported by the Russian Science Foundation, project 23-11-00133.

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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)
https://doi.org/10.4230/LIPIcs.MFCS.2023.78

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Probabilistic computation
  • Theory of computation → Formal languages and automata theory
Keywords
  • Finite automata
  • probabilistic automata
  • input-driven automata
  • visibly pushdown automata
  • state complexity

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