Equivalence Problems for Circuits over Sets of Natural Numbers

  • Christian Glaßer
  • Katrin Herr
  • Christian Reitwießner
  • Stephen Travers
  • Matthias Waldherr
Conference paper

DOI: 10.1007/978-3-540-74510-5_15

Part of the Lecture Notes in Computer Science book series (LNCS, volume 4649)
Cite this paper as:
Glaßer C., Herr K., Reitwießner C., Travers S., Waldherr M. (2007) Equivalence Problems for Circuits over Sets of Natural Numbers. In: Diekert V., Volkov M.V., Voronkov A. (eds) Computer Science – Theory and Applications. CSR 2007. Lecture Notes in Computer Science, vol 4649. Springer, Berlin, Heidelberg

Abstract

We investigate the complexity of equivalence problems for { ∪ , ∩ , , + ,×}-circuits computing sets of natural numbers. These problems were first introduced by Stockmeyer and Meyer (1973). We continue this line of research and give a systematic characterization of the complexity of equivalence problems over sets of natural numbers. Our work shows that equivalence problems capture a wide range of complexity classes like NL, C=L, P,\({\rm \Pi^P_{2}}\), PSPACE, NEXP, and beyond. McKenzie and Wagner (2003) studied related membership problems for circuits over sets of natural numbers. Our results also have consequences for these membership problems: We provide an improved upper bound for the case of { ∪ , ∩ , , + ,×}-circuits.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Christian Glaßer
    • 1
  • Katrin Herr
    • 1
  • Christian Reitwießner
    • 1
  • Stephen Travers
    • 1
  • Matthias Waldherr
    • 1
  1. 1.Julius-Maximilians-Universität Würzburg, Theoretische InformatikGermany

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