A Critique of "Solving the P/NP Problem Under Intrinsic Uncertainty", arXiv:0811.0463

Andrew Keenan Richardson; Cole Arthur Brown

Home/Archive/arXiv

arXiv · 0904.3927

A Critique of "Solving the P/NP Problem Under Intrinsic Uncertainty", arXiv:0811.0463

Andrew Keenan Richardson·Cole Arthur Brown

View original source ↗Read source document ↗Export metadata ↓

Abstract

Although whether P equals NP is an important, open problem in computer science, and although Jaeger's 2008 paper, "Solving the P/NP Problem Under Intrinsic Uncertainty" (arXiv:0811.0463) presents an attempt at tackling the problem by discussing the possibility that all computation is uncertain to some degree, there are a number of logical oversights present in that paper which preclude it from serious consideration toward having resolved P-versus-NP. There are several differences between the model of computation presented in Jaeger's paper and the standard model, as well as several bold assumptions that are not well supported in Jaeger's paper or in the literature. In addition, we find several omissions of rigorous proof that ultimately weaken this paper to a point where it cannot be considered a candidate solution to the P-versus-NP problem.

Explore related subjects

cs.CC

Keep this discovery

BibTeX RIS

Andrew Keenan Richardson, Cole Arthur Brown. 2009-04-24. A Critique of "Solving the P/NP Problem Under Intrinsic Uncertainty", arXiv:0811.0463. https://arxiv.org/abs/0904.3927

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

The Computational Complexity of Holant Problems on 4-regular Graphs from the Stable Subgroup Sequence of $SL(2,\mathbb{C})$

The Holant framework provides a general setting for studying counting problems and includes graph homomorphisms (\#GH) and counting constraint satisfaction problems (\#CSP) as special cases. Over the past twenty years, a series of computational complexity dichotomies have been established for Holant problems, but the classification for complex-valued signatures is still open. The main obstacle is the case in which all signatures have even arity. In this paper, we establish a dichotomy for Holant problems with a complex-valued 4-ary signature, which is a key base case for the full classification of Holant problems. We present a new strategy by introducing Schur's theorem, the classification of finite subgroups of $\mathrm{SL}(2,\mathbb{C})$ and stable subgroup sequences into the proof. These new techniques are of independent interest.

cs.CC↗

arXiv2026

Max Independent Set Remains NP-hard when Excluding a Planar Induced Minor

We show that there is a fixed planar graph $H$, namely the $5 \times 5$ grid, such that Max Independent Set remains NP-hard in $H$-induced-minor-free graphs. This refutes the Dallard--Milani\v{c}--\v{S}torgel conjecture and a weakening of it by Gartland and Lokshtanov, and by Korhonen.

cs.CC↗

arXiv2026

Topology inside NC$^1$

We show that ACC$^0$ is precisely what can be computed with constant-width circuits of polynomial size and polylogarithmic genus. This extends a characterization given by Hansen, showing that planar constant-width circuits also characterize ACC$^0$. Thus polylogarithmic genus provides no additional computational power in this model. We consider other generalizations of planarity, including crossing number and thickness. We show that constant-width circuits of polynomial size and thickness two already suffice to capture all of NC$^1$.

cs.CC↗