Section: New Results

Semantic translation of CCSL constraints into appropriate Büchi automata for trace recognition

Participants : Frédéric Mallet, Julien Deantoni, Robert de Simone, Ling Yin.

Our CCSL language expresses timing and scheduling constraints for a system, based on the notion of abstract logical clocks providing time events, and contraints linking them with relations of "asynchronous" nature (precedence, faster than) or of "synchronous" origin (subclocking, included in). Of course in a large system design both types coexist, and functional definitions also live next to declarative specifications to allow several timing solutions. Such a solution, called a schedule, must enforce that each logical clock either ticks endlessly, or terminates properly, in a way that globally respects the constraints. In previous works we have shown how a large variety of semantic scheduling constraints from the literature could soundly be represented in CCSL.

This year we focused on the semantic foundation of our CCSL language, by defining a structral operational semantic translation into a specific type of transition systems. Because we deal with infinite traces we had to consider acceptance mechanisms such as Büchi repeated states (as already used for translation of LTL temporal logic formulae in classical model-checking). Next we found out that, while state-labeled acceptance conditions were fine to obtain a direct and intuitive translation of individual constraints, building the composition of such models when dealing with multiple constraints was much easier in the case of transition-labeled Büchi automata (with repeated acceptance criteria now on transitions); the theory carries over to such case quite naturally, and has already been studied in the past. Finally, because traces must include infinite occurrences for each clock, we had to move to so-called extended Büchi automata, again a model already studied previously.

We provided a complete semantic translation for all CCSL kernel constructs. Most importantly, we provided an efficient and simple fix-point algorithm to check the existance of a valid schedule, based on the type of automata just defined. This is (we believe) a genuine improvement on existing results, with potential applications outside our direct scope. These results are presented in a technical report, submitted for publication [46] .