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41st Annual Symposium on Foundations of Computer Science
Existential secondorder logic over graphs: charting the tractability frontier
Redondo Beach, California
November 12November 14
ISBN: 0769508502
ASCII Text  x  
G. Gottlob, P.G. Kolaitis, T. Schwentick, "Existential secondorder logic over graphs: charting the tractability frontier," 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, pp. 664, 41st Annual Symposium on Foundations of Computer Science, 2000.  
BibTex  x  
@article{ 10.1109/SFCS.2000.892334, author = {G. Gottlob and P.G. Kolaitis and T. Schwentick}, title = {Existential secondorder logic over graphs: charting the tractability frontier}, journal ={2013 IEEE 54th Annual Symposium on Foundations of Computer Science}, volume = {0}, year = {2000}, issn = {02725428}, pages = {664}, doi = {http://doi.ieeecomputersociety.org/10.1109/SFCS.2000.892334}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  CONF JO  2013 IEEE 54th Annual Symposium on Foundations of Computer Science TI  Existential secondorder logic over graphs: charting the tractability frontier SN  02725428 SP EP A1  G. Gottlob, A1  P.G. Kolaitis, A1  T. Schwentick, PY  2000 KW  formal logic; computational complexity; graph theory; existential secondorder logic; graphs; tractability; descriptive complexity; existential secondorder formula; prefix class; firstorder quantifiers; computational complexity; directed graphs; undirected graphs; NPcomplete problems; polynomialtime solvable problem VL  0 JA  2013 IEEE 54th Annual Symposium on Foundations of Computer Science ER   
Fagin's (1974) theorem, the first important result of descriptive complexity, asserts that a property of graphs is in NP if and only if it is definable by an existential secondorder formula. We study the complexity of evaluating existential secondorder formulas that belong to prefix classes of existential secondorder logic, where a prefix class is the collection of all existential secondorder and the firstorder quantifiers obey a certain quantifier pattern. We completely characterize the computation complexity of prefix classes of existential secondorder logic in three different contexts: over directed graphs; over undirected graphs with selfloops; and over undirected graphs without selfloops. Our main result is that in each of these three contexts a dichotomy holds, i.e., each prefix class of existential secondorder logic either contains sentences that can express NPcomplete problems or each of its sentences expresses a polynomialtime solvable problem. Although the boundary of the dichotomy coincides for the first two cases, it changes, as one move to undirected graphs without selfloops.
Index Terms:
formal logic; computational complexity; graph theory; existential secondorder logic; graphs; tractability; descriptive complexity; existential secondorder formula; prefix class; firstorder quantifiers; computational complexity; directed graphs; undirected graphs; NPcomplete problems; polynomialtime solvable problem
Citation:
G. Gottlob, P.G. Kolaitis, T. Schwentick, "Existential secondorder logic over graphs: charting the tractability frontier," focs, pp.664, 41st Annual Symposium on Foundations of Computer Science, 2000
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