Approximate SMT Counting Beyond Discrete Domains
This work addresses a bottleneck in automated reasoning for hybrid systems, though it appears incremental as it extends hashing-based methods to a new domain.
The paper tackled the problem of counting solutions for hybrid SMT formulas, which involve both discrete and continuous variables, by introducing pact, an approximate model counter that achieved significant performance improvements, finishing on 603 out of 14,202 instances compared to a baseline that finished on only 13 instances.
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 14,202 instances, pact successfully finished on 603 instances, while Baseline could only finish on 13 instances.