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Arithmetic Circuits and Polynomial Replacement Systems

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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))

Abstract

This paper addresses the problems of counting proof trees (as introduced by Venkateswaran and Tompa) and counting proof circuits, a related but seemingly more natural question. These problems lead to a common generalization of straight-line programs which we call polynomial replacement systems. We contribute a classification of these systems and we investigate their complexity. Diverse problems falling in the scope of this study include, for example, counting proof circuits, and evaluating ∪,+-circuits over the natural numbers. The former is shown #P-complete, the latter to be equivalent to a particular problem for replacement systems.

Research performed in part while on leave at the Universität Tübingen. Supported by the (German) DFG, the (Canadian) NSERC and the (Québec) FCAR.

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Author information

Authors and Affiliations

  1. Informatique et recherche opérationnelle, Université de Montréal, C.P. 6128 Succ. Centre-Ville, H3C 3J7, Montréal (Québec), Canada

    Pierre McKenzie

  2. Theoretische Informatik, Universität Würzburg, Am Hubland, 97074, Würzburg, Germany

    Heribert Vollmer & Klaus W. Wagner

Authors
  1. Pierre McKenzie
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  2. Heribert Vollmer
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  3. Klaus W. Wagner
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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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© 2000 Springer-Verlag Berlin Heidelberg

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McKenzie, P., Vollmer, H., Wagner, K.W. (2000). Arithmetic Circuits and Polynomial Replacement Systems. 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_13

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  • DOI: https://doi.org/10.1007/3-540-44450-5_13

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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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