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Comparing the succinctness of monadic query languages over finite trees

Published online by Cambridge University Press:  15 October 2004

Martin Grohe  and
Nicole Schweikardt
Martin Grohe
Affiliation:
Institut für Informatik, Humboldt-Universität Berlin, Germany; grohe@informatik.hu-berlin.de.; schweika@informatik.hu-berlin.de.
Nicole Schweikardt
Affiliation:
Institut für Informatik, Humboldt-Universität Berlin, Germany; grohe@informatik.hu-berlin.de.; schweika@informatik.hu-berlin.de.
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Abstract

We study the succinctness of monadic second-order logic and a variety of monadic fixed point logics on trees. All these languages are known to have the same expressive power on trees, but some can express the same queries much more succinctly than others. For example, we show that, under some complexity theoretic assumption, monadic second-order logic is non-elementarily more succinct than monadic least fixed point logic, which in turn is non-elementarily more succinct than monadic datalog.
Succinctness of the languages is closely related to the combined and parameterised complexity of query evaluation for these languages.

Keywords

Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 38 , Issue 4: Fixed Points in Computer Science (FICS'03) , October 2004 , pp. 343 - 373
Copyright
© EDP Sciences, 2004

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