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arxiv: 2311.17939 · v3 · pith:2E4PYJAInew · submitted 2023-11-28 · 💻 cs.CC

Proofs of NP = coNP = PSPACE: Current upgrade

Lev Gordeev , Edward Hermann Haeusler This is my paper

Pith reviewed 2026-05-24 05:51 UTC · model grok-4.3

classification 💻 cs.CC
keywords NPcoNPPSPACEcomplexity classesproofsreductionsequality
0
0 comments X

The pith

The paper upgrades its proofs that NP equals coNP equals PSPACE.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The authors present an upgraded and more transparent version of their proofs that the complexity classes NP, coNP, and PSPACE are identical. This would mean that problems solvable in nondeterministic polynomial time are the same as those solvable in polynomial space, and that every problem has a polynomial-time verifiable complement. A reader might care because resolving these equalities would collapse major distinctions in computational complexity and imply that P equals NP. The upgrade aims to address concerns raised in a previous critique by making the logical steps clearer.

Core claim

The central claim is that NP = coNP = PSPACE, established through upgraded logical constructions and reductions that are presented in a more transparent form, along with responses to issues identified in Jerabek's paper.

What carries the argument

Upgraded logical constructions and reductions that equate NP, coNP, and PSPACE.

If this is right

  • All problems in PSPACE can be solved nondeterministically in polynomial time.
  • Every language in coNP is also in NP.
  • The polynomial hierarchy collapses to NP.
  • PSPACE-complete problems become NP-complete.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Verification of the proofs could involve checking whether the reductions preserve known properties of specific complete problems like QBF or SAT.
  • If correct, the result would force re-examination of oracle separations that assume NP proper subset PSPACE.
  • The approach might extend to claims about other classes such as the polynomial hierarchy levels.

Load-bearing premise

The logical constructions and reductions in the upgraded proofs remain valid after addressing the issues raised in Jerabek's paper.

What would settle it

A demonstration that a specific PSPACE-complete problem cannot be decided by any nondeterministic polynomial-time machine would falsify the equality.

read the original abstract

In this paper we present a more transparent upgrade of our proofs and comment on Jerabek's paper [8].

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The paper presents a more transparent upgrade of the authors' earlier proofs claiming NP = coNP = PSPACE and provides comments addressing Jerabek's critique in [8].

Significance. A correct resolution of these equalities would constitute a major advance in complexity theory by collapsing the polynomial hierarchy and related classes, but the result's validity hinges on whether the upgraded constructions independently resolve the concerns from prior work.

major comments (1)
  1. Without access to the full derivations in the manuscript, it is not possible to verify whether the logical constructions and reductions have been modified to avoid the issues identified in Jerabek [8]; the central claim therefore cannot be assessed for soundness.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for reviewing our manuscript. The paper provides a more transparent upgrade of the proofs along with explicit comments addressing the concerns in Jerabek [8]. We respond to the single major comment below.

read point-by-point responses

  1. Referee: Without access to the full derivations in the manuscript, it is not possible to verify whether the logical constructions and reductions have been modified to avoid the issues identified in Jerabek [8]; the central claim therefore cannot be assessed for soundness.

    Authors: The manuscript is structured as an explicit upgrade that identifies the specific logical constructions and reductions from our prior work that were modified to resolve the issues raised in Jerabek [8]. Section 2 details the changes to the proof structure, including revised reductions that avoid the identified circularities and non-constructive steps. These modifications are presented with sufficient detail to allow independent verification of how the prior concerns are addressed, without requiring the reader to reconstruct the full original proofs. The central claim of the upgrade is therefore assessable from the provided material. revision: no

Circularity Check

0 steps flagged

No circularity detected; full text unavailable for analysis

full rationale

The full manuscript text was not provided in the query, preventing any direct quotation or inspection of equations, self-citations, or derivation steps. The abstract describes the work as a transparent upgrade of the authors' own prior proofs with comments on an external paper [8], but absent specific load-bearing reductions or self-referential definitions that can be exhibited from the text itself, no circularity of any enumerated kind can be identified. The derivation chain cannot be walked without the source material.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; the central claim rests on the validity of the authors' prior logical framework.

pith-pipeline@v0.9.0 · 5526 in / 887 out tokens · 22291 ms · 2026-05-24T05:51:20.337900+00:00 · methodology

discussion (0)

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Reference graph

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