Abstract
We show that a graph decision problem can be defined in the Counting Monadic Second-order logic if the partial 3-trees that are yes-instances can be recognized by a finite-state tree automaton. The proof generalizes to also give this result for k-connected partial k-trees. The converse—definability implies recognizability—is known to hold over all partial k-trees. It has been conjectured that recognizability implies definability over partial k-trees; but a proof was previously known only for k≤2. This paper proves the conjecture—and hence the equivalence of definability and recognizability—over partial 3-trees and k-connected partial k-trees.
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© 1997 Springer-Verlag Berlin Heidelberg
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Kaller, D. (1997). Definability equals recognizability of partial 3-trees. In: d'Amore, F., Franciosa, P.G., Marchetti-Spaccamela, A. (eds) Graph-Theoretic Concepts in Computer Science. WG 1996. Lecture Notes in Computer Science, vol 1197. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62559-3_20
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DOI: https://doi.org/10.1007/3-540-62559-3_20
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