Least Fixpoint and Greatest Fixpoint in a Process Algebra with Conjunction and Disjunction

We have already proposed a process algebra μLOTOS as a mathematical framework to synthesize a process from a number of (incomplete) specifications, in which requirements for the process do not have to be completely determined. It is guaranteed that the synthesized process satisfies all the given specifications, if they are consistent. For example, μLOTOS is useful for incremental design. The advantage of μLOTOS is that liveness properties can be expressed by least fixpoints and disjunctions ∨. In this paper, we present μLOTOSR, which is a refined μLOTOS. The improvement is that μLOTOSR has a conjunction operator ∧. Therefore, the consistency between a number of specifications S1, · · · , S2 can be checked by the satisfiability of the conjunction specification S1 ∧ · · · ∧ S2. μLOTOSR does not need the complex consistency check used in μLOTOS. key words: process algebra, process logic, process synthesis, least fixpoint, greatest fixpoint, disjunction, conjunction