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Generalising and Unifying SLUR and Unit-Refutation Completeness

Matthew Gwynne, Oliver Kullmann Orcid Logo

SOFSEM 2013: Theory and Practice of Computer Science. LCNS, Volume: 7741, Pages: 220 - 232

Swansea University Author: Oliver Kullmann Orcid Logo

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Abstract

The class SLUR (Single Lookahead Unit Resolution) was introduced in [Schlipf, Annexstein, Franco, Swaminathan, 1995] as an umbrella class for efficient SAT solving. Balyo, Gursky, Cepek, Kucera, Vlcek in 2012 extended this class in various ways to hierarchies covering all of CNF (all clause-sets). W...

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Published in: SOFSEM 2013: Theory and Practice of Computer Science. LCNS
ISSN: 0302-9743 1611-3349
Published: Springer 2013
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URI: https://cronfa.swan.ac.uk/Record/cronfa13748
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spelling 2013-10-17T14:56:09.1324491 v2 13748 2012-12-17 Generalising and Unifying SLUR and Unit-Refutation Completeness 2b410f26f9324d6b06c2b98f67362d05 0000-0003-3021-0095 Oliver Kullmann Oliver Kullmann true false 2012-12-17 SCS The class SLUR (Single Lookahead Unit Resolution) was introduced in [Schlipf, Annexstein, Franco, Swaminathan, 1995] as an umbrella class for efficient SAT solving. Balyo, Gursky, Cepek, Kucera, Vlcek in 2012 extended this class in various ways to hierarchies covering all of CNF (all clause-sets). We introduce a hierarchy SLUR_k which we argue is the natural “limit” of such approaches. The second source for our investigations is the class UC of unit-refutation complete clause-sets introduced in [del Val 1994]. Via the theory of (tree-resolution based) “hardness” of clause-sets as developed in ECCC-report, Annals-paper and [Ansotegui, Bonet, Levy, Manya, 2008], we obtain a natural generalisation UC_k, containing those clause-sets which are “unit-refutation complete of level k”, which is the same as having hardness at most k. Utilising the strong connections to (tree-)resolution complexity and (nested) input resolution, we develop fundamental methods for the determination of hardness (the level k in UCk ). A fundamental insight now is that SLUR_k = UC_k holds for all k. We can thus exploit both streams of intuitions and methods for the investigations of these hierarchies. Conference Paper/Proceeding/Abstract SOFSEM 2013: Theory and Practice of Computer Science. LCNS 7741 220 232 Springer 0302-9743 1611-3349 algorithms, satisfiability, polynomial time, knowledge compilation 31 12 2013 2013-12-31 10.1007/978-3-642-35843-2_20 http://www.cs.swan.ac.uk/~csoliver/papers.html#SLUR2012SOFSEM COLLEGE NANME Computer Science COLLEGE CODE SCS Swansea University 2013-10-17T14:56:09.1324491 2012-12-17T22:40:14.2987438 College of Science Computer Science Matthew Gwynne 1 Oliver Kullmann 0000-0003-3021-0095 2
title Generalising and Unifying SLUR and Unit-Refutation Completeness
spellingShingle Generalising and Unifying SLUR and Unit-Refutation Completeness
Oliver Kullmann
title_short Generalising and Unifying SLUR and Unit-Refutation Completeness
title_full Generalising and Unifying SLUR and Unit-Refutation Completeness
title_fullStr Generalising and Unifying SLUR and Unit-Refutation Completeness
title_full_unstemmed Generalising and Unifying SLUR and Unit-Refutation Completeness
title_sort Generalising and Unifying SLUR and Unit-Refutation Completeness
author_id_str_mv 2b410f26f9324d6b06c2b98f67362d05
author_id_fullname_str_mv 2b410f26f9324d6b06c2b98f67362d05_***_Oliver Kullmann
author Oliver Kullmann
author2 Matthew Gwynne
Oliver Kullmann
format Conference Paper/Proceeding/Abstract
container_title SOFSEM 2013: Theory and Practice of Computer Science. LCNS
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publishDate 2013
institution Swansea University
issn 0302-9743
1611-3349
doi_str_mv 10.1007/978-3-642-35843-2_20
publisher Springer
college_str College of Science
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hierarchy_parent_title College of Science
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url http://www.cs.swan.ac.uk/~csoliver/papers.html#SLUR2012SOFSEM
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description The class SLUR (Single Lookahead Unit Resolution) was introduced in [Schlipf, Annexstein, Franco, Swaminathan, 1995] as an umbrella class for efficient SAT solving. Balyo, Gursky, Cepek, Kucera, Vlcek in 2012 extended this class in various ways to hierarchies covering all of CNF (all clause-sets). We introduce a hierarchy SLUR_k which we argue is the natural “limit” of such approaches. The second source for our investigations is the class UC of unit-refutation complete clause-sets introduced in [del Val 1994]. Via the theory of (tree-resolution based) “hardness” of clause-sets as developed in ECCC-report, Annals-paper and [Ansotegui, Bonet, Levy, Manya, 2008], we obtain a natural generalisation UC_k, containing those clause-sets which are “unit-refutation complete of level k”, which is the same as having hardness at most k. Utilising the strong connections to (tree-)resolution complexity and (nested) input resolution, we develop fundamental methods for the determination of hardness (the level k in UCk ). A fundamental insight now is that SLUR_k = UC_k holds for all k. We can thus exploit both streams of intuitions and methods for the investigations of these hierarchies.
published_date 2013-12-31T03:23:22Z
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