Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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              MSO     2          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,  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 quantifications). Here,  adapt these FA to  incidence graphs   , so that they can check              MSO     2          properties of graphs of bounded tree-width. This is possible because: (1) an              MSO     2          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.  detail concrete constructions of automata in this perspective.
['Bruno Courcelle']
I am writing a research paper on a idea Fly-automata for checking MSO 2 graph properties
[{"from": "human", "value": "I am writing a research paper on a idea Fly-automata for checking MSO 2 graph properties"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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 \u00a0 .\u00a0Such properties are called              MSO     2          in short.  Fly-automata  ( FA ) run bottom-up on terms denoting graphs and compute \u201con the fly\u201d the necessary states and transitions instead of\u00a0looking into huge,\u00a0actually unimplementable tables.\u00a0In previous works,  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 quantifications).\u00a0Here,  adapt these FA to  incidence graphs \u00a0 , so that they can check              MSO     2          properties of graphs of bounded tree-width.\u00a0This is possible because: (1) an              MSO     2          property of a graph is nothing but an MSO\u00a0property 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.\u00a0Our constructions are actually implementable and usable.\u00a0 detail concrete constructions of automata in this perspective."}]