Section: New Results

Weighted Logics with Navigation for Trees

We continued our study of the verification of quantitative properties and applications to queries over XML documents. Verification of quantitative systems follow a classical scheme in three steps: specification, modeling, and algorithmics. Hence, we started by exhibiting a specification language. To describe natural qualitative properties, we chose to use, as a fragment, boolean logic like first-order logic or monadic second-order logic. We then encapsulate this properties into the quantitative formalism, allowing sums and products computations in a specified general semiring. In the word case, we obtained very strong results relating this kind of specification/computation languages with the well-known weighted finite automata, and the new weighted pebble automata, which permit to model several interesting quantitative computations over words. We extended these results to trees, and in particular, finite unranked trees or nested words, which are a natural model for XML documents. We published preliminary results in a research report [57] , and we have worked on a submission of these results to several conferences. Our next goal is to tackle some of the algorithmic questions that naturally arise in this context, like satisfiability or model checking.