A concurrent specification of Brzozowski's DFA construction algorithm

In this paper two concurrent versions of Brzozowski’s deterministic finite automaton (DFA) construction algorithm are developed from first principles, the one being a slight refinement of the other. We rely on Hoare’s CSP as our notation. The specifications that are proposed of the Brzozowski algorithm are in terms of the concurrent composition of a number of top-level processes, each participating process itself composed of several other concurrent processes. After considering a number of alternatives, this particular overall architectural structure seemed like a natural and elegant mapping from the sequential algorithm’s structure. While we have carefully argued the reasons for constructing the concurrent versions as proposed in the paper, there are of course, a large range of alternative design choices that could be made. There might also be scope for a more fine-grained approach to updating sets or checking for similarity of regular expressions. At this stage, we have chosen to abstract away from these considerations, and leave their exploration to future research.