Non-regular iterators in process algebra

We consider three forms of non-regular iteration in process algebra: the push-down operation $, de5ned by x $ y = x((x $ y)(x $ y)) + y, the nesting operation ), de5ned by x ) y = x((x ) y)x )+ y, and the back and forth operation � , de5ned by xy = x((xy)y )+ y. In the process algebraic framework ACP with abstraction and one of $, ) orwe 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, whereis 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.