List of open problems in finite model theory. Available at http://speedy.informatik.rwth-aachen.de/ WWW/FMT.html.  Home/Search   Document Not in Database   Summary   Related Articles

....polynomial time on arbitrary planar graphs. 2) Planar graphs can be characterized up to isomorphism in a logic with finitely many variables and counting. This answers a question of Immerman [7] 3) The class of planar graphs is definable in IFP. This answers a question of Dawar and Gr adel [16]. 1. Introduction The basic problem of descriptive complexity theory is to find a logic L for a given complexity class K such that an isomorphism invariant property of finite structures can be defined in L if, and only if, it belongs to K. If this is the case, we say that L captures K. A ....

....and counting quantifiers 9 m x i , for m 2 N; i k (saying that there exists at least m elements x i ) Theorem 1.2 There is a k 1 such that for all planar graphs G there is a C k formula G that characterizes G up to isomorphism. A third Theorem answers a question of Gradel and Dawar [16]: Theorem 1.3 The class of planar graphs is definable in the logic IFP. This follows from the facts that a graph is planar if, and only if, its 3 connected components are, and that planarity can be decided in P together with our results that IFP captures P on 3 connected planar graphs and that ....

List of open problems in finite model theory. Available at http://speedy.informatik.rwth-aachen.de/ WWW/FMT.html.

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