Abstract
This chapter provides an overview of the addition of various forms of iteration, i.e., recursive operations, to process algebra. Of these operations (the original, binary version of) the Kleene star is considered most basic, and an equational axiomatization of its combination with basic process algebra is explained in detail. The focus on iteration in process algebra raised interest in a number of variations of the Kleene star operation, of which an overview, including various completeness and expressivity results, is presented. Though most of these variations concern regular (iterative) operations, also the combination of process algebra and some non-regular operations are discussed, leading to undecidability and stronger expressivity results. Finally, some attention is paid to the interplay between iteration and the special process algebra constants representing the silent step and the empty process.
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