FO Model Checking on Posets of Bounded Width

Over the past two decades the main focus of research into first-order (FO) model checking algorithms have been sparse relational structures-culminating in the FPT-algorithm by Grohe, Kreutzer and Siebertz for FO model checking of nowhere dense classes of graphs [STOC'14], with dense structures...

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Bibliographic Details
Main Authors: Gajarsky, Jakub, Hlineny, Petr, Lokshtanov, Daniel, Obdrzalek, Jan, Ordyniak, Sebastian, Ramanujan, M.S., Saurabh, Saket
Format: Conference Proceeding
Language:English
Subjects:
Algorithm design and analysis
algorithmic meta-theorems
Boolean functions
Complexity theory
Data structures
Electronic mail
first-order logic
Games
Model checking
parameterized complexity
partially ordered sets
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Summary:Over the past two decades the main focus of research into first-order (FO) model checking algorithms have been sparse relational structures-culminating in the FPT-algorithm by Grohe, Kreutzer and Siebertz for FO model checking of nowhere dense classes of graphs [STOC'14], with dense structures starting to attract attention only recently. Bova, Ganian and Szeider [CSL-LICS'14] initiated the study of the complexity of FO model checking on partially ordered sets (posets). Bova, Ganian and Szeider showed that model checking existential FO logic is fixed-parameter tractable (FPT) on posets of bounded width, where the width of a poset is the size of the largest antichain in the poset. The existence of an FPT algorithm for general FO model checking on posets of bounded width, however, remained open. We resolve this question in the positive by giving an algorithm that takes as its input an n-element poset P of width w and an FO logic formula φ, and determines whether φ holds on P in time f(φ, w) · n 2 .
ISSN:0272-5428
DOI:10.1109/FOCS.2015.63