Abstract
Scalability of cache coherence protocol is a key component in future shared-memory multi-core or multi-processor systems. The state space explosion is the first hurdle while applying model-checking to scalable protocols. In order to validate parameterized cache coherence protocols effectively, we present a new method of reducing the state space of parameterized systems, two-dimensional abstraction (TDA). Drawing inspiration from the design principle of parameterized systems, an abstract model of an unbounded system is constructed out of finite states. The mathematical principles underlying TDA is presented. Theoretical reasoning demonstrates that TDA is correct and sound. An example of parameterized cache coherence protocol based on MESI illustrates how to produce a much smaller abstract model by TDA. We also demonstrate the power of our method by applying it to various well-known classes of protocols. During the development of TH-1A supercomputer system, TDA was used to verify the coherence protocol in FT-1000 CPU and showed the potential advantages in reducing the verification complexity.
Highlights
Model checking is an automatic technique for verifying finite state concurrent systems, which uses a finite state machine to describe the system under consideration and temporal logic to state the properties that the system must satisfy
Formal verification of parameterized systems is known to be undecidable and cannot be automated. Symbolic methods such as BDD or SAT, which can enable scalable formal verification methods, can be ineffective when it comes to cache coherence protocols because most of the state variables are relevant in protocol property verification
We propose a novel generic approach called two-dimensional abstraction (TDA), which could effectively reduce the state space of parameterized systems
Summary
Model checking is an automatic technique for verifying finite state concurrent systems, which uses a finite state machine to describe the system under consideration and temporal logic to state the properties that the system must satisfy. Fong Pong [3] presented a comprehensive survey of various approaches to the verification of cache coherence protocol based on state enumeration, model checking, and symbolic state models. Monolithic formal verification methods that treat the protocol as a whole have been used fairly routinely for verifying cache coherence protocols from the early 1990s [4, 5] These monolithic techniques will not be able handle the very large state space of parameterized protocols. All successful applications of model checking far have made use of domain specification abstraction techniques Continuing this trend and drawing inspiration from recent work like environment abstraction [8, 9], we exploit the domain knowledge about parameterized systems to devise an appropriate abstraction method.
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