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Resolution is Not Automatizable Unless W[P] is Tractable

Summary: Resolution is Not Automatizable Unless W[P]
is Tractable
Michael Alekhnovich  , Alexander A. Razborov y
October 2, 2001
We show that neither Resolution nor tree-like Resolution is autom-
atizable unless the class W[P] from the hierarchy of parameterized
problems is xed-parameter tractable by randomized algorithms with
one-sided 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 e∆cient 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


Source: Alekhnovich, Michael - Institute for Advanced Study, Princeton University


Collections: Mathematics; Computer Technologies and Information Sciences