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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 varietyof monadic fixed point logics on trees. All these languages are known to havethe same expressive power on trees, but some can express the samequeries much more succinctly than others. For example, we show that, undersome complexity theoretic assumption, monadic second-order logic isnon-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 andparameterised complexity of query evaluation for these languages.

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