PROCESS ALGEBRA WITH ITERATION AND NESTING

We introduce iteration in process algebra by means of (the original, binary version of) Kleene's star operation: x*y is the process that chooses between x and y, and upon termination of x has this choice again. We add this operation to a whole range of process algebra axiom systems, starting from BPA (Basic Process Algebra). In the case of the most complex system under consideration, ACP(tau), every regular process can be defined with handshaking (two-party communication) and auxiliary actions. Next we introduce nesting in process algebra: x(#)y is defined by the equation x(#)y = x(x(#)y)x+y. We show that * and # are not interdefinable in most of the axiom systems we regard. The extension with #, and the extension with * and # of the systems considered also give a genuine hierarchy in expressivity. Finally, it is argued that each finitely branching, computable graph can be defined in ACP, extended with * and #, and using handshaking and auxiliary actions.