Section: New Results
Mildly Context-Sensitive formalisms
Participants : Pierre Boullier, Benoît Sagot.
Pierre Boullier and Benoît Sagot have worked on formal aspects of Mildly Context-Sensitive formalisms in three directions. First, Pierre Boullier and Benoît Sagot have published an algorithm for parsing an input DAG (or lattice) with a general Range Concatenation Grammar (RCG)  . The feasability of this task, as well as its possible exponential time complexity, were known, but no algorithm had been published before (to our best knowledge).
Second, Pierre Boullier and Benoît Sagot have put together the TIG (Tree Insertion Grammars) formalism and the multiple components paradigm underlying the MC-TAG (Multiple-Component Tree Adjoining Grammars), and therefore defined and studied the properties of MC-TIGs (Multiple-Component Tree Insertion Grammars)  . This hierarchy of formalisms define a hierarchy of languages that exhibit interesting properties. For example, 2-MC-TIGs are strictly more powerful than TAGs, they are parsable in time O(n6) just as TAGs, and allow for grammatical descriptions using bi-component structures — the drawback being that so-called wrapping auxiliary trees are prohibited.
Third, Benoît Sagot has been working in collaboration with Giorgio Satta (University of Padova, Italy), on the optimal reduction of the rank of 2-LCFRS (Linear Context-Free Rewriting Systems), that are equivalent to simple (linear) RCGs with at most 2 arguments per predicate. This work has led Benoît Sagot to go to Padova for a 1-month stay. Publications should appear on that topic in 2010.