P versus NP

Frank Vega (1)

1 Datys

There are some function problems in $FEXP-complete$, which has a corresponding function problem in $FNP$, such that each of these function problems in $FEXP-complete$ could be solved by some solution that has the corresponding function problem in $FNP$ for the same input, when the solution for this input in the $FEXP-complete$ function problem exists. This event is not necessary true when the solution for the input in the $FEXP-complete$ function problem does not exist, that is, the corresponding function problem in $FNP$ could not answer $''no"$ when the input does not have a solution in the respective function problem in $FEXP-complete$. In this way, if $FP = FNP$, then we might find the solutions by a polynomial time algorithm when those solutions exist for the inputs in some $FEXP-complete$ function problem, but this is not possible by the time hierarchy theorem. Therefore, $P \neq NP$.

Mots clés: Complexity classes; Turing Machines; NP; EXP

Domaines: Complexité [cs.CC]

Frank Vega. P versus NP. 2014. ⟨hal-00984866v1⟩