Abstract
Specification decomposition is a theoretically interesting and practically relevant problem for which two approaches were independently developed by the control theory and verification communities: natural projection and partial model checking. In this paper we show that, under reasonable assumptions, natural projection reduces to partial model checking and, when cast in a common setting, the two are equivalent. Aside from their theoretical interest, our results build a bridge whereby the control theory community can reuse algorithms and results developed by the verification community. In addition, we present an algorithm and a tool for the partial model checking of finite-state automata that can be used as an alternative to natural projection.
Highlights
A local specification applies to a single component, whereas a global specification should hold for the entire system
Our work goes in the same direction of [12] and provides results that build a new bridge between supervisory control theory and formal verification
We have formally established the relationship between partial model checking and natural projection by reducing natural projection to partial model checking and proving them equivalent under common assumptions
Summary
System verification requires comparing a system’s behavior against a specification. When the system consists of several components, we can distinguish between local and global specifications. Partial model checking tackles this problem by decomposing a specification, given as a formula of the μ-calculus [22], using a quotienting operator, thereby supporting the analysis of the individual processes independently. Since natural projection and partial model checking apply to different formalisms, they cannot be directly compared without defining a common framework (see below). [...] It would be worthwhile to develop case studies that would allow a detailed comparison of these two frameworks in terms of plant and specification modeling, computational complexity of synthesis, and implementation of derived supervisor/ controller.”. As for the first remark, we show that, under reasonable assumptions, natural projection reduces to partial model checking and, when cast in a common setting, they are equivalent To this end, we first define a common theoretical framework for both. The formal proofs together with the correctness and the complexity of our algorithm, and our experimental results are available at https://github.com/SCPTeam/pests/ blob/master/proofs and experiments.pdf
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