TY - JOUR
T1 - Separating signs in the propositional satisfiability problem
AU - Hirsch, E. A.
PY - 2000
Y1 - 2000
N2 - In 1980, Monien and Speckenmeyer and (independently) Dantsin proved that the satisfiability of a propositional formula in CNF can be checked in less than 2N steps (N is the number of variables). Later, many other upper bounds for SAT and its subproblems were proved. A formula in CNF is in CNF- (1, ∞) if each positive literal occurs in it at most once. In 1984, Luckhardt studied formulas in CNF-(1, ∞). In this paper, we prove several a new upper bounds for formulas in CNF-(l.∞) by introducing new signs separation principle. Namely, we present algorithms working in time of order 1.1939K and 1.0644L for a formula consisting of K clauses containing L literal occurrences. We also present an algorithm for formulas in CNF-(1, ∞) whose clauses are bounded in length.
AB - In 1980, Monien and Speckenmeyer and (independently) Dantsin proved that the satisfiability of a propositional formula in CNF can be checked in less than 2N steps (N is the number of variables). Later, many other upper bounds for SAT and its subproblems were proved. A formula in CNF is in CNF- (1, ∞) if each positive literal occurs in it at most once. In 1984, Luckhardt studied formulas in CNF-(1, ∞). In this paper, we prove several a new upper bounds for formulas in CNF-(l.∞) by introducing new signs separation principle. Namely, we present algorithms working in time of order 1.1939K and 1.0644L for a formula consisting of K clauses containing L literal occurrences. We also present an algorithm for formulas in CNF-(1, ∞) whose clauses are bounded in length.
UR - http://www.scopus.com/inward/record.url?scp=52849120789&partnerID=8YFLogxK
U2 - 10.1007/BF02362266
DO - 10.1007/BF02362266
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AN - SCOPUS:52849120789
SN - 1072-3374
VL - 98
SP - 442
EP - 463
JO - Journal of Mathematical Sciences
JF - Journal of Mathematical Sciences
IS - 4
ER -