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Published in:
2010 | OriginalPaper | Chapter
On Monadic Second-Order Theories of Multidominance Structures
Author : Stephan Kepser
Published in: The Mathematics of Language
Publisher: Springer Berlin Heidelberg
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Multidominance structures were introduced by Kracht [4] to provide a data structure for the formalisation of various aspects of GB-Theory. Kracht studied the PDL-theory of MDSes and showed that this theory is decidable in [5], actually 2EXPTIME-complete. He continues to conjecture that thus the MSO-theory of MDSes should be decidable, too. We show here the contrary. Actually, both the MSO-theory over vertices only and the MSO-theory over vertices and edges turn out to be undecidable.