Regular Algebra Applied to Path-finding Problems

In an earlier paper, one of the authors presented an algebra for formulating and solving extremal path problems. There are striking similarities between that algebra and the algebra of regular languages, which lead one to consider whether the previous results can be generalized—for instance to path enumeration problems—and whether the algebra of regular languages can itself be profitably used for the general study of path-finding problems. This paper gives affirmative answers to both these questions.