Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  prove a conjecture of Courcelle, which states that a graph property is definable in MSO with modular counting predicates on graphs of constant treewidth if, and only if it is recognizable in the following sense: constant-width tree decompositions of graphs satisfying the property can be recognized by tree automata. While the forward implication is a classic fact known as Courcelle's theorem, the converse direction remained open.
['Mikołaj Bojańczyk', 'Michał Pilipczuk']
I am writing a research paper on a idea Definability equals recognizability for graphs of bounded treewidth
[{"from": "human", "value": "I am writing a research paper on a idea Definability equals recognizability for graphs of bounded treewidth"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  prove a conjecture of Courcelle, which states that a graph property is definable in MSO with modular counting predicates on graphs of constant treewidth if, and only if it is recognizable in the following sense: constant-width tree decompositions of graphs satisfying the property can be recognized by tree automata. While the forward implication is a classic fact known as Courcelle's theorem, the converse direction remained open."}]