Blumensath, Achim and Otto, Martin and Weyer, Mark - Decidability Results for the Boundedness Problem

lmcs:1225 - Logical Methods in Computer Science, August 15, 2014, Volume 10, Issue 3
Decidability Results for the Boundedness Problem

Authors: Blumensath, Achim and Otto, Martin and Weyer, Mark

We prove decidability of the boundedness problem for monadic least fixed-point recursion based on positive monadic second-order (MSO) formulae over trees. Given an MSO-formula phi(X,x) that is positive in X, it is decidable whether the fixed-point recursion based on phi is spurious over the class of all trees in the sense that there is some uniform finite bound for the number of iterations phi takes to reach its least fixed point, uniformly across all trees. We also identify the exact complexity of this problem. The proof uses automata-theoretic techniques. This key result extends, by means of model-theoretic interpretations, to show decidability of the boundedness problem for MSO and guarded second-order logic (GSO) over the classes of structures of fixed finite tree-width. Further model-theoretic transfer arguments allow us to derive major known decidability results for boundedness for fragments of first-order logic as well as new ones.


Source : oai:arXiv.org:1406.7684
DOI : 10.2168/LMCS-10(3:2)2014
Volume: Volume 10, Issue 3
Published on: August 15, 2014
Submitted on: March 17, 2011
Keywords: Computer Science - Logic in Computer Science


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