An Abstract Schema for Equivalence-Checking Games

Equivalence games have been shown as an efficient way to diagnose design systems. Nevertheless, like other diagnostic routines, equivalence games utilize the information already computed by equivalence checker during verification. Therefore, these diagnostic routines tightly gear to the data structure of checker being used, and their ability of migrating to a different checker is not always guaranteed. Moreover, different equivalence relations demand different game schemas, which makes it tedious to implement equivalence games. We solve the first problem by utilizing a generalized version of partition refinement tree (PRT) as an abstract of proof structures. With a little bookkeeping, a partition refinement-based checker is able to supply PRT as the evidence to support its result. The diagnostic routines built on PRTs are independent of equivalence checkers being used. PRTs may also be used to certify the equivalence-checking result.To solve the second problem, we introduce a semantics hierarchy. Implementation following this hierarchy enjoys greater code sharing among different games. The prototype of this schema, including PRT-friendly algorithms and the architecture of semantics hierarchy, has been implemented on the Concurrency Workbench.