License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2020.44
URN: urn:nbn:de:0030-drops-132850
URL: https://drops.dagstuhl.de/opus/volltexte/2020/13285/
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Droste, Manfred ; Dziadek, Sven ; Kuich, Werner

Nivat-Theorem and Logic for Weighted Pushdown Automata on Infinite Words

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LIPIcs-FSTTCS-2020-44.pdf (0.5 MB)


Abstract

Recently, weighted ω-pushdown automata have been introduced by Droste, Ésik, Kuich. This new type of automaton has access to a stack and models quantitative aspects of infinite words. Here, we consider a simple version of those automata. The simple ω-pushdown automata do not use ε-transitions and have a very restricted stack access. In previous work, we could show this automaton model to be expressively equivalent to context-free ω-languages in the unweighted case. Furthermore, semiring-weighted simple ω-pushdown automata recognize all ω-algebraic series.
Here, we consider ω-valuation monoids as weight structures. As a first result, we prove that for this weight structure and for simple ω-pushdown automata, Büchi-acceptance and Muller-acceptance are expressively equivalent. In our second result, we derive a Nivat theorem for these automata stating that the behaviors of weighted ω-pushdown automata are precisely the projections of very simple ω-series restricted to ω-context-free languages. The third result is a weighted logic with the same expressive power as the new automaton model. To prove the equivalence, we use a similar result for weighted nested ω-word automata and apply our present result of expressive equivalence of Muller and Büchi acceptance.

BibTeX - Entry

@InProceedings{droste_et_al:LIPIcs:2020:13285,
  author =	{Manfred Droste and Sven Dziadek and Werner Kuich},
  title =	{{Nivat-Theorem and Logic for Weighted Pushdown Automata on Infinite Words}},
  booktitle =	{40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)},
  pages =	{44:1--44:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-174-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{182},
  editor =	{Nitin Saxena and Sunil Simon},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/13285},
  URN =		{urn:nbn:de:0030-drops-132850},
  doi =		{10.4230/LIPIcs.FSTTCS.2020.44},
  annote =	{Keywords: Weighted automata, Pushdown automata, Infinite words, Weighted logic}
}

Keywords: Weighted automata, Pushdown automata, Infinite words, Weighted logic
Collection: 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)
Issue Date: 2020
Date of publication: 04.12.2020


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