With the slowdown of improvement in conventional von Neumann systems, increasing attention is paid to novel paradigms such as Ising machines. They have very different approach to solving combinatorial optimization problems. Ising machines have shown great potential in solving binary optimization problems like MaxCut. In this paper, we present an analysis of these systems in boolean satisfiability (SAT) problems. We demonstrate that, in the case of 3-SAT, a basic architecture fails to produce meaningful acceleration, largely due to the relentless progress made in conventional SAT solvers. Nevertheless, careful analysis attributes part of the failure to the lack of two important components: cubic interactions and efficient randomization heuristics. To overcome these limitations, we add proper architectural support for cubic interaction on a state-of-the-art Ising machine. More importantly, we propose a novel semantic-aware annealing schedule that makes the search-space navigation much more efficient than existing annealing heuristics. Using numerical simulations, we show that such an “Augmented” Ising Machine for SAT is projected to outperform state-of-the-art software-based, GPU-based and conventional hardware SAT solvers by orders of magnitude.
Leibniz International Proceedings in Informatics (LIPIcs):26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)
Dynamical solvers for combinatorial optimization are usually based on 2superscript{nd} degree polynomial interactions, such as the Ising model. These exhibit high success for problems that map naturally to their formulation. However, SAT requires higher degree of interactions. As such, these quadratic dynamical solvers (QDS) have shown poor solution quality due to excessive auxiliary variables and the resulting increase in search-space complexity. Thus recently, a series of cubic dynamical solver (CDS) models have been proposed for SAT and other problems. We show that such problem-agnostic CDS models still perform poorly on moderate to large problems, thus motivating the need to utilize SAT-specific heuristics. With this insight, our contributions can be summarized into three points. First, we demonstrate that existing make-only heuristics perform poorly on scale-free, industrial-like problems when integrated into CDS. This motivates us to utilize break counts as well. Second, we derive a relationship between make/break and the CDS formulation to efficiently recover break counts. Finally, we utilize this relationship to propose a new make/break heuristic and combine it with a state-of-the-art CDS which is projected to solve SAT problems several orders of magnitude faster than existing software solvers.
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- Award ID(s):
- 2233378
- NSF-PAR ID:
- 10481573
- Editor(s):
- Mahajan, Meena; Slivovsky, Friedrich
- Publisher / Repository:
- Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- Date Published:
- Subject(s) / Keyword(s):
- Satisfiability Ising machines Stochastic Heuristics Natural Computation Mathematics of computing → Probabilistic algorithms Computer systems organization → Analog computers
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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