an:06073517
Zbl 1245.68133
Courcelle, Bruno
Special tree-width and the verification of monadic second-order graph properties
EN
Lodaya, Kamal (ed.) et al., IARCS annual conference on foundations of software technology and theoretical computer science (FSTTCS 2010), December 15--18, 2010, Chennai, India. Wadern: Schloss Dagstuhl -- Leibniz Zentrum f??r Informatik (ISBN 978-3-939897-23-1). LIPIcs -- Leibniz International Proceedings in Informatics 8, 13-29, electronic only (2010).
2010
a
68Q60 68R10 03B70 68Q45
model-checking; monadic second-order logic; fixed-parameter tractability; special tree-width
Summary: The model-checking problem for monadic second-order logic on graphs is fixed-parameter tractable with respect to tree-width and clique-width. The proof constructs finite deterministic automata from monadic second-order sentences, but this computation produces automata of hyper-exponential sizes, and this is not avoidable. To overcome this difficulty, we propose to consider particular monadic second-order graph properties that are nevertheless interesting for graph theory and to interpret automata instead of trying to compile them (joint work with I. Durand).
For checking monadic second-order sentences written with edge set quantifications, the appropriate parameter is tree-width. We introduce special tree-width, a graph complexity measure between path-width and tree-width. The corresponding automata are easier to construct than those for tree-width.
For the entire collection see [Zbl 1213.68048].