Automated Analysis of Parametric Timing-Based Mutual Exclusion Algorithms

A Small Model Theorem for Rectangular Hybrid Automata Networks

“…To the best of our knowledge, this is the first positive result on automatic parameterized verification of hybrid automata, beyond previous results for timed automata [4,3,25,14,21,13]. The modeling framework and process of inductive invariant checking are amenable to automation, so we implemented a prototype called Passel using the SMT solver Z3.…”

“…Related Work To the best of our knowledge, the automatic parameterized verification problem has not been addressed previously for RHA, but there are several works addressing parameterized verification for networks of the special subclass of timed automata [4,3,25,14,21,13]. Parameterized verification of RHA networks is useful to show, for instance, that for arbitrarily many aircraft participating in a given distributed air traffic control protocol like the Small Aircraft Transportation System (SATS), no two aircraft ever collide [34,38,31].…”

Parametrized Verification of Distributed Cyber-Physical Systems: An Aircraft Landing Protocol Case Study

“…Thus, to prove a safety property automatically, it suffices to take the negation of the safety property, and ensure the set of backward reachable states have an empty intersection with the initial set of states. This is the method used by the verification tool we used, the Model Checker Modulo Theories (MCMT) [24], [16], [22], [25]. If the intersection of the backward reachable states and the initial states is empty and the backward reachability process terminates-that is, the backward reachability computation reaches a fixed point and no new states are added on a preimage computation-then the system is proven safe.…”

“…If the timed automata have urgent transitions, then checking safety properties is undecidable [21]. While checking general liveness properties is undecidable for these networks [21], some recent work develops methods for checking some liveness properties [25].…”

“…The property would state that all aircraft eventually land and that they land in order according to their sequence numbers. Some very recent work attempts to allow verification of some classes of liveness properties [25], but general liveness properties for parameterized timed systems were shown to be undecidable in [21].…”