Splitting bisimulations and retrospective conditions

We investigate conditional expressions in the setting of ACP, an algebraic theory about processes. We introduce ACPc, an extension of ACP with conditional expressions in which the conditions are taken from a free Boolean algebra over a set of generators, and also its main models, called full splitting bisimilation models. We add two simple mechanisms for condition evaluation to ACPc; and we show their connection with state operators and signal emission, mechanisms from other extensions of ACP usable for condition evaluation. To allow for looking back on conditions under which preceding actions have been performed, we add a retrospection operator on conditions to ACPc. The choice of conditions forces us to introduce a new variant of bisimulation. However, without the generality implied by that choice, it would not have been possible to extend ACPc with retrospection. The addition of retrospection is a basic way to increase expressiveness