Natural Projection as Partial Model Checking

Verifying the correctness of a system as a whole requires establishing that it satisfies a global specification. When it does not, it would be helpful to determine which modules are incorrect. As a consequence, specification decomposition is a relevant problem from both a theoretical and practical point of view. Until now, specification decomposition has been independently addressed by the control theory and verification communities through natural projection and partial model checking, respectively. We prove that natural projection reduces to partial model checking and, when cast in a common setting, the two are equivalent. Apart from their foundational interest, our results build a bridge whereby the control theory community can reuse algorithms and results developed by the verification community. Furthermore, we extend the notions of natural projection and partial model checking from finite-state to symbolic transition systems and we show that the equivalence still holds. Symbolic transition systems are more expressive than traditional finite-state transition systems, as they can model large systems, whose behavior depends on the data handled, and not only on the control flow. Finally, we present an algorithm for the partial model checking of both kinds of systems that can be used as an alternative to natural projection.