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Circuits with monoidal gates

Extended abstract
  • Martin Beaudry
  • Pierre McKenzie
  • Pierre Péladeau
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 665)

Abstract

The problem of evaluating a circuit whose wires carry values from a fixed finite monoid M and whose non-input gates perform the monoid's operation is a natural extension to the well studied word problem over M, known to characterize NC1 and most of its subclasses in terms of the algebraic properties of M [2, 5, 4, 18]. Here we investigate the circuit evaluation problem over M. We show that the case of any nonsolvable monoid is P-complete, while circuits over solvable monoids can be evaluated in DET\(\subseteq\)NC2. We completely elucidate the case of the aperiodic monoids, which either lies in AC0, or is L-complete, or is NL-complete. Finally, we show that the case of the cyclic group q , for fixed q ≥ 2, is complete for the logspace counting class co-MOD q L.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Martin Beaudry
    • 1
  • Pierre McKenzie
    • 2
  • Pierre Péladeau
    • 3
  1. 1.Dép. de mathématíques et d'informatiqueUniversité de SherbrookeSherbrookeCanada
  2. 2.Dép. d'informatique et recherche opérationnelleUniversité de MontréalMontréalCanada
  3. 3.Laboratoire Informatique Théorique et Programmation, Institut Blaise PascalUniversité Paris 6ParisFrance

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