The complexity of class TAUTOLOGY-NP

2018-04-17T13:09:13Z (GMT) by Frank Vega
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? This question was first mentioned in a letter written by John Nash to the National Security Agency in 1955. A precise statement of the P versus NP problem was introduced independently in 1971 by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this problem have failed. TAUTOLOGY-L is a problem of deciding given an instance x of a language L whether every possible appropriate answer for x is actually a solution in L. The class TAUTOLOGY-NP contains those languages TAUTOLOGY-L where L is in NP. Another major complexity class is NP-complete. To attack the P versus NP question the concept of NP-completeness has been very useful. We define the completeness of TAUTOLOGY-NP using the polynomial time reduction as well. We demonstrate there is a TAUTOLOGY-L language that is not only complete for TAUTOLOGY-NP, but it is also in P.