Mapping finite state machines to zk-SNARKS Using Category Theory

Abstract

We provide a categorical procedure to turn graphs corresponding to state spaces of finite state machines into boolean circuits, leveraging on the fact that boolean circuits can be easily turned into zk-SNARKS. Our circuits verify that a given sequence of edges and nodes is indeed a path in the graph they represent. We then generalize to circuits verifying paths in arbitrary graphs. We prove that all of our correspondences are pseudofunctorial, and behave nicely with respect to each other.