Efficient Parallel Algorithm for Decomposing Hard CircuitSAT Instances

2026-02-19

AI Summary

This work proposes a parameterized parallel solving algorithm to address the inefficiency of existing approaches on hard CircuitSAT instances, such as those arising in logic equivalence verification and preimage attacks on cryptographic hash functions. The method decomposes the original problem into multiple weakened subformulas by introducing specialized constraints and dynamically guides the generation of high-quality decompositions through a hardness estimation mechanism tailored for parallel computing environments. By innovatively integrating parameterized decomposition strategies with runtime difficulty assessment, the approach achieves efficient structural decoupling of complex CircuitSAT instances. Experimental results demonstrate that the algorithm significantly improves solving efficiency on representative hard instances, exhibiting both practical utility and strong scalability.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability
• Search and Optimization: Combinatorial Optimization
• Machine Learning: Hardware-aware ML

Application Category

• Security and Privacy: Applications of cryptography
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

We propose a novel parallel algorithm for decomposing hard CircuitSAT instances. The technique employs specialized constraints to partition an original SAT instance into a family of weakened formulas. Our approach is implemented as a parameterized parallel algorithm, where adjusting the parameters allows efficient identification of high-quality decompositions, guided by hardness estimations computed in parallel. We demonstrate the algorithm's practical efficacy on challenging CircuitSAT instances, including those encoding Logical Equivalence Checking of Boolean circuits and preimage attacks on cryptographic hash functions.

Problem

• CircuitSAT
• parallel algorithm
• problem decomposition
• hardness estimation
• Boolean circuits

Innovation

• parallel algorithm
• CircuitSAT decomposition
• weakened formulas
• hardness estimation
• parameterized decomposition