求解布尔可满足性的振子激励动力系统公式
Formulating Oscillator-Inspired Dynamical Systems to Solve Boolean Satisfiability
摘要：
动力系统可以提供一种新的非布尔计算方法。具体而言，系统中能量的自然最小化对于最小化组合最优化问题的目标函数是有价值的性质，其中许多问题仍然具有挑战性，难以使用传统的数字求解器来解决。在这项工作中，我们制定了两个启发式的动力系统，以解决典型的布尔可满足性（SAT）计算棘手的问题。系统动力学的设计，使他们促进解决方案的两种不同口味的SAT问题。我们构造了第一个动力系统来计算3-SAT问题的解，而对于第二个系统，我们证明了其动力学映射到Max-NAE-3-SAT问题的解。我们的工作推进了对这种物理启发的方法如何用于解决计算中具有挑战性的问题的理解。
英文摘要：
Dynamical systems can offer a novel non-Boolean approach to computing. Specifically, the natural minimization of energy in the system is a valuable property for minimizing the objective functions of combinatorial optimization problems, many of which are still challenging to solve using conventional digital solvers. In this work, we formulate two oscillator-inspired dynamical systems to solve quintessential computationally intractable problems in Boolean satisfiability (SAT). The system dynamics are engineered such that they facilitate solutions to two different flavors of the SAT problem. We formulate the first dynamical system to compute the solution to the 3-SAT problem, while for the second system, we show that its dynamics map to the solution of the Max-NAE-3-SAT problem. Our work advances understanding of how this physics-inspired approach can be used to address challenging problems in computing.
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