Philosophical Solution to P=?NP: P is Equal to NP

TL;DR

This paper claims to solve the P=?NP problem by demonstrating that P equals NP within the MRAM computational model, arguing that the problem is scientific rather than mathematical and challenging previous assumptions.

Contribution

It introduces the MRAM model as a superior empirical framework for the P=?NP problem and argues that P equals NP in this model, contradicting traditional views.

Findings

P equals NP in the MRAM model

The P=?NP problem is a scientific, not mathematical, issue

Previous assumptions based on NDTMs are criticized

Abstract

The P=?NP problem is philosophically solved by showing P is equal to NP in the random access with unit multiply (MRAM) model. It is shown that the MRAM model empirically best models computation hardness. The P=?NP problem is shown to be a scientific rather than a mathematical problem. The assumptions involved in the current definition of the P?=NP problem as a problem involving non deterministic Turing Machines (NDTMs) from axiomatic automata theory are criticized. The problem is also shown to be neither a problem in pure nor applied mathematics. The details of The MRAM model and the well known Hartmanis and Simon construction that shows how to code and simulate NDTMs on MRAM machines is described. Since the computation power of MRAMs is the same as NDTMs, P is equal to NP. The paper shows that the justification for the NDTM P?=NP problem using a letter from Kurt Godel to John Von Neumann is incorrect by showing Von Neumann explicitly rejected automata models of computation hardness and used his computer architecture for modeling computation that is exactly the MRAM model. The paper argues that Deolalikar's scientific solution showing P not equal to NP if assumptions from statistical physics are used, needs to be revisited.