Accelerating Hybrid XOR$-$CNF Boolean Satisfiability Problems Natively with In-Memory Computing
For hardware designers and SAT solver users, this work offers a novel in-memory computing approach to accelerate hybrid SAT problems, though it is incremental as it applies known memristor technology to a specific problem representation.
The paper proposes a hardware accelerator for hybrid XOR-CNF SAT problems using in-memory computing with memristor crossbars, achieving ~10x speedup and ~1000x energy efficiency over CPU solvers on cryptographic benchmarks.
The Boolean satisfiability (SAT) problem is a computationally challenging decision problem central to many industrial applications. For SAT problems in cryptanalysis, circuit design, and telecommunication, solutions can often be found more efficiently by representing them with a combination of exclusive OR (XOR) and conjunctive normal form (CNF) clauses. We propose a hardware accelerator architecture that natively embeds and solves such hybrid XOR--CNF problems using in-memory computing hardware. To achieve this, we introduce an algorithm and demonstrate, both experimentally and through simulations, how it can be efficiently implemented with memristor crossbar arrays. Compared to the conventional approaches that translate XOR--CNF problems to pure CNF problems, our simulations show that the accelerator improves computation speed, energy efficiency, and chip area utilization of in-memory accelerators by $\sim$10$\times$ for a set of hard cryptographic benchmarking problems. Moreover, the accelerator achieves a $\sim$10$\times$ speedup and a $\sim$1000$\times$ gain in energy efficiency over state-of-the-art SAT solvers running on CPUs.