Fly-automata for checking MSO 2 graph properties

A more descriptive but too long title would be : Constructing fly-automata to check properties of graphs of bounded tree-width expressed by monadic second-order formulas written with edge quantifications. Such properties are called MSO2 in short. Fly-automata (FA) run bottom-up on terms denoting graphs and compute " on the fly " the necessary states and transitions instead of looking into huge, actually unimplementable tables. In previous works, we have constructed FA that process terms denoting graphs of bounded clique-width, in order to check their monadic second-order (MSO) properties (expressed by formulas without edge quan-tifications). Here, we adapt these FA to incidence graphs, so that they can check MSO2 properties of graphs of bounded tree-width. This is possible because: (1) an MSO2 property of a graph is nothing but an MSO property of its incidence graph and (2) the clique-width of the incidence graph of a graph is linearly bounded in terms of its tree-width. Our constructions are actually implementable and usable. We detail concrete constructions of automata in this perspective.