Building a refinement checker for Z

In previous work we have described how refinements can be checked using a temporal logic based model-checker, and how we have built a model-checker for Z by providing a translation of Z into the SAL input language. In this paper we draw these two strands of work together and discuss how we have implemented refinement checking in our Z2SAL toolset. The net effect of this work is that the SAL toolset can be used to check refinements between Z specifications supplied as input files written in the LaTeX mark-up. Two examples are used to illustrate the approach and compare it with a manual translation and refinement check.Comment: In Proceedings Refine 2011, arXiv:1106.348

Building a refinement checker for Z

In previous work we have described how refinements can be checked using a temporal logic based model-checker, and how we have built a model-checker for Z by providing a translation of Z into the SAL input language. In this paper we draw these two strands of work together and discuss how we have implemented refinement checking in our Z2SAL toolset. The net effect of this work is that the SAL toolset can be used to check refinements between Z specifications supplied as input files written in the LaTeX mark-up. Two examples are used to illustrate the approach and compare it with a manual translation and refinement check

Z2SAL: a translation-based model checker for Z

Despite being widely known and accepted in industry, the Z formal specification language has not so far been well supported by automated verification tools, mostly because of the challenges in handling the abstraction of the language. In this paper we discuss a novel approach to building a model-checker for Z, which involves implementing a translation from Z into SAL, the input language for the Symbolic Analysis Laboratory, a toolset which includes a number of model-checkers and a simulator. The Z2SAL translation deals with a number of important issues, including: mapping unbounded, abstract specifications into bounded, finite models amenable to a BDD-based symbolic checker; converting a non-constructive and piecemeal style of functional specification into a deterministic, automaton-based style of specification; and supporting the rich set-based vocabulary of the Z mathematical toolkit. This paper discusses progress made towards implementing as complete and faithful a translation as possible, while highlighting certain assumptions, respecting certain limitations and making use of available optimisations. The translation is illustrated throughout with examples; and a complete working example is presented, together with performance data

Symbolic Reachability Analysis of B through ProB and LTSmin

We present a symbolic reachability analysis approach for B that can provide a significant speedup over traditional explicit state model checking. The symbolic analysis is implemented by linking ProB to LTSmin, a high-performance language independent model checker. The link is achieved via LTSmin's PINS interface, allowing ProB to benefit from LTSmin's analysis algorithms, while only writing a few hundred lines of glue-code, along with a bridge between ProB and C using ZeroMQ. ProB supports model checking of several formal specification languages such as B, Event-B, Z and TLA. Our experiments are based on a wide variety of B-Method and Event-B models to demonstrate the efficiency of the new link. Among the tested categories are state space generation and deadlock detection; but action detection and invariant checking are also feasible in principle. In many cases we observe speedups of several orders of magnitude. We also compare the results with other approaches for improving model checking, such as partial order reduction or symmetry reduction. We thus provide a new scalable, symbolic analysis algorithm for the B-Method and Event-B, along with a platform to integrate other model checking improvements via LTSmin in the future