  In this article, we present the potential benefits of incorporating jumps
into the dynamics of digital memcomputing machines (DMMs), which have been
developed to address complex optimization problems. We illustrate the potential
speed improvement of a DMM solver with jumps over an unmodified DMM solver by
solving Boolean satisfiability (SAT) problems of different complicatedness. Our
findings suggest that jumps can modify scaling exponents and improve solving
times by up to 75 %. Interestingly, the advantages of jumps can be seen in
cases where the size of the jump is so large that otherwise the continuous
dynamics of voltage variables becomes almost binary.
