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Algorithms for Ordinal Arithmetic

  • Conference paper
Automated Deduction – CADE-19 (CADE 2003)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2741))

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Abstract

Proofs of termination are essential for establishing the correct behavior of computing systems. There are various ways of establishing termination, but the most general involves the use of ordinals. An example of a theorem proving system in which ordinals are used to prove termination is ACL2. In ACL2, every function defined must be shown to terminate using the ordinals up to ε 0. We use a compact notation for the ordinals up to ε 0 (exponentially more succinct than the one used by ACL2) and define efficient algorithms for ordinal addition, subtraction, multiplication, and exponentiation. In this paper we describe our notation and algorithms, prove their correctness, and analyze their complexity.

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Author information

Authors and Affiliations

  1. Georgia Institute of Technology, College of Computing, CERCS Lab, 801 Atlantic Drive, Atlanta, Georgia, 30332, USA

    Panagiotis Manolios & Daron Vroon

Authors
  1. Panagiotis Manolios
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  2. Daron Vroon
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Editor information

Editors and Affiliations

  1. Theoretical Computer Science, TU Dresden, Germany

    Franz Baader

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Manolios, P., Vroon, D. (2003). Algorithms for Ordinal Arithmetic. In: Baader, F. (eds) Automated Deduction – CADE-19. CADE 2003. Lecture Notes in Computer Science(), vol 2741. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45085-6_19

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  • DOI: https://doi.org/10.1007/978-3-540-45085-6_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40559-7

  • Online ISBN: 978-3-540-45085-6

  • eBook Packages: Springer Book Archive

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