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The Bounded Weak Monadic Quantifier Alternation Hierarchy of Equational Graphs Is Infinite

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FST TCS 2000: Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1974))

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Abstract

Here we deal with the question of definability of infinite graphs up to isomorphism by weakmo nadic second-order formulæ. In this respect, we prove that the quantifier alternation bounded hierarchy of equational graphs is infinite. Two proofs are given: the first one is based on the Ehrenfeucht-Fraissé games; the second one uses the arithmetical hierarchy. Next, we give a new proof of the Thomas’s result according to which the bounded hierarchy of the weakmo nadic second-order logic of the complete binary tree is infinite.

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Author information

Authors and Affiliations

  1. LaBRI, Université Bordeaux I, Bordeaux

    Olivier Ly

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  1. Olivier Ly
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology, Delhi, Hauz Khas, 110016, New Delhi, India

    Sanjiv Kapoor  & Sanjiva Prasad  & 

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Ly, O. (2000). The Bounded Weak Monadic Quantifier Alternation Hierarchy of Equational Graphs Is Infinite. In: Kapoor, S., Prasad, S. (eds) FST TCS 2000: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2000. Lecture Notes in Computer Science, vol 1974. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44450-5_15

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  • DOI: https://doi.org/10.1007/3-540-44450-5_15

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41413-1

  • Online ISBN: 978-3-540-44450-3

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