We are currently experiencing intermittent issues impacting performance. We apologize for the inconvenience.
By Topic

Equivalence in finite-variable logics is complete for polynomial time

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

1 Author(s)
Grohe, M. ; Inst. fur Math. Logik, Albert-Ludwigs-Univ., Freiburg, Germany

How difficult is it to decide whether two finite structures can be distinguished in a given logic? For first order logic, this question is equivalent to the graph isomorphism problem with its well-known complexity theoretic difficulties. Somewhat surprisingly, the situation is much clearer when considering the fragments Lk of first-order logic whose formulae contain at most k (free or bound) variables (for some k⩾1). We show that for each k⩾2, equivalence in the k-variable logic Lk is complete for polynomial time under quantifier-free reductions (a weak form of NC0 reductions). Moreover, we show that the same completeness result holds for the powerful extension Ck of Lk with counting quantifiers (for every k⩾2)

Published in:

Foundations of Computer Science, 1996. Proceedings., 37th Annual Symposium on

Date of Conference:

14-16 Oct 1996