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Integer Weighted Automata on Infinite Words

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Developments in Language Theory (DLT 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12811))

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Abstract

In this paper we combine two classical generalisations of finite automata (weighted automata and automata on infinite words) into a model of integer weighted automata on infinite words and study the universality and the emptiness problems under zero weight acceptance. We show that the universality problem is undecidable for three-state automata by a direct reduction from the infinite Post correspondence problem. We also consider other more general acceptance conditions as well as their complements with respect to the universality and the emptiness problems. Additionally, we build a universal integer weighted automaton where the automaton is fixed and the word problem is undecidable.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Turku, Turku, Finland

    Vesa Halava & Tero Harju

  2. Department of Computer Science, University of Liverpool, Liverpool, UK

    Reino Niskanen & Igor Potapov

Authors
  1. Vesa Halava
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  2. Tero Harju
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  3. Reino Niskanen
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  4. Igor Potapov
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Corresponding author

Correspondence to Reino Niskanen .

Editor information

Editors and Affiliations

  1. University of Porto, Porto, Portugal

    Nelma Moreira

  2. University of Porto, Porto, Portugal

    Rogério Reis

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Halava, V., Harju, T., Niskanen, R., Potapov, I. (2021). Integer Weighted Automata on Infinite Words. In: Moreira, N., Reis, R. (eds) Developments in Language Theory. DLT 2021. Lecture Notes in Computer Science(), vol 12811. Springer, Cham. https://doi.org/10.1007/978-3-030-81508-0_14

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  • DOI: https://doi.org/10.1007/978-3-030-81508-0_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-81507-3

  • Online ISBN: 978-3-030-81508-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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