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On Monadic Second-Order Theories of Multidominance Structures

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The Mathematics of Language (MOL 2009, MOL 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6149))

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Introduction

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.

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References

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Kepser, S. (2010). On Monadic Second-Order Theories of Multidominance Structures. In: Ebert, C., Jäger, G., Michaelis, J. (eds) The Mathematics of Language. MOL MOL 2009 2007. Lecture Notes in Computer Science(), vol 6149. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14322-9_10

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  • DOI: https://doi.org/10.1007/978-3-642-14322-9_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14321-2

  • Online ISBN: 978-3-642-14322-9

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