Least fixpoint and greatest fixpoint in a process algebra with conjunction and disjunction
We have already proposed a process algebra mu LOTOS 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, mu LOTOS is useful for incremental design. The advantage of mu LOTOS is that liveness properties can be expressed by least fixpoints and disjunctions boolean OR. In this paper, we present mu LOTOSR, which is a refined mu LOTOS. The improvement is that mu LOTOSR has a conjunction operator boolean AND. Therefore, the consistency between a number of specifications S-1,...,S-2 can be checked by the satisfiability of the conjunction specification S(1)boolean AND...boolean AND S-2. mu LOTOSR does not need the complex consistency check used in mu LOTOS.
least fixpoint greatest fixpoint process algebra process logic process synthesis