ScholarLens Back to search
2019•viXraRequires access

Refutation of the Schaefer Theorem for the P, NP Problem (Undecided)

Colin James

Open publisher page 0 citations

Abstract

We evaluate the Schaefer theorem for the P, NP problem by two examples for Graph-SAT(Ψ ). Neither example is tautologous; while claimed to be different, they result in the same truth table values. (The injection of NP-intermediate does not describe our result.) This refutes NP-complete (and P, NP, NP-hard). We also evaluate the P, NP problem as based on P≤NP with the same result. Therefore P, NP, NP-complete, NP-hard, NP-intermediate form a non tautologous fragment of the universal logic VŁ4.

About this research paper

What this paper is about

We evaluate the Schaefer theorem for the P, NP problem by two examples for Graph-SAT(Ψ ). Neither example is tautologous; while claimed to be different, they result in the same truth table values. (The injection of NP-intermediate does not describe our result.) This refutes NP-complete (and P, NP, NP-hard). We also evaluate the P, NP problem as based on P≤NP with the same result. Therefore P, NP, NP-complete, NP-hard, NP-intermediate form a non tautologous fragment of the universal logic VŁ4.

Why it matters

A significance statement is not available in the OpenAlex record.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

We evaluate the Schaefer theorem for the P, NP problem by two examples for Graph-SAT(Ψ ). Neither example is tautologous; while claimed to be different, they result in the same truth table values. (The injection of NP-intermediate does not describe our result.) This refutes NP-complete (and P, NP, NP-hard). We also evaluate the P, NP problem as based on P≤NP with the same result. Therefore P, NP, NP-complete, NP-hard, NP-intermediate form a non tautologous fragment of the universal logic VŁ4.

Key concepts: NP-complete, P versus NP problem, Combinatorics, Mathematics, Discrete mathematics, Time complexity

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
Refutation of the Schaefer Theorem for the P, NP Problem (Undecided) — Research Paper | ScholarLens