Exact and efficient verification of parameterized cache coherence protocols

We propose new, tractably (in some cases provably) efficient algorithmic methods for exact (sound and complete) parameterized reasoning about cache coherence protocols. For reasoning about general snoopy cache protocols, we introduce the guarded broadcast protocols model and show how an abstract history graph construction can be used to reason about safety properties for this framework. Although the worst case size of the abstract history graph can be exponential in the size of the transition diagram of the given protocol, the actual size is small for standard cache protocols as is evidenced by our experimental results. The framework can handle all 8 of the cache protocols in [19] as well as their split-transaction versions. We next identify a framework called initialized broadcast protocols suitable for reasoning about invalidation-based snoopy cache protocols and show how to reduce reasoning about such systems with an arbitrary number of caches to a system with at most 7 caches. This yields a provably polynomial time algorithm for the parameterized verification of invalidation based snoopy protocols. Our results apply to both safety and liveness properties. Finally, we present a methodology for reducing parameterized reasoning about directory based protocols to snoopy protocols, thus leveraging techniques developed for verifying snoopy protocols to directory based ones, which are typically are much harder to reason about. We demonstrate by reducing reasoning about a directory based protocol suggested by German [17] to the ESI snoopy protocol, a modification of the MSI snoopy protocol.