Error-Completion in Interface Theories

Abstract

Interface theories are compositional theories where components are represented as abstract, formal interfaces which describe the component’s input/output behavior. A key characteristic of interface theories is that interfaces are non-input-complete, meaning that they allow specification of illegal inputs. As a result of non-input-completeness, interface theories use game-theoretic definitions of composition and refinement, which are both conceptually and computationally more complicated than standard notions of composition and refinement that work with input-complete models. In this paper we propose a lossless transformation, called error-completion, which allows to transform a non-input-complete interface into an input-complete interface while preserving and allowing to retrieve completely the information on illegal inputs. We show how to perform composition of relational interfaces on the error-complete domain. We also show that refinement of such interfaces is equivalent to standard implication of their error-completions.