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A Bit of Nondeterminism Makes Pushdown Automata Expressive and Succinct

Authors Shibashis Guha , Ismaël Jecker , Karoliina Lehtinen , Martin Zimmermann

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Author Details

Shibashis Guha
  • Tata Institute of Fundamental Research, Mumbai, India
Ismaël Jecker
  • IST Austria, Klosterneuburg, Austria
Karoliina Lehtinen
  • CNRS, Aix-Marseille University and University of Toulon, LIS, Marseille, France
Martin Zimmermann
  • University of Liverpool, UK

Funding

  • Jecker, Ismaël: Funded by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 754411.
  • Lehtinen, Karoliina: Funded by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 892704.

Cite AsGet BibTex

Shibashis Guha, Ismaël Jecker, Karoliina Lehtinen, and Martin Zimmermann. A Bit of Nondeterminism Makes Pushdown Automata Expressive and Succinct. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 53:1-53:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.MFCS.2021.53

Abstract

We study the expressiveness and succinctness of good-for-games pushdown automata (GFG-PDA) over finite words, that is, pushdown automata whose nondeterminism can be resolved based on the run constructed so far, but independently of the remainder of the input word. We prove that GFG-PDA recognise more languages than deterministic PDA (DPDA) but not all context-free languages (CFL). This class is orthogonal to unambiguous CFL. We further show that GFG-PDA can be exponentially more succinct than DPDA, while PDA can be double-exponentially more succinct than GFG-PDA. We also study GFGness in visibly pushdown automata (VPA), which enjoy better closure properties than PDA, and for which we show GFGness to be ExpTime-complete. GFG-VPA can be exponentially more succinct than deterministic VPA, while VPA can be exponentially more succinct than GFG-VPA. Both of these lower bounds are tight. Finally, we study the complexity of resolving nondeterminism in GFG-PDA. Every GFG-PDA has a positional resolver, a function that resolves nondeterminism and that is only dependant on the current configuration. Pushdown transducers are sufficient to implement the resolvers of GFG-VPA, but not those of GFG-PDA. GFG-PDA with finite-state resolvers are determinisable.

Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
Keywords
  • Pushdown Automata
  • Good-for-games
  • Synthesis
  • Succintness

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