Title: Query evaluation via tree-decompositions

Authors: Jörg Flum, Markus Frick, and Martin Grohe

Abstract: A number of efficient methods for evaluating
first-order and monadic-second order queries on finite relational
structures are based on tree-decompositions of structures or
queries. We systematically study these methods.

In the first-part of the paper we consider arbitrary formulas on
tree-like structures. We generalize a theorem of Courcelle (1990) by
showing that on structures of bounded tree-width a monadic
second-order formula (with free first- and second-order variables) can
be evaluated in time linear in the structure size plus the size of the
output.

In the second part we study tree-like formulas on arbitrary
structures. We generalize the notions of acyclicity and bounded
tree-width from conjunctive queries to arbitrary first-order formulas
in a straightforward way and analyze the complexity of evaluating
formulas of these fragments. Moreover, we show that the acyclic and
bounded tree-width fragments have the same expressive power as the
well-known guarded fragment and the finite-variable fragments of
first-order logic, respectively.