Bit-Vector Model Counting using Statistical Estimation

TL;DR

This paper introduces a statistical estimation-based method for approximate model counting of bit-vector SMT formulas, improving efficiency and enabling applications like differential privacy analysis.

Contribution

It presents a novel approach that refines probabilistic estimates iteratively, enhancing model counting accuracy and speed over previous XOR-streamlining techniques.

Findings

Faster than previous XOR-based methods

Enables model counting over floating-point constraints

Demonstrates application to differential privacy vulnerability

Abstract

Approximate model counting for bit-vector SMT formulas (generalizing \#SAT) has many applications such as probabilistic inference and quantitative information-flow security, but it is computationally difficult. Adding random parity constraints (XOR streamlining) and then checking satisfiability is an effective approximation technique, but it requires a prior hypothesis about the model count to produce useful results. We propose an approach inspired by statistical estimation to continually refine a probabilistic estimate of the model count for a formula, so that each XOR-streamlined query yields as much information as possible. We implement this approach, with an approximate probability model, as a wrapper around an off-the-shelf SMT solver or SAT solver. Experimental results show that the implementation is faster than the most similar previous approaches which used simpler refinement strategies. The technique also lets us model count formulas over floating-point constraints, which we demonstrate with an application to a vulnerability in differential privacy mechanisms.