Compositional Nonblocking Verification Using Generalized Nonblocking Abstractions

Abstract

This paper proposes a method for compositional verification of the standard and generalised nonblocking properties of large discrete event systems. The method is efficient as it avoids the explicit construction of the complete state space by considering and simplifying individual subsystems before they are composed further. Simplification is done using a set of abstraction rules preserving generalised nonblocking equivalence, which are shown to be correct and computationally feasible. Experimental results demonstrate the suitability of the method to verify several large-scale discrete event systems models both for standard and generalised nonblocking.

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

“…The compositional nonblocking verification algorithm and many simplification rules had already been implemented here. These included the rules that I have now extended such as Silent Continuation and Silent Incoming [16]. I have also needed to add support for always enabled and selfloop-only events.…”

“…The estimate is obtained by multiplying the product of the state numbers of the automata forming the candidate with the ratio of the numbers of events in the synchronous composition of the candidate after and before removing any local events. This strategy is called MustL/MinS [10,16]. A new heuristic was written to try maximise the number of always enabled events, however this had no significant improvement over the existing heuristic that was instead chosen.…”

“…First, τ-loops (definition 8) and observation equivalent redundant transitions [9] are removed from the automaton. This is followed by the Only Silent Incoming Rule (proposition 6), the Only Silent Outgoing Rule [10], the Limited Certain Conflicts Rule (proposition 7), Observation Equivalence (proposition 1), the Non-α Determinisation Rule [16], the Active Events Rule [10], and the Silent Continuation Rule (proposition 5).…”

“…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.…”

“…Previous approaches for compositional nonblocking verification [10,16,23] make no assumption about the remainder T = G 2 · · · G n of the system apart from its event set. Typically, G 1 has some local events, i.e., events used only by G 1 .…”