Weighted modal transition systems

Sebastian S. Bauer (1) , Uli Fahrenberg (2) , Line Juhl (3) , Kim Guldstrand Larsen (3) , Axel Legay (2) , Claus Thrane (3)

1 TUM - Technische Universität Munchen - Technical University Munich - Université Technique de Munich
2 ESTASYS - Efficient STAtistical methods in SYstems of systems
3 CISS - Center for Indlejrede Software Systemer

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.

Mots clés: reducing complexity of design; modal specification; quantitative reasoning

Domaines: Informatique [cs]; Théorie et langage formel [cs.FL]

Sebastian S. Bauer, Uli Fahrenberg, Line Juhl, Kim Guldstrand Larsen, Axel Legay, et al.. Weighted modal transition systems. Formal Methods in System Design, 2013, 42 (2), pp.193 - 220. ⟨10.1007/s10703-012-0178-9⟩. ⟨hal-01087925⟩