Equivalences and Preorders of Transition Systems

Two transition systems are logically equivalent if they satisfy the same formulas of a given logic. For some of these logics, such as Hennessy-Milner's logic, there is an algebraic characterization of this equivalence involving particular homomorphisms of transition systems. This logical equivalence is associated with a preorder: a transition system S is less than S' if all formulas satisfied by S are satisfied by S'. For particular logics, this preorder can also be algebraically characterized, using homomorphisms and a specific notion of inclusion of transition systems.