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Theoretical Computer Science
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We study extensions of the process algebra axiom system ACP with two recursive operations: the binary Kleene star *, which is defined by x*y = x(x*y + y, and the push-down operation $, defined by x$y = x((x$y)(x$y)) + y. In this setting it is easy to represent register machine computation, and an equational theory results that is not decidable. In order to increase the expressive power, abstraction is then added: with rooted branching bisimulation equivalence each computable process can be expressed, and with rooted ô-bisimilarity each semi-computable process that initially is finitely branching can be expressed. Moreover, with abstraction and a finite number of auxiliary actions these results can be obtained without binary Kleene star. Finally, we consider two alternatives for the push-down operation. Each of these gives rise to similar results.