Research Paper#Computational Complexity, Approximation Algorithms, Decision Theory🔬 ResearchAnalyzed: Jan 3, 2026 17:06
Approximate Computation Framework via Le Cam Simulability
Published:Dec 31, 2025 13:40
•1 min read
•ArXiv
Analysis
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.
Key Takeaways
- •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.
Reference
“The paper introduces computational deficiency ($δ_{\text{poly}}$) and the class LeCam-P (Decision-Robust Polynomial Time).”