Approximate SMT Counting Beyond Discrete Domains

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 appr...

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Published in:2025 62nd ACM/IEEE Design Automation Conference (DAC) pp. 1 - 7
Main Authors: Shaw, Arijit, Meel, Kuldeep S.
Format: Conference Proceeding
Language:English
Published: IEEE 22.06.2025
Subjects:
Benchmark testing
Cognition
Design automation
Hash functions
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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 \mathbf{1 4, 2 0 2} instances, pact successfully finished on 603 instances, while Baseline could only finish on 13 instances.
AbstractList 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 \mathbf{1 4, 2 0 2} instances, pact successfully finished on 603 instances, while Baseline could only finish on 13 instances.
Author Shaw, Arijit
Meel, Kuldeep S.
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  givenname: Kuldeep S.
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  fullname: Meel, Kuldeep S.
  organization: Georgia Institute of Technology,USA
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Snippet Satisfiability Modulo Theory (SMT) solvers have advanced automated reasoning, solving complex formulas across discrete and continuous domains. Recent progress...
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SubjectTerms Benchmark testing
Cognition
Design automation
Hash functions
Title Approximate SMT Counting Beyond Discrete Domains
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