 
Summary: Treewidth for first order formulae
Isolde Adler1
and Mark Weyer2
1
Department of Informatics, University of Bergen, Norway
2
Humboldt Universit¨at zu Berlin, Berlin, Germany
Abstract We introduce treewidth for first order formulae , fotw().
We show that computing fotw is fixedparameter 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 kvariable fragment Lk
of first order logic. For fixed
k, the question whether a given first order formula is equivalent to an
Lk
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 treewidth generalises treewidth of conjunctive queries to
