A Bit of Nondeterminism Makes Pushdown Automata Expressive and Succinct.

Shibashis Guha, Ismaël Jecker, Karoliina Lehtinen, Martin Zimmermann

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

4 Citations (Scopus)


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 ExpTimecomplete. 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.

Original languageEnglish
Title of host publication46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)
EditorsFilippo Bonchi, Simon J. Puglisi
Publication date18 Aug 2021
Article number53
ISBN (Electronic)9783959772013
Publication statusPublished - 18 Aug 2021
Externally publishedYes

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  • Good-for-games
  • Pushdown automata
  • Succintness
  • Synthesis


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