By Topic

Existential second-order logic over graphs: charting the tractability frontier

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

3 Author(s)
Gottlob, G. ; Tech. Univ. Wien, Austria ; Kolaitis, P.G. ; Schwentick, T.

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 second-order formula. We study the complexity of evaluating existential second-order formulas that belong to prefix classes of existential second-order logic, where a prefix class is the collection of all existential second-order and the first-order quantifiers obey a certain quantifier pattern. We completely characterize the computation complexity of prefix classes of existential second-order logic in three different contexts: over directed graphs; over undirected graphs with self-loops; and over undirected graphs without self-loops. Our main result is that in each of these three contexts a dichotomy holds, i.e., each prefix class of existential second-order logic either contains sentences that can express NP-complete problems or each of its sentences expresses a polynomial-time solvable problem. Although the boundary of the dichotomy coincides for the first two cases, it changes, as one move to undirected graphs without self-loops

Published in:

Foundations of Computer Science, 2000. Proceedings. 41st Annual Symposium on

Date of Conference:

2000