Weighted Modal Transition Systems

TL;DR

This paper introduces a novel quantitative specification theory using weighted modal transition systems, enabling more robust modeling of systems by capturing optional behaviors and measuring behavioral distances.

Contribution

It presents the first framework that incorporates quantitative aspects into specification theories, extending satisfaction and refinement notions with a distance measure.

Findings

Quantitative refinement and satisfaction are formalized with distances.

Parallel composition and quotient operations preserve properties in the quantitative setting.

Weighted modal transition systems effectively model optional behaviors in specifications.

Abstract

Specification theories as a tool in model-driven development processes of component-based software systems have recently attracted a considerable attention. Current specification theories are however qualitative in nature, and therefore fragile in the sense that the inevitable approximation of systems by models, combined with the fundamental unpredictability of hardware platforms, makes it difficult to transfer conclusions about the behavior, based on models, to the actual system. Hence this approach is arguably unsuited for modern software systems. We propose here the first specification theory which allows to capture quantitative aspects during the refinement and implementation process, thus leveraging the problems of the qualitative setting. Our proposed quantitative specification framework uses weighted modal transition systems as a formal model of specifications. These are labeled transition systems with the additional feature that they can model optional behavior which may or may not be implemented by the system. Satisfaction and refinement is lifted from the well-known qualitative to our quantitative setting, by introducing a notion of distances between weighted modal transition systems. We show that quantitative versions of parallel composition as well as quotient (the dual to parallel composition) inherit the properties from the Boolean setting.