Compositional Verification in Supervisory Control

Compositional Nonblocking Verification with Always Enabled Events and Selfloop-Only Events

“…This is not possible with every equivalence relation. It is possible with an observation equivalence relation, and another possibility is incoming equivalence [10].…”

“…To confirm that an automaton quotient modulo a given equivalence relation is conflict equivalent to the original automaton, it is usually necessary to establish a relationship between the paths in an automaton and its quotient [10]. Firstly, it follows immediately from definition 6 that every path between in an automaton also links the corresponding classes in its quotient automaton.…”

“…Lemma 3 [10] Let G = A, Q, →, Q • be an automaton, and let ∼ ⊆ Q × Q be an equivalence relation such that ∼ ⊆ ∼ inc .…”

“…When simplifying the automata it is important to ensure this does not change the nonblocking property of the system. Various abstraction rules preserving conflict equivalence have been proposed and implemented [10,19,22,23]. These include rules such as Observational Equivalence, Tau-Loop Removal and Certain Conflicts.…”

“…Symbolic model checking has been used successfully to reduce the amount of memory required by representing the state space symbolically rather than enumerating it explicitly [2]. Compositional verification [10,16] is an effective alternative that can be used independently of, or in combination with, symbolic methods. Compositional verification works by simplifying individual automata before each composition, gradually reducing the state space of the system and allowing much larger systems to be verified in the end.…”