Affiliations: MPLA, Department of Mathematics, National and
Capodistrian University of Athens, Panepistimiopolis, 15784 Athens, Greece.
aflaw@otenet.gr, eugenie@aueb.gr; lkalan@math.uoa.gr
Note: [] Address for correspondence: MPLA, Department of
Mathematics, National and Capodistrian University of Athens, Panepistimiopolis,
15784 Athens, Greece
Abstract: We model the monadic second-order logic (MSO) evaluation problem on
finite colored trees in a purely database theoretic framework, based on the
well-knownMSO-automata connection: we reduce the problem to an acyclic
conjunctive query evaluation problem on the one hand and to a monadic datalog
evaluation problem on the other hand. This approach offers the possibility to
solve the MSO problem using optimized evaluation methods for relational algebra
expressions and for datalog programs (such as Yannakakis algorithm [27] and the
rewriting method using resolutionbased filtering referred to as
"magic sets" method in [3]): we use these methods for
evaluating our queries and giving estimates of their complexity. This is the
first time, to our knowledge, that a solution to the MSO evaluation problem
related to relational algebra is given; furthermore, thanks to this reduction,
we prove that the automata-based algorithm given in [8] constitutes a
particular "instance" of Yannakakis algorithm. Besides
the optimized database methods that we propose for solving the MSO evaluation
problem, our results prove that MSO-definable queries over colored trees are
datalog-definable; this result subsumes the corresponding result in [12] which
states that unary MSO queries are monadic datalog-definable and it also
subsumes the well-known result that any MSO-definable class of trees is monadic
datalog-definable.
