 
Summary: Resolution is Not Automatizable Unless W[P]
is Tractable
Michael Alekhnovich , Alexander A. Razborov y
October 2, 2001
Abstract
We show that neither Resolution nor treelike Resolution is autom
atizable unless the class W[P] from the hierarchy of parameterized
problems is xedparameter tractable by randomized algorithms with
onesided error.
1. Introduction
The analysis of potential usefulness of proof search heuristics and automated
theorem proving procedures based on a proof system P amounts (on the
theoretical level) to the following two basic questions:
Question 1. Which theorems in principle possess eÆcient P proofs?
Question 2. How to nd the optimal (or, at least, nearly the optimal) proof
of a given theorem in P ?
The traditional proof complexity mostly dealt, and still deals with the rst
question. Recently, however, there has been a growing interest in the second
one, too. An additional motivation to study the complexity of nding optimal
Institute for Advanced Study, Princeton, US, misha@ias.edu. Supported by AMIAS
