DeepAI

# Separation of P and NP

There have been many attempts to solve the P versus NP problem. However, with a new proof method, already used in arXiv:2104.14316, P not equal NP can be proved. A time limit is set for an arbitrary Turing machine and an input word is rejected on a timeout. The time limit goes toward infinity. Due to the halting problem, whether a word is accepted can only be determined at runtime. It can be shown by Rice's theorem, if a finite set of words are to be checked, they all have to be tested by brute force.

04/28/2021

### Separation of PSPACE and EXP

This article shows that PSPACE not equal EXP. A simple but novel proof t...
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### Interpretation of NDTM in the definition of NP

In this paper, we interpret NDTM (NonDeterministic Turing Machine) used ...
04/30/2020

### A class of examples demonstrating that P is different from NP in the "P vs NP" problem

The CMI Millennium "P vs NP Problem" can be resolved e.g. if one shows a...
09/12/2018

### A Simple Elementary Proof of P=NP based on the Relational Model of E. F. Codd

The P versus NP problem is studied under the relational model of E. F. C...
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### Philosophical Solution to P=?NP: P is Equal to NP

The P=?NP problem is philosophically solved by showing P is equal to NP ...