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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2509.22995 |
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| _version_ | 1866911219231752192 |
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| author | Nishiyama, Yumiko |
| author_facet | Nishiyama, Yumiko |
| contents | The Boolean satisfiability problem (SAT) holds a central place in computational complexity theory as the first shown NP-complete problem. Due to this role, SAT is often used as the benchmark for polynomial-time reductions: if a problem can be reduced to SAT, it is at least as hard as SAT, and hence considered NP-complete. However, the CDF framework offers a structural inversion of this traditional view. Rather than treating SAT as merely a representative of NP-completeness, we investigate whether the syntactic structure of SAT itself -- especially in its 3SAT form -- is the source of semantic explosion and computational intractability observed in NP problems. In other words, SAT is not just the yardstick of NP-completeness, but may be the structural archetype that induces NP-type complexity. This reframing suggests that the P vs NP question is deeply rooted not only in computational resource limits, but in the generative principles of problem syntax, with 3SAT capturing the recursive and non-local constructions that define the boundary between tractable and intractable problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_22995 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Structural Origin and the Minimal Syntax of NP-Hardness: Analysis of SAT from Syntactic Generativity and Compositional Collapse Nishiyama, Yumiko Logic in Computer Science Computational Complexity The Boolean satisfiability problem (SAT) holds a central place in computational complexity theory as the first shown NP-complete problem. Due to this role, SAT is often used as the benchmark for polynomial-time reductions: if a problem can be reduced to SAT, it is at least as hard as SAT, and hence considered NP-complete. However, the CDF framework offers a structural inversion of this traditional view. Rather than treating SAT as merely a representative of NP-completeness, we investigate whether the syntactic structure of SAT itself -- especially in its 3SAT form -- is the source of semantic explosion and computational intractability observed in NP problems. In other words, SAT is not just the yardstick of NP-completeness, but may be the structural archetype that induces NP-type complexity. This reframing suggests that the P vs NP question is deeply rooted not only in computational resource limits, but in the generative principles of problem syntax, with 3SAT capturing the recursive and non-local constructions that define the boundary between tractable and intractable problems. |
| title | Structural Origin and the Minimal Syntax of NP-Hardness: Analysis of SAT from Syntactic Generativity and Compositional Collapse |
| topic | Logic in Computer Science Computational Complexity |
| url | https://arxiv.org/abs/2509.22995 |