## Interpolation Theorems, Lower Bounds for Proof Systems, and Independence Results for Bounded Arithmetic

Citations: | 88 - 2 self |

### BibTeX

@MISC{Krajícek_interpolationtheorems,,

author = {Jan Krajícek},

title = {Interpolation Theorems, Lower Bounds for Proof Systems, and Independence Results for Bounded Arithmetic},

year = {}

}

### Years of Citing Articles

### OpenURL

### Abstract

A proof of the (propositional) Craig interpolation theorem for cut-free sequent calculus yields that a sequent with a cut-free proof (or with a proof with cut-formulas of restricted form; in particular, with only analytic cuts) with k inferences has an interpolant whose circuit-size is at most k. We give a new proof of the interpolation theorem based on a communication complexity approach which allows a similar estimate for a larger class of proofs. We derive from it several corollaries: 1. Feasible interpolation theorems for the following proof systems: (a) resolution. (b) a subsystem of LK corresponding to the bounded arithmetic theory S 2 2 (ff). (c) linear equational calculus. (d) cutting planes. 2. New proofs of the exponential lower bounds (for new formulas) (a) for resolution ([15]). (b) for the cutting planes proof system with coefficients written in unary ([4]). 3. An alternative proof of the independence result of [43] concerning the provability of circuit-size lower bounds ...