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

Authors Manfred Droste, Sven Dziadek, Werner Kuich

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Manfred Droste
  • Institut für Informatik, Universität Leipzig, Germany
Sven Dziadek
  • Institut für Informatik, Universität Leipzig, Germany
Werner Kuich
  • Institut für Diskrete Mathematik und Geometrie, Technische Unversität Wien, Austria

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Manfred Droste, Sven Dziadek, and Werner Kuich. Greibach Normal Form for omega-Algebraic Systems and Weighted Simple omega-Pushdown Automata. In 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 150, pp. 38:1-38:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Automata over infinite objects
  • Theory of computation → Quantitative automata
  • Theory of computation → Grammars and context-free languages
  • Weighted omega-Context-Free Grammars
  • Algebraic Systems
  • Greibach Normal Form
  • Weighted Automata
  • omega-Pushdown Automata


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