Section: New Results

Weighted Systems

Alongside boolean properties, automatic verification of quantitative properties such as lifespan of an equipment, energy consumption of an application or reliability of a program is gaining importance rapidly. In the thesis [14] and the articles [32] , [14] , several weight-enabled formalisms for specification of such properties were examined, including denotational ones such as regular expressions, first-order logic with transitive closure, or temporal logics, as well as more operational ones such as navigating automata, possibly extended with pebbles. A unified framework of graph structures allows to compare these formalisms with respect to expressiveness, using efficient translations from denotational to operational formalisms. Several decidability and complexity results for the algorithmic questions that arise were obtained, depending on the underlying semiring from which weights are chosen, and on the structures (words, trees, ... ) considered.