Exploiting Symmetry and Transactions for Partial Order Reduction of Rule Based Specifications

Rule based specifications are popular for specifying protocols, e.g., cache coherence protocols specified in TLA+ [12], Murphi [7], or the BlueSpec language [1]. Specifications in these notations are a collection of unordered rules of the form guard(state) → atomic updates. There is no notion of a sequential process with local scopes or channels, and each rule tends to update multiple fields of the global state. It is believed that partial order (PO) reduction is difficult to achieve in such a setting. In our preliminary work [2], we reported a suitable algorithm for this purpose. In this paper, we expand on this algorithm and show that this algorithm can exploit the transactional nature of many protocols in this area, during ample-set computation. Second, we show that, in the presence of symmetry, the SAT-based computation of the independence relation between rules can be computed once and for all in a manner that is accurate for all parameterized instances of the protocol; Third, we show that sharpening the SAT-based independence computation through local invariants can aid PO reduction. Here, we propose a way by which users may guess these invariants: we can check these invariants and the property of interest in one combined phase under PO reduction (we prove that there is no circularity in this process). Our results indicate that with the above measures, rule based systems can have efficient and effective PO reduction algorithms.