The Isolationist Thesis: Reclassifying Computational Complexity through Finitude and Valid Comparison
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| Natura: | Recurso digital |
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Zenodo
2025
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| _version_ | 1866901236914061312 |
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| author | Tantisukarom, Chaiya |
| author_facet | Tantisukarom, Chaiya |
| contents | <p>The fundamental question of $\mathbf{P} \stackrel{?}{=} \mathbf{NP}$ is often presented as the ultimate test of computational limits. This paper formalizes the \textbf{Isolationist Thesis}, arguing that the $\mathbf{NP}$ complexity class, as currently defined in the literature \cite{AroraBarak09}, is flawed because it conflates problems of \textbf{finite but intractable time} ($\mathbf{P}'$) with problems requiring \textbf{true mathematical infinitude} (a reclassified $\mathbf{NP}$). We demonstrate that $\mathbf{P}$ (Fast, Finite) and our redefined $\mathbf{NP}$ (Infinite, Unsolvable) are fundamentally isolated by the concept of \textbf{finitude}, rendering the traditional $\mathbf{P} \stackrel{?}{=} \mathbf{NP}$ equation a comparison of finite to infinite--a comparison that is trivially true yet computationally irrelevant because it attempts to measure something that, by definition, \textbf{doesn't exist} as a solvable problem. We propose that the only valid and meaningful comparison (\textquotedblleft apple to apple\textquotedblright) is between the two sets of finite-time problems: $\mathbf{P} \stackrel{?}{=} \mathbf{P}'$.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17772710 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Isolationist Thesis: Reclassifying Computational Complexity through Finitude and Valid Comparison Tantisukarom, Chaiya <p>The fundamental question of $\mathbf{P} \stackrel{?}{=} \mathbf{NP}$ is often presented as the ultimate test of computational limits. This paper formalizes the \textbf{Isolationist Thesis}, arguing that the $\mathbf{NP}$ complexity class, as currently defined in the literature \cite{AroraBarak09}, is flawed because it conflates problems of \textbf{finite but intractable time} ($\mathbf{P}'$) with problems requiring \textbf{true mathematical infinitude} (a reclassified $\mathbf{NP}$). We demonstrate that $\mathbf{P}$ (Fast, Finite) and our redefined $\mathbf{NP}$ (Infinite, Unsolvable) are fundamentally isolated by the concept of \textbf{finitude}, rendering the traditional $\mathbf{P} \stackrel{?}{=} \mathbf{NP}$ equation a comparison of finite to infinite--a comparison that is trivially true yet computationally irrelevant because it attempts to measure something that, by definition, \textbf{doesn't exist} as a solvable problem. We propose that the only valid and meaningful comparison (\textquotedblleft apple to apple\textquotedblright) is between the two sets of finite-time problems: $\mathbf{P} \stackrel{?}{=} \mathbf{P}'$.</p> |
| title | The Isolationist Thesis: Reclassifying Computational Complexity through Finitude and Valid Comparison |
| url | https://doi.org/10.5281/zenodo.17772710 |