A. Blumensath. Axiomatising tree-interpretable structures. In H. Alt and A. Ferreira, editors, STACS 2002, LNCS 2285, pages 596607, Antibes  Juan les Pins, Mar. 2002. Springer.

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Using Transitiveclosure Logic for Deciding - Linear Properties Of   (Correct)

....pre x recognizable graphs [9] Using Theorem 4.6 of [10] we conclude that G 0 G PrefRec . Since G 1 G 0 , we have also G 1 G PrefRec . Since the reachability is expressible in monadic second order (MSO) logic, each graph of G 2 is de nable within a graph of G 1 . According to [3] see also [4]) each graph of G 2 is therefore in G PrefRec . Since G 2 and G 2 are equal up to graph isomorphism, we have the following lemma. Lemma 3.6. f CG(S; is pre x recognizable for every recognizable sts which is su x on Irr(S) Now, since MCP(MSO,G PrefRec ) is decidable [9] and FO(TC ) ....

A. Blumensath. Axiomatising tree-interpretable structures. In H. Alt and A. Ferreira, editors, STACS 2002, LNCS 2285, pages 596607, Antibes  Juan les Pins, Mar. 2002. Springer.

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