Refinement and state machine abstraction

Abstract

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A Single Complete Refinement Rule for Demonic Specifications

“…In [10], a refinement semantics is presented for so-called demonic specifications that lifts the refinement of operations defined in formal specifiation languages such as Z and VDM to the refinement of state machines. The semantics is consistent with the conventional refinement semantics for the system underlying a specification in Z [14].…”

“…In this paper, we build on the relational approach of [10] to further investigate the completeness of refinement. As refinement semantics we will use the partial ordering on prefix-closed and demonic languages introduced in [10].…”

“…In this paper, we build on the relational approach of [10] to further investigate the completeness of refinement. As refinement semantics we will use the partial ordering on prefix-closed and demonic languages introduced in [10]. We then extend the results from [10], by proving that this ordering defines a natural lattice structure on the prefix-closed and demonic languages, and discuss its importance for refinement proofs.…”

“…As refinement semantics we will use the partial ordering on prefix-closed and demonic languages introduced in [10]. We then extend the results from [10], by proving that this ordering defines a natural lattice structure on the prefix-closed and demonic languages, and discuss its importance for refinement proofs. This is in analogy to the subset ordering on languages and its interpretation in refinements [3,1,5,11,14,13].…”

“…In Section 2 we introduce the notions of prefix-closed and demonic languages, and demonic specifications from [10]. In Section 3, we present the lattice structure on these languages, and in Section 4 we introduce a notion of refinement on specifications and show its soundness and completeness.…”