Yumiko Nishiyama | Searcharxiv

arXiv2025

Construction Defining Functionality:A Constructive Perspective on Functions through Their Generated Structures

In this work, we propose the concept of Construction Defining Functionality (CDF), which characterizes functions by the structural spaces they generate through iteration,recursion, and logical application. By viewing functions as generators of hierarchical structures, we formalize these generated structural spaces and organize a framework to classify and mathematically model their properties. The organized CDF framework captures the intrinsic constructive behaviors of functions via their generated structural spaces.

cs.LO↗

arXiv2025

Structural Origin and the Minimal Syntax of NP-Hardness: Analysis of SAT from Syntactic Generativity and Compositional Collapse

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.

cs.LO↗