Efficient Parallel Algorithm for Decomposing Hard CircuitSAT Instances

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.

💡 Research Summary

The paper introduces a novel parallel algorithm designed to decompose hard CircuitSAT instances, with a focus on problems such as Logical Equivalence Checking (LEC) and pre‑image attacks on cryptographic hash functions. The authors observe that reducing circuit equivalence or inversion problems to SAT often yields formulas that are extremely difficult for state‑of‑the‑art CDCL solvers, even on modestly sized instances. To address this, they adopt a partitioning strategy that splits the original CNF into a family of weaker sub‑formulas, each corresponding to a specific interval of input assignments.

The core technical contribution is an “interval‑based SAT partitioning” built on a bijection between binary input vectors and integers in the range