Compliant Conditions for Polynomial Time Approximation of Operator Counts

TL;DR

This paper introduces a simplified, efficient polynomial-time approximation method for operator counts in specific domains, utilizing Lagrangian duality and compressed sensing techniques to improve heuristic computation.

Contribution

It presents a novel closed-form approximation for operator counts, applies compressed sensing for integer solutions, and explores the method's relation to existing heuristics.

Findings

Efficient polynomial-time approximation for operator counts.

Use of compressed sensing yields integer solutions.

Applicable to domains where heuristics are beneficial.

Abstract

In this paper, we develop a computationally simpler version of the operator count heuristic for a particular class of domains. The contribution of this abstract is threefold, we (1) propose an efficient closed form approximation to the operator count heuristic using the Lagrangian dual; (2) leverage compressed sensing techniques to obtain an integer approximation for operator counts in polynomial time; and (3) discuss the relationship of the proposed formulation to existing heuristics and investigate properties of domains where such approaches appear to be useful.