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.2019.38
URN: urn:nbn:de:0030-drops-116003
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11600/
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Droste, Manfred ; Dziadek, Sven ; Kuich, Werner

Greibach Normal Form for omega-Algebraic Systems and Weighted Simple omega-Pushdown Automata

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Abstract

In weighted automata theory, many classical results on formal languages have been extended into a quantitative setting. Here, we investigate weighted context-free languages of infinite words, a generalization of omega-context-free languages (Cohen, Gold 1977) and an extension of weighted context-free languages of finite words (Chomsky, Schützenberger 1963). As in the theory of formal grammars, these weighted languages, or omega-algebraic series, can be represented as solutions of mixed omega-algebraic systems of equations and by weighted omega-pushdown automata.
In our first main result, we show that mixed omega-algebraic systems can be transformed into Greibach normal form. Our second main result proves that simple omega-reset pushdown automata recognize all omega-algebraic series that are a solution of an omega-algebraic system in Greibach normal form. Simple reset automata do not use epsilon-transitions and can change the stack only by at most one symbol. These results generalize fundamental properties of context-free languages to weighted languages.

BibTeX - Entry

@InProceedings{droste_et_al:LIPIcs:2019:11600,
  author =	{Manfred Droste and Sven Dziadek and Werner Kuich},
  title =	{{Greibach Normal Form for omega-Algebraic Systems and Weighted Simple omega-Pushdown Automata}},
  booktitle =	{39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)},
  pages =	{38:1--38:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-131-3},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{150},
  editor =	{Arkadev Chattopadhyay and Paul Gastin},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2019/11600},
  URN =		{urn:nbn:de:0030-drops-116003},
  doi =		{10.4230/LIPIcs.FSTTCS.2019.38},
  annote =	{Keywords: Weighted omega-Context-Free Grammars, Algebraic Systems, Greibach Normal Form, Weighted Automata, omega-Pushdown Automata}
}

Keywords: Weighted omega-Context-Free Grammars, Algebraic Systems, Greibach Normal Form, Weighted Automata, omega-Pushdown Automata
Collection: 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)
Issue Date: 2019
Date of publication: 04.12.2019

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