A CONCURRENT SPECIFICATION OF BRZOZOWSKI'S DFA CONSTRUCTION ALGORITHM

Abstract

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 for a subsequent step in our research.