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Equivalence Problems for Circuits over Sets of Natural Numbers

  • Christian Glaßer
  • Katrin Herr
  • Christian Reitwießner
  • Stephen Travers
  • Matthias Waldherr
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4649)

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.

Keywords

Natural Number Equivalence Problem Membership Problem Direct Predecessor Boolean Hierarchy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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