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Preprints, Working Papers, ... Year : 2016

UP versus NP

Frank Vega
  • Function : Author

Abstract

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.
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Dates and versions

hal-01304025 , version 1 (19-04-2016)
hal-01304025 , version 2 (29-04-2016)
hal-01304025 , version 3 (01-08-2016)
hal-01304025 , version 4 (29-08-2016)
hal-01304025 , version 5 (24-09-2016)
hal-01304025 , version 6 (25-01-2017)
hal-01304025 , version 7 (24-09-2018)
hal-01304025 , version 8 (12-10-2018)

Identifiers

  • HAL Id : hal-01304025 , version 3

Cite

Frank Vega. UP versus NP. 2016. ⟨hal-01304025v3⟩
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