# P versus NP

Published articles for P versus NP.

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## Six Millennium Problems, Two Teams, One Shared Bottleneck

DevFeed: [Six Millennium Problems, Two Teams, One Shared Bottleneck](<https://devfeed.tech/articles/six-millennium-problems-two-teams-one-shared-bottleneck-61836.md>)

Original publisher: [Read original article](<https://hackernoon.com/six-millennium-problems-two-teams-one-shared-bottleneck?source=rss>)

Author: Ioannis Tsiokos

Published: 2026-09-29T14:38:29Z

Content type: article

Language: en

Sources: [HackerNoon](<https://devfeed.tech/sources/hackernoon.md>)

Topics: [Quantum Computing](<https://devfeed.tech/topics/quantum-computing.md>), [Lean](<https://devfeed.tech/topics/lean.md>), [Computer science](<https://devfeed.tech/topics/computer-science.md>)

Tags: [formal-verification](<https://devfeed.tech/tags/formal-verification.md>), [invariant](<https://devfeed.tech/tags/invariant.md>), [lean](<https://devfeed.tech/tags/lean.md>), [lean-4](<https://devfeed.tech/tags/lean-4.md>), [mathematical-formalization](<https://devfeed.tech/tags/mathematical-formalization.md>), [millennium-prize-problems](<https://devfeed.tech/tags/millennium-prize-problems.md>), [p-versus-np](<https://devfeed.tech/tags/p-versus-np.md>), [quantum](<https://devfeed.tech/tags/quantum.md>), [quantum-computing](<https://devfeed.tech/tags/quantum-computing.md>), [quantum-proof-verification](<https://devfeed.tech/tags/quantum-proof-verification.md>), [six-birds-theory](<https://devfeed.tech/tags/six-birds-theory.md>), [spectral-computation](<https://devfeed.tech/tags/spectral-computation.md>), [verification](<https://devfeed.tech/tags/verification.md>)

### AI overview

The article compares Six Birds Theory with AIX Global's claimed quantum-computing pipeline for addressing six Clay Millennium Problems. It describes a workflow involving problem-specific operators or invariants, spectral computation on IBM Heron hardware, fixed-point certificates, and Lean 4 formal verification. The article emphasizes that the reported results require scrutiny and that the approaches rely on distinct, partly conditional proof claims.

### Source excerpt

A structural comparison of Six Birds Theory and AIX's claimed quantum proof pipeline explores certificates, Lean verification, and unproven assumptions.

## P vs. NP, A Primer (And a Proof Written in Racket)

DevFeed: [P vs. NP, A Primer (And a Proof Written in Racket)](<https://devfeed.tech/articles/p-vs-np-a-primer-and-a-proof-written-in-racket-40263.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2012/02/23/p-vs-np-a-primer-and-a-proof-written-in-racket/>)

Published: 2012-02-23T19:57:35Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Computing](<https://devfeed.tech/topics/computing.md>), [Algorithms](<https://devfeed.tech/topics/algorithms.md>), [computational complexity](<https://devfeed.tech/topics/computational-complexity.md>), [Racket](<https://devfeed.tech/topics/racket.md>), [Programming](<https://devfeed.tech/topics/programming.md>)

Tags: [algorithm](<https://devfeed.tech/tags/algorithm.md>), [algorithms](<https://devfeed.tech/tags/algorithms.md>), [analysis](<https://devfeed.tech/tags/analysis.md>), [big-o-notation](<https://devfeed.tech/tags/big-o-notation.md>), [class](<https://devfeed.tech/tags/class.md>), [computational-complexity](<https://devfeed.tech/tags/computational-complexity.md>), [computing](<https://devfeed.tech/tags/computing.md>), [decidability](<https://devfeed.tech/tags/decidability.md>), [efficiency](<https://devfeed.tech/tags/efficiency.md>), [fast](<https://devfeed.tech/tags/fast.md>), [halting-problem](<https://devfeed.tech/tags/halting-problem.md>), [input](<https://devfeed.tech/tags/input.md>), [language](<https://devfeed.tech/tags/language.md>), [machine](<https://devfeed.tech/tags/machine.md>), [np-completeness](<https://devfeed.tech/tags/np-completeness.md>), [p-versus-np](<https://devfeed.tech/tags/p-versus-np.md>), [primer](<https://devfeed.tech/tags/primer.md>), [racket](<https://devfeed.tech/tags/racket.md>), [solve](<https://devfeed.tech/tags/solve.md>), [theory](<https://devfeed.tech/tags/theory.md>), [turing-machine](<https://devfeed.tech/tags/turing-machine.md>), [turing-machines](<https://devfeed.tech/tags/turing-machines.md>)

### AI overview

A primer on the distinction between decidability and computational efficiency, introducing the complexity class P and its definition in terms of polynomial-time decision by a Turing machine. It also discusses efficient algorithms and gives a card-sorting example.

### Source excerpt

Decidability Versus Efficiency In the early days of computing theory, the important questions were primarily about decidability. What sorts of problems are beyond the power of a Turing machine to solve? As we saw in our last primer on Turing machines, the halting problem is such an example: it can never be solved a finite amount of time by a Turing machine. However, more recently (in the past half-century) the focus of computing theory has shifted away from possibility in favor of determining feasibility.