Local Redundancy in SAT: Generalizations of Blocked Clauses
Clause-elimination procedures that simplify formulas in conjunctive normal form play an important role in modern SAT solving. Before or during the actual solving process, such procedures identify and remove clauses that are irrelevant to the solving result. These simplifications usually rely on so-c...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Logical Methods in Computer Science e.V.
2018-10-01
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| Series: | Logical Methods in Computer Science |
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| Online Access: | https://lmcs.episciences.org/3152/pdf |
| _version_ | 1797268538478559232 |
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| author | Benjamin Kiesl Martina Seidl Hans Tompits Armin Biere |
| author_facet | Benjamin Kiesl Martina Seidl Hans Tompits Armin Biere |
| author_sort | Benjamin Kiesl |
| collection | DOAJ |
| description | Clause-elimination procedures that simplify formulas in conjunctive normal
form play an important role in modern SAT solving. Before or during the actual
solving process, such procedures identify and remove clauses that are
irrelevant to the solving result. These simplifications usually rely on
so-called redundancy properties that characterize cases in which the removal of
a clause does not affect the satisfiability status of a formula. One
particularly successful redundancy property is that of blocked clauses, because
it generalizes several other redundancy properties. To find out whether a
clause is blocked---and therefore redundant---one only needs to consider its
resolution environment, i.e., the clauses with which it can be resolved. For
this reason, we say that the redundancy property of blocked clauses is local.
In this paper, we show that there exist local redundancy properties that are
even more general than blocked clauses. We present a semantic notion of
blocking and prove that it constitutes the most general local redundancy
property. We furthermore introduce the syntax-based notions of set-blocking and
super-blocking, and show that the latter coincides with our semantic blocking
notion. In addition, we show how semantic blocking can be alternatively
characterized via Davis and Putnam's rule for eliminating atomic formulas.
Finally, we perform a detailed complexity analysis and relate our novel
redundancy properties to prominent redundancy properties from the literature. |
| first_indexed | 2024-04-25T01:34:04Z |
| format | Article |
| id | doaj.art-051649b49eab4027b9e518c0167889bc |
| institution | Directory Open Access Journal |
| issn | 1860-5974 |
| language | English |
| last_indexed | 2024-04-25T01:34:04Z |
| publishDate | 2018-10-01 |
| publisher | Logical Methods in Computer Science e.V. |
| record_format | Article |
| series | Logical Methods in Computer Science |
| spelling | doaj.art-051649b49eab4027b9e518c0167889bc2024-03-08T10:27:52ZengLogical Methods in Computer Science e.V.Logical Methods in Computer Science1860-59742018-10-01Volume 14, Issue 410.23638/LMCS-14(4:3)20183152Local Redundancy in SAT: Generalizations of Blocked ClausesBenjamin KieslMartina SeidlHans TompitsArmin BiereClause-elimination procedures that simplify formulas in conjunctive normal form play an important role in modern SAT solving. Before or during the actual solving process, such procedures identify and remove clauses that are irrelevant to the solving result. These simplifications usually rely on so-called redundancy properties that characterize cases in which the removal of a clause does not affect the satisfiability status of a formula. One particularly successful redundancy property is that of blocked clauses, because it generalizes several other redundancy properties. To find out whether a clause is blocked---and therefore redundant---one only needs to consider its resolution environment, i.e., the clauses with which it can be resolved. For this reason, we say that the redundancy property of blocked clauses is local. In this paper, we show that there exist local redundancy properties that are even more general than blocked clauses. We present a semantic notion of blocking and prove that it constitutes the most general local redundancy property. We furthermore introduce the syntax-based notions of set-blocking and super-blocking, and show that the latter coincides with our semantic blocking notion. In addition, we show how semantic blocking can be alternatively characterized via Davis and Putnam's rule for eliminating atomic formulas. Finally, we perform a detailed complexity analysis and relate our novel redundancy properties to prominent redundancy properties from the literature.https://lmcs.episciences.org/3152/pdfcomputer science - logic in computer science |
| spellingShingle | Benjamin Kiesl Martina Seidl Hans Tompits Armin Biere Local Redundancy in SAT: Generalizations of Blocked Clauses Logical Methods in Computer Science computer science - logic in computer science |
| title | Local Redundancy in SAT: Generalizations of Blocked Clauses |
| title_full | Local Redundancy in SAT: Generalizations of Blocked Clauses |
| title_fullStr | Local Redundancy in SAT: Generalizations of Blocked Clauses |
| title_full_unstemmed | Local Redundancy in SAT: Generalizations of Blocked Clauses |
| title_short | Local Redundancy in SAT: Generalizations of Blocked Clauses |
| title_sort | local redundancy in sat generalizations of blocked clauses |
| topic | computer science - logic in computer science |
| url | https://lmcs.episciences.org/3152/pdf |
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