Feasible interpolation for lifted sequents
نویسنده
چکیده
The idea of feasible interpolation for propositional proof systems is to derive lower bounds for propositional proofs using circuit lower bounds for Craig’s interpolant. However, as far as we know, proof systems such as constant-depth Frege do not admit feasible interpolation. We extend the notion of feasible interpolation so that it is admitted by a number of treelike propositional proof systems. This allows us to derive new lower bounds for treelike Frege proof systems and new conditional lower bounds for treelike Frege proof systems with modular counting connectives (all of constant depth). We obtain our results by augmenting Kraj́ıček’s argument from [Kra97] with the idea from Maciel and Pitassi [MP06].
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