"Insignificant Choice Polynomial Time" -- P != NP

[Serguei Mokhov]

Posting for discussion by experts... A newest proof of P != NP:

https://arxiv.org/abs/2005.04598
by Klaus-Dieter Schewe

"""
In the late 1980s Gurevich conjectured that there is no logic
capturing PTIME, where "logic" has to be understood in a very general
way comprising computation models over isomorphism classes of
structures. In this article we first show that Gurevich's conjecture
is false. For this we extend the seminal research of Blass, Gurevich
and Shelah on {\em choiceless polynomial time} (CPT), which exploits
deterministic Abstract State Machines (ASMs) supporting unbounded
parallelism to capture the choiceless fragment of PTIME. CPT is
strictly included in PTIME. We observe that choice is unavoidable, but
that a restricted version suffices, which guarantees that the final
result is independent from the choice. Such a version of polynomially
bounded ASMs, which we call {\em insignificant choice polynomial time}
(ICPT) will indeed capture PTIME. This can be expressed in the logic
of non-deterministic ASMs plus inflationary fixed-point.
We use this result for our second contribution showing that PTIME
differs from NP. For the proof we build again on the research on CPT
first establishing a limitation on permutation classes of the sets
that can be activated by an ICPT computation. We then prove an
equivalence theorem, which characterises structures that cannot be
distinguished by the logic. In particular, this implies that SAT
cannot be decided by an ICPT computation.
"""

-- 
Serguei Mokhov