Non-regular iterators in process algebra

We consider three forms of non-regular iteration in process algebra: the push-down operation $, de5ned by xy = x((xy)(xy)) + y, the nesting operation ], de5ned by xy = x((xy)x) + y, and the back and forth operation , de5ned by x y= x((x y)y) + y. In the process algebraic framework ACP with abstraction and one of $, ] or we provide de5nitions of the following standard processes: stack, context-free process, bag, and queue. These de5nitions apply to all standard behavioural equivalences (we only use x = x, where is the silent step). Moreover, these results yield the expressive power to express computable processes modulo rooted branching bisimulation equivalence, and hence support the equational founding of process algebra: standard processes can be represented as terms. c © 2001 Elsevier Science B.V. All rights reserved.