Karp's NP-complete problems over first-order definable structures

2026-09-29

AI Summary

This study investigates the decidability of Karp’s classical NP-complete problems over first-order definable structures in equational theories, aiming to delineate the complexity boundaries of computational problems within orbit-finite sets with atoms, also known as nominal sets. Methodologically, this work extends traditional NP-completeness theory to symmetric models and the framework of nominal set theory, employing a synthesis of first-order logic, group action analysis, and nominal set-theoretic techniques for formal characterization. The core contribution lies in establishing decidability results for specific NP-complete problems over designated algebraic structures. Consequently, this research provides a novel theoretical foundation and analytical paradigm for understanding computational complexity under symmetry constraints.

Abstract

We determine the decidability of Karp's NP-complete problems on structures which are first-order definable over the theory of equality, also known as orbit-finite sets with atoms or nominal sets.

Problem

• NP-complete problems
• first-order definable structures
• decidability
• nominal sets
• orbit-finite sets

Innovation

• NP-complete problems
• first-order definable structures
• orbit-finite sets
• nominal sets
• decidability