The expressive power of two-variable least fixed-point logics

Authors:
Martin Grohe;Stephan Kreutzer;Nicole Schweikardt
Affiliations:
Institut für Informatik, Humboldt-Universität, Berlin;Institut für Informatik, Humboldt-Universität, Berlin;Institut für Informatik, Humboldt-Universität, Berlin
Venue:
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Year:
2005

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Abstract

The present paper gives a classification of the expressive power of two-variable least fixed-point logics. The main results are: The two-variable fragment of monadic least fixed-point logic with parameters is as expressive as full monadic least fixed-point logic (on binary structures). The two-variable fragment of monadic least fixed-point logic without parameters is as expressive as the two-variable fragment of binary least fixed-point logic without parameters. The two-variable fragment of binary least fixed-point logic with parameters is strictly more expressive than the two-variable fragment of monadic least fixed-point logic with parameters (even on finite strings).