  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.
