SAT Has No Wizards
Abstract
Description
An (encoded) decision problem is a pair (E, F) where E=words that encode instances of the problem, F=words to be accepted. We use "strings" in a technical sense. With an NP problem (E, F) we associate the "logogram" of F relative to E, which conveys structural information on E, F, and how F is embedded in E. The kernel Ker(P) of a program P that solves (E, F) consists of those strings in the logogram that are used by P. There are relations between Ker(P) and the complexity of P. We develop an application to SAT that relies upon a property of internal independence of SAT. We show that SAT cannot have in its logogram strings serving as collective certificates. As consequence, all programs that solve SAT have same kernel.
19 pages
19 pages