UC San Diego

This dissertation will review and compile several advancements in the development of digital memcomputing machines. Memcomputing is an efficient computing paradigm that uses memory to process and store information in the same physical location. Digital memcomputing machines have been introduced as a scalable version of the memcomputing paradigm. The memcomputing paradigm can be used to solve difficult constraint satisfaction and combinatorial optimization problems. Herein, Boolean satisfiability problems will be used as benchmarks. This dissertation will introduce the digital memcomputing machine, detailing self-organizing logic circuits and investigating the operation of their fundamental units: self-organizing logic gates. The dynamical system that describes a digital memcomputing machine will be numerically integrated with a forward-Euler scheme. The robustness of the dynamical system to noise allows for the use of a simple integration scheme. We find power-law scalability in the typical-case of hard clause distribution control instances of 3-SAT. We anticipate our results to broaden research directions in physics-inspired computing paradigms ranging from theory to application, from simulation to hardware implementation.