UP versus NP

Frank Vega (1)

1 Chavanasoft

We consider two new complexity classes that are called equivalent-P and equivalent-UP which have a close relation to the P versus NP problem. The class equivalent-P contains those languages that are ordered-pairs of instances of two specific problems in P, such that the elements of each ordered-pair have the same solution, which means, the same certificate. The class equivalent-UP has almost the same definition, but in each case we define the pair of languages explicitly in UP. In addition, we define the class double-NP as the set of languages that contain each instance of another language in NP, but in a double way, that is, in form of a pair with two identical instances. We demonstrate that double-NP is a subset of equivalent-P. Moreover, we prove that equivalent-UP is a subset of UP. In this way, we show not only that every problem in double-NP can be reformulated as the pairs of elements of two languages in P which have the same certificate, but we also show UP = NP.

Mots clés: P; UP; NP; logarithmic space; certificate

Domaines: Complexité [cs.CC]

Frank Vega. UP versus NP. 2016. ⟨hal-01304025v4⟩