Berkholz, Christoph - Lower Bounds for Existential Pebble Games and k-Consistency Tests

lmcs:1010 - Logical Methods in Computer Science, October 8, 2013, Volume 9, Issue 4
Lower Bounds for Existential Pebble Games and k-Consistency Tests

Authors: Berkholz, Christoph

The existential k-pebble game characterizes the expressive power of the existential-positive k-variable fragment of first-order logic on finite structures. The winner of the existential k-pebble game on two given finite structures can be determined in time O(n2k) by dynamic programming on the graph of game configurations. We show that there is no O(n(k-3)/12)-time algorithm that decides which player can win the existential k-pebble game on two given structures. This lower bound is unconditional and does not rely on any complexity-theoretic assumptions. Establishing strong k-consistency is a well-known heuristic for solving the constraint satisfaction problem (CSP). By the game characterization of Kolaitis and Vardi our result implies that there is no O(n(k-3)/12)-time algorithm that decides if strong k-consistency can be established for a given CSP-instance.


Source : oai:arXiv.org:1205.0679
DOI : 10.2168/LMCS-9(4:2)2013
Volume: Volume 9, Issue 4
Published on: October 8, 2013
Submitted on: November 14, 2012
Keywords: Computer Science - Logic in Computer Science,Computer Science - Computational Complexity


Share

Consultation statistics

This page has been seen 74 times.
This article's PDF has been downloaded 23 times.