Compositionality for Quantitative Specifications

Abstract

We provide a framework for compositional and iterative design and verification of systems with quantitative information, such as rewards, time or energy. It is based on disjunctive modal transition systems where we allow actions to bear various types of quantitative information. Throughout the design process the actions can be further refined and the information made more precise. We show how to compute the results of standard operations on the systems, including the quotient (residual), which has not been previously considered for quantitative non-deterministic systems. Our quantitative framework has close connections to the modal nu-calculus and is compositional with respect to general notions of distances between systems and the standard operations.

Computing Branching Distances Using Quantitative Games

“…In the future, we intend to expand our work to also cover quantitative specification theories. Together with several coauthors, we have in [17,18] developed a comprehensive setting for satisfaction and refinement distances in quantitative specification theories. Using our work in [22] on a qualitative linear-timebranching-time spectrum of specification theories, we plan to introduce a quantitative linear-time-branching-time spectrum of specification distances and to use the setting developed here to devise methods for computing them through path-building games.…”

Behavioral Specification Theories: an Algebraic Taxonomy

“…In [14] it is shown that the specification theory (HML R , χ, ≤), and thus also the specification theories based on DMTS and AA, are unital complete compositional when enriched with CSP-style composition . (In [27] this is generalized to other types of composition. )…”

“…All throughout Sections 2 to 6, we give plenty of examples, taken from our own work in [14,27,31], of specification theories which have the required operations. In the final Section 7 we survey a few other behavioral specification theories, for real-time and probabilistic models, in order to expose their particular algebraic properties.…”