Fig. 5: SAT solver area advantage for the proposed approach over quadratic HNN/IM.

The area advantage is defined as the ratio of the total number of memory devices in the crossbar arrays required for both implementations. The studied benchmark problems SATLIB, XOR, SAT2020, JHN, and SEMIPRIME correspond to, respectively, uniform random 3-SAT problems⁴⁷, custom-generated K-input XOR problems, competition 3-SAT problems⁴⁸, “JHN” DIMACS benchmark instances from SATLIB benchmark⁴⁷, and custom-generated 3-SAT problems for semiprime factoring⁴⁹. The higher order problems were first converted to 3-SAT with the order-reduction technique and then converted to corresponding QUBO problems using the Rosenberg approach²⁹. Note that a more compact QUBO formulation can be obtained for XOR and other problems by using Tseytin transformation⁶³, though at the cost of substantial preprocessing overhead. Supplementary Fig. S11 shows the data used for this figure.