Symbolic Refinement of Extended State Machines with Applications to the Automatic Derivation of Sub-Components and Controllers

Nowadays, extended state machines are prominent requirements specification techniques due to their capabilities of modeling complex systems in a compact way. These machines extend the standard state machines with variables and have transitions guarded by enabling predicates and may include variable update statements. Given a system modeled as an extended state machine, with possibly infinite state space and some non-controllable (parameterized) interactions, a pruning procedure is proposed to symbolically derive a maximal sub-machine of the original system that satisfies certain conditions; namely, some safeness and absence of undesirable deadlocks which could be produced during pruning. In addition, the user may specify, as predicates associated with states, some general goal assertions that should be preserved in the obtained sub-machine. Further, one may also specify some specific requirements such as the elimination of certain undesirable deadlocks at states, or fail states that should never be reached. Application examples are given considering deadlock avoidance and loops including infinite loops over non-controllable interactions showing that the procedure may not terminate. In addition, the procedure is applied for finding a controller of a system to be controlled. The approach generalizes existing work in respect to the considered extended machine model and the possibility of user defined control objectives written as assertions at states.