Abstract
3-SAT is a class of NP-hard combinatorial optimization problems that Ising machines have had difficulty solving successfully. Solution success rate depends not only on the choice of Ising machine, but crucially, also on the mapping from 3-SAT to Ising form. We evaluate the performance of Oscillator Ising Machines (OIMs) on several existing 3-SAT-to-Ising mappings, finding that they yield mediocre or poor results. We propose two novel enhancements to logic-synthesis-based Ising mapping schemes that improve solution success rate significantly (from 0% to about 56% on SATLIB’s uf20 problem set). We then propose a new circuit- and clause-based 3-SAT-to-Ising mapping scheme that employs 3-input OR gates. Using this mapping increases OIM’s success rate on uf20 to 95.9%—we believe this is by far the best raw performance achieved on any 3-SAT problem class by any Ising machine scheme. We also present a comparison of OIM vs. simulated annealing on Ising-mapped 3-SAT problems, revealing that OIM’s performance is significantly superior.
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Notes
- 1.
The term “ground state" means a state that achieves the minimum Hamiltonian.
- 2.
Note that sizing in this context does not mean physical scaling.
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Acknowledgments
We gratefully acknowledge support from the US Defense Advanced Research Projects Agency (DARPA) and the US National Science Foundation (NSF). Additional support was provided by Berkeley’s Bakar Prize Award.
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Sikhakollu, V.P.S., Sreedhara, S., Manohar, R., Mishchenko, A., Roychowdhury, J. (2024). High Quality Circuit-Based 3-SAT Mappings for Oscillator Ising Machines. In: Cho, DJ., Kim, J. (eds) Unconventional Computation and Natural Computation. UCNC 2024. Lecture Notes in Computer Science, vol 14776. Springer, Cham. https://doi.org/10.1007/978-3-031-63742-1_19
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