Artificial Intelligence and Electrical & Electronics Engineering: AIEEE Open Access
A Hybrid DynamicalâComputational Model and Conditional Limitations for the PâNP Problem
Abstract
Chur Chin
The P–NP problem remains one of the most fundamental open questions in theoretical computer science. Rather than proposing a direct resolution, this paper introduces a hybrid computational model combining discrete Turing computation with continuous-time dynamical constraints inspired by dissipative partial differential equations. The model is formalized as a constrained computation system acting on symbolic problem instances. We place the model within known complexity classes under explicit assumptions on precision, energy, and time. We then prove conditional impossibility results showing that, under physically reasonable bounds, the hybrid model cannot decide NP-complete problems in polynomial time unless P = NP. The results clarify the limitations of hybrid and analog computation as a pathway to resolving the P–NP problem, while providing a rigorous framework for analyzing such models.