Verifying Sequential Consistency on Shared-Memory Multiprocessors by Model Checking

Abstract

The memory model of a shared-memory multiprocessor is a contract between the designer and programmer of the multiprocessor. The sequential consistency memory model specifies a total order among the memory (read and write) events performed at each processor. A trace of a memory system satisfies sequential consistency if there exists a total order of all memory events in the trace that is both consistent with the total order at each processor and has the property that every read event to a location returns the value of the last write to that location. Descriptions of shared-memory systems are typically parameterized by the number of processors, the number of memory locations, and the number of data values. It has been shown that even for finite parameter values, verifying sequential consistency on general shared-memory systems is undecidable. We observe that, in practice, shared-memory systems satisfy the properties of causality and data independence. Causality is the property that values of read events flow from values of write events. Data independence is the property that all traces can be generated by renaming data values from traces where the written values are distinct from each other. If a causal and data independent system also has the property that the logical order of write events to each location is identical to their temporal order, then sequential consistency can be verified algorithmically. Specifically, we present a model checking algorithm to verify sequential consistency on such systems for a finite number of processors and memory locations and an arbitrary number of data values.