Approximate SMT Counting Beyond Discrete Domains

TL;DR

This paper introduces pact, an approximate model counter for hybrid SMT formulas that uses hashing to efficiently estimate the number of solutions with theoretical guarantees, outperforming existing methods.

Contribution

We present pact, a novel hashing-based approximate SMT model counter for hybrid formulas, extending counting capabilities beyond discrete domains with improved performance.

Findings

pact successfully finished on 456 out of 3119 instances, outperforming baseline.

pact makes a logarithmic number of SMT solver calls relative to projection variables.

pact achieves significant performance improvements over baselines.

Abstract

Satisfiability Modulo Theory (SMT) solvers have advanced automated reasoning, solving complex formulas across discrete and continuous domains. Recent progress in propositional model counting motivates extending SMT capabilities toward model counting, especially for hybrid SMT formulas. Existing approaches, like bit-blasting, are limited to discrete variables, highlighting the challenge of counting solutions projected onto the discrete domain in hybrid formulas. We introduce pact, an SMT model counter for hybrid formulas that uses hashing-based approximate model counting to estimate solutions with theoretical guarantees. pact makes a logarithmic number of SMT solver calls relative to the projection variables, leveraging optimized hash functions. pact achieves significant performance improvements over baselines on a large suite of benchmarks. In particular, out of 3119 instances, pact successfully finished on 456 instances, while Baseline could finish on 83 instances.