Service Incident: New DOI registrations are working again. Re-registration of failed DOI registrations (~500) are still affected by the service incident at DataCite (our DOI registration agency).

There is a newer version of the record available.

Published November 22, 2019 | Version v9
Preprint Open

Logarithmic Space Verifiers on NP-complete

Creators

  • 1. Joysonic

Description

P versus NP is considered as one of the most important open problems in computer science. This consists in knowing the answer of the following question: Is P equal to NP? A precise statement of the P versus NP problem was introduced independently by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this problem have failed. NP is the complexity class of languages defined by polynomial time verifiers M such that when the input is an element of the language with its certificate, then M outputs a string which belongs to a single language in P. Another major complexity classes are L and NL. The certificate-based definition of NL is based on logarithmic space Turing machine with an additional special read-once input tape: This is called a logarithmic space verifier. NL is the complexity class of languages defined by logarithmic space verifiers M such that when the input is an element of the language with its certificate, then M outputs 1. To attack the P versus NP problem, the NP-completeness is a useful concept. We demonstrate there is an NP-complete language defined by a logarithmic space verifier M such that when the input is an element of the language with its certificate, then M outputs a string which belongs to a single language in L. In this way, we obtain if L is not equal to NL, then P = NP. In addition, we show that L is not equal to NL. Hence, we prove the complexity class P is equal to NP.

Files

manuscript.pdf

Files (419.5 kB)

Name Size Download all
md5:045cdc77cd00e76423e80fbefa13737c
419.5 kB Preview Download