Invariance of Initial Conditions in P and NP and Structural Incompatibility Between Problems with Hypothetical "Additional Hidden Properties" Allowing Partial Solutions to Each
Description
The question of the relationship between the classes P and NP is one of the central problems in modern complexity theory. The usual line of attack on the problem seeks either to find a polynomial-time algorithm for solving an NP-complete problem or to prove its nonexistence. In the present work, we will consider an alternative approach: we will explore the possibility of resolving the P versus NP problem by establishing a contradiction between the necessary conditions for efficiently solving different NP-complete problems. That is, if a solution is found for one problem through some new hidden property, this property would be in conflict with an analogous property needed to solve another problem. The focus will be on the role of hidden properties in the input of the problems and their impact on the possibility of universal mutual reduction between them.