Conceptual

Universal Search algorithm for factoring composite numbers in Computer Science

Universal Search is a fundamental algorithmic framework within computational complexity theory that constructs an asymptotically optimal procedure for any search problem where efficient verification exists. The principle asserts that if the fastest known solver for a specific instance has time complexity $f(n)$, Universal Search guarantees termination in time proportional to the sum of all previously discovered solvers' complexities and their running times on current inputs, formally establishing it as universally asymptotically optimal ($O(\Sigma f_i + \sum f_{\text{current}}^2/ \dots)$). This concept relates computer science theory by providing a constructive existence proof for efficient solutions in unstructured search spaces without requiring prior knowledge of the specific algorithm's implementation.