Adequate Path Expressions

The object of this paper is to present some results in the formal study of path expressions. Path expressions, or GR-paths, are syntactic objects, that is, terminals strings of a grammar. GR-paths themselves may also be regarded as grammars; each GR-path determines a trace language, in the sense of [Maz 77]. In this sense, GR-paths may be thought of as a defining systems, in that each is associated with a set of possible histories of concurrent behaviour, represented formally by traces. In this exposition, traces are represented as n-tuples of strings and it is briefly shown how such n-tuples determine labelled, partially ordered sets, a popular way of modelling concurrent histories.