From polynomial time queries to graph structure theory
Proceedings of the 13th International Conference on Database Theory
Database theory: query languages
Algorithms and theory of computation handbook
Fields of logic and computation
A logic for PTIME and a parameterized halting problem
Fields of logic and computation
Fixed-point definability and polynomial time on chordal graphs and line graphs
Fields of logic and computation
Making queries tractable on big data with preprocessing: through the eyes of complexity theory
Proceedings of the VLDB Endowment
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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.