Lower Bounds for Existential Pebble Games and k-Consistency Tests

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...

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Veröffentlicht in:	Logical methods in computer science Jg. 9, Issue 4
1. Verfasser:	Berkholz, Christoph
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Logical Methods in Computer Science e.V 08.10.2013
Schlagworte:	computer science - computational complexity computer science - logic in computer science
ISSN:	1860-5974, 1860-5974
Online-Zugang:	Volltext
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Zusammenfassung:	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.
ISSN:	1860-5974 1860-5974
DOI:	10.2168/LMCS-9(4:2)2013