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Propositional Logic for Circuit Classes Klaus Aehlig1

Summary: Propositional Logic for Circuit Classes
Klaus Aehlig1
and Arnold Beckmann2
Department of Computer Science
University of Toronto
10 King's College Road, Toronto, ON M5S 3G4, Canada
Department of Computer Science
University of Wales Swansea
Singleton Park, Swansea, SA2 8PP, United Kingdom
Abstract. By introducing a parallel extension rule that is aware of inde-
pendence of the introduced extension variables, a calculus for quantified
propositional logic is obtained where heights of derivations correspond
to heights of appropriate circuits. Adding an uninterpreted predicate on
bit-strings (analog to an oracle in relativised complexity classes) this
statement can be made precise in the sense that the height of the most
shallow proof that a circuit can be evaluated is, up to an additive con-
stant, the height of that circuit.
The main tool for showing lower bounds on proof heights is a variant of


Source: Aehlig, Klaus T. - Institut für Informatik, Ludwig-Maximilians-Universität München
Beckmann, Arnold - Department of Computer Science, University of Wales Swansea


Collections: Computer Technologies and Information Sciences; Mathematics