Linear Circuits, Two-Variable Logic and Weakly Blocked Monoids

  • Christoph Behle
  • Andreas Krebs
  • Mark Mercer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4708)


Following recent works connecting two-variable logic to circuits and monoids, we establish, for numerical predicate sets Open image in new window satisfying a certain closure property, a one-to-one correspondence between \(FO[<,\ensuremath{\mathfrak{P}}]\)-uniform linear circuits, two-variable formulae with \(\ensuremath{\mathfrak{P}}\) predicates, and weak block products of monoids. In particular, we consider the case of linear TC0, majority quantifiers, and finitely typed monoids. This correspondence will hold for any numerical predicate set which is FO[ < ]-closed and whose predicates do not depend on the input length.


Closure Property Input Gate Output Gate Binary Predicate Majority Gate 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Christoph Behle
    • 1
  • Andreas Krebs
    • 1
  • Mark Mercer
    • 2
  1. 1.WSI - University of Tuebingen, Sand 13, 72076 TuebingenGermany
  2. 2.McGill University, MontrealCanada

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