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Summary: Propositional Logic for Circuit Classes
Klaus Aehlig1
and Arnold Beckmann2
1
Department of Computer Science
University of Toronto
10 King's College Road, Toronto, ON M5S 3G4, Canada
2
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
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