Conflict-Driven SAT Solving with XOR‑OR‑AND Normal Forms

Researchers Julian Danner and Martin Kreuzer published their work on August 5, 2026, describing a SAT solver based on the XOR‑OR‑AND normal form (XNF) ¹. They introduced Xorricane, a solver that leverages the XLIN proof system—polynomially equivalent to RES(⊕)—to learn conflicts more efficiently than conventional resolution-based solvers ¹.

Their approach encodes XOR‑rich constraints compactly, reducing clause blowup seen in Conjunctive Normal Form (CNF) representations used by most existing tools ¹.

The authors proved that XLIN is polynomially equivalent to both RES(⊕) and SRES, establishing theoretical foundations for their conflict learning strategy ¹. They then devised XLIN‑based learning methods tailored to XNF formulas, creating a variant optimized for practical efficiency.

Implementation details show that Xorricane can process benchmark suites consisting of random examples and cryptographic instances efficiently ¹.

Expert analysis notes that this development could extend beyond pure cryptography. The XLIN system shares connections with Boolean constraint satisfaction problem solvers widely employed in hardware design automation tools like those used by Cadence Design Systems, implying potential applications where XOR constraints dominate.

Scalability remains a challenge; the study acknowledges difficulties in scaling efficient learning to larger problems.

Xorricane introduces a new SAT solving approach using XNF and XLIN, offering theoretical foundations and effective handling of XOR-rich problems demonstrated on random and cryptographic benchmarks.