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June 24, 2008 to June 27, 2008

ISBN: 978-0-7695-3183-0

pp: 267-271

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/LICS.2008.11

ABSTRACT

The question of whether there is a logic that captures polynomial time is thecentral open problem in descriptive complexity theory. In my talk, I will review the question and the early, mostly negative results that were obtained until the mid 1990s, and then move on to positive results about capturing polynomial time on specific classes of graphs. This will include recent results on definability in fixed-point logic and graph structure theory. Finally, I will dicuss stronger logics and propose directions for further research.The purpose of this accompanying note is to give the basic definitions in detail, state the main results, mention some open problems, and give a list of references.

INDEX TERMS

descriptive complexity, finite model theory, query languages

CITATION

Martin Grohe,
"The Quest for a Logic Capturing PTIME",

*LICS*, 2008, Logic in Computer Science, Symposium on, Logic in Computer Science, Symposium on 2008, pp. 267-271, doi:10.1109/LICS.2008.11