Linear Circuits, Two-Variable Logic and Weakly Blocked Monoids

Following recent works connecting two-variable logic to circuits and monoids, we establish, for numerical predicate sets P satisfying a certain closure property, a one-to-one correspondence between FO[<, P]-uniform linear circuits, two-variable formulas with 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.

• Type: Conference
• Year: 2007
• Where: MFCS
• Authors: Christoph Behle, Andreas Krebs, Mark Mercer
• Keywords: Certain Closure Property, MFCS 2007, Numerical Predicate Set, P]-uniform Linear Circuits