Formal verification of complex coherence protocols using symbolic state models

Abstract

Directory-based coherence protocols in shared-memory multiprocessors are so complex that verification techniques based on automated procedures are required to establish their correctness. State enumeration approaches are well-suited to the verification of cache protocols but they face the problem of state space explosion, leading to unacceptable verification time and memory consumption even for small system configurations. One way to manage this complexity and make the verification feasible is to map the system model to verify onto a symbolic state model (SSM). Since the number of symbolic states is considerably less than the number of system states, an exhaustive state search becomes possible, even for large-scale sytems and complex protocols. In this paper, we develop the concepts and notations to verifiy some properties of a directory-based protocol designed for non-FIFO interconnection networks. We compare the verification of the protocol with SSM and with the Stanford Mur φ, a verification tool enumerating system states. We show that SSM is much more efficient in terms of verification time and memory consumption and therefore holds that promise of verifying much more complex protocols. A unique feature of SSM is that it verifies protocols for any system size and therefore provides reliable verification results in one run of the tool.