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

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. Nivat-Theorem and Logic for Weighted Pushdown Automata on Infinite Words. In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, pp. 44:1-44:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
  • Theory of computation → Quantitative automata
  • Theory of computation → Automata over infinite objects
  • Theory of computation → Grammars and context-free languages
  • Weighted automata
  • Pushdown automata
  • Infinite words
  • Weighted logic


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