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The Computer Journal 1994 37(4):243-258; doi:10.1093/comjnl/37.4.243
© 1994 by British Computer Society
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Process Algebra with Iteration and Nesting

J. A. Bergstra1,2 * §, I. Bethke2,3 § ¶ and A. Ponse1 *

1 University of Amsterdam, Programming Research Group, Kruislaan 403, 1098 SJ Amsterdam, The Netherlands, 2 Department of Philosophy, Heidelberglaan 8, 3584 CS Utrecht, The Netherlands, 3 CWI, Department of Software Technology, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands

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{tau} extended with * and #, and using handshaking and auxiliary actions.


* University of Amsterdam, Programming Research Group, Kruislaan 403, 1098 SJ Amsterdam, The Netherlands

§ Department of Philosophy, Heidelberglaan 8, 3584 CS Utrecht, The Netherlands

CWI, Department of Software Technology, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands


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