Section: New Results

Fundamental results and algorithms: quantitative model checking and quantitative specification theories

Participants : Ulrich Fahrenberg, Blaise Genest, Axel Legay, Sundararaman Akshay, Louis-Marie Traonouez, Benoit Delahaye.

In 2012 we have successfully widened the applicability of interface and specification theories to systems with quantitative information such as energy usage, time constraints, or hybrid variables. Building on work done in 2011, we have introduced general quantitative specification theories. These provide a framework for reasoning about a wide range of different specification theories for different quantitative settings. We have provide one particularly important instantiation of the framework, which allows quantitative reasoning about real-time specifications.

Work on timed specifications theory has been continued in 2012 around the tool ECDAR. New case studies have been tested using the tool. These results, published in STTT, demonstrate the interest of the compositional approach for analyzing large systems. Besides the theory of robust specifications has been extended to allow a parametric estimation of the robustness. These results have been implemented in a new tool PyECDAR.

In 2012, we also successfully pursued our work on probabilistic specification theories by enhancing the framework of Abstract Probabilistic Automata, that we introduced in 2010, with several new operators. We first introduced a notion of satisfaction for stuttering implementations and showed how this new notion fits in the framework of APAs. Stuttering implementations are Probabilistic Automata that allow "silent" transitions by using local variables that are invisible to the specification. In this context, we also introduced a new logic, called ML-(A)PA that allows specifying properties of APA specifications and stuttering PA implementations. Our next contribution was to introduce a new difference operator. Given two specification APAs, their difference is a new APA that represents all implementations satisfying the one but not the other. This novel operator brings a new light to the well-known domain of counter-example generation.

Concerning Markov Chains, we have developed a new logic, LTL-I, which can only reason about fixed intervals instead of point values. We developed $ϵ$ under and over approximation of formulas of this logics in [17] , with associated algorithms. In all but few cases, we know that results of these algorithms are exact answers, while we didn't need to compute precisely and explicitly every probability involved. Another line of research is to consider very large Markov chain represented by Dynamic Bayesian Network. In [15] , we compute only approximated results, as the size of the underlying Markov Chain is too big. However, evaluation of the algorithm shows small errors of our algorithm compared with the exact value.