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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| Published in: | Logical methods in computer science Vol. 9, Issue 4 |
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| Main Author: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
Logical Methods in Computer Science e.V
08.10.2013
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| Subjects: | |
| ISSN: | 1860-5974, 1860-5974 |
| Online Access: | Get full text |
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| Summary: | 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. |
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| ISSN: | 1860-5974 1860-5974 |
| DOI: | 10.2168/LMCS-9(4:2)2013 |