Minimizing the Number of Transitions with Respect to Observation Equivalence

Labeled transition systems (lts) provide an operational semantics for many speciication languages. In order to abstract unrelevant details of lts's, many behavioural equivalences have been deened; here observation equivalence is considered. We are interested in the following problem: Given a nite lts, which is the minimal observation equivalent lts corresponding to it ? It is well known that the number of states of an lts can be minimized by applying an rela-tional coarsest partition algorithm. However, the obtained lts is not unique (up to the renaming of the states): for an lts there may exist several observation equivalent lts's which have the minimal number of states but varying number of transitions. In this paper we show how the number of transitions can be minimized, obtaining a unique lts.