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B. Kiesl, M. Seidl, H. Tompits, A. Biere:
"Local Redundancy in SAT: Generalizations of Blocked Clauses";
Logical Methods in Computer Science, 14 (2018), 4.

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.

SAT, propositional logic, blocked clauses, redundancy properties

http://dx.doi.org/10.23638/LMCS-14(4:3)2018

https://publik.tuwien.ac.at/files/publik_277593.pdf