Monadic datalog over finite structures with bounded treewidth

Bounded treewidth and Monadic Second Order (MSO) logic have proved to be key concepts in establishing fixed-parameter tractability results. Indeed, by Courcelle's Theorem we know: Any property of finite structures, which is expressible by an MSO sentence, can be decided in linear time (data complexity) if the structures have bounded treewidth. In principle, Courcelle's Theorem can be applied directly to construct concrete algorithms by transforming the MSO evaluation problem into a tree language recognition problem. The latter can then be solved via a finite tree automaton (FTA). However, this approach has turned out to be problematical, since even relatively simple MSO formulae may lead to a "state explosion" of the FTA. In this work we propose monadic datalog (i.e., datalog where all intentional predicate symbols are unary) as an alternative method to tackle this class of fixed-parameter tractable problems. We show that if some property of finite structures is ex...

• Type: Conference
• Year: 2007
• Where: PODS
• Authors: Georg Gottlob, Reinhard Pichler, Fang Wei
• Keywords: Database, Monadic Datalog Program, MSO Evaluation Problem, PODS 2007, Simple Mso Formulae