Approximate Computation Framework via Le Cam Simulability

This paper introduces a novel decision-theoretic framework for computational complexity, shifting focus from exact solutions to decision-valid approximations. It defines computational deficiency and introduces the class LeCam-P, characterizing problems that are hard to solve exactly but easy to approximate. The paper's significance lies in its potential to bridge the gap between algorithmic complexity and decision theory, offering a new perspective on approximation theory and potentially impacting how we classify and approach computationally challenging problems.

• •Proposes a decision-theoretic framework for computational complexity.
• •Focuses on decision-valid approximations rather than exact solutions.
• •Introduces computational deficiency and the class LeCam-P.
• •Connects classical Karp reductions to zero-deficiency simulations.
• •Establishes the No-Free-Transfer Inequality.