Summary: Tree-width for first order formulae
and Mark Weyer2
Department of Informatics, University of Bergen, Norway
Humboldt Universit¨at zu Berlin, Berlin, Germany
Abstract We introduce tree-width for first order formulae , fotw().
We show that computing fotw is fixed-parameter tractable with parame-
ter fotw. Moreover, we show that on classes of formulae of bounded fotw,
model checking is fixed parameter tractable, with parameter the length
of the formula. This is done by translating a formula with fotw() < k
into a formula of the k-variable fragment Lk
of first order logic. For fixed
k, the question whether a given first order formula is equivalent to an
formula is undecidable. In contrast, the classes of first order formu-
lae with bounded fotw are fragments of first order logic for which the
equivalence is decidable.
Our notion of tree-width generalises tree-width of conjunctive queries to