Lower Bounds for Existential Pebble Games and k-Consistency Tests
Abstract
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.
Keywords
Cite
@article{arxiv.1205.0679,
title = {Lower Bounds for Existential Pebble Games and k-Consistency Tests},
author = {Christoph Berkholz},
journal= {arXiv preprint arXiv:1205.0679},
year = {2015}
}