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- W2567850168 abstract "A conjunctive normal form (CNF) formula F is minimal unsatisfiable if F is unsatisfiable and the resulting formula removing any clause from F is satisfiable. (r,s)-CNF is a subclass of CNF in which each clause of formula has exactly r distinct literals and every variable occurs at most s times. The corresponding satisfiable problem (r,s)-SAT means that the instances are restricted in (r,s)-CNF. For positive integer r≥3, there exists a critical function f(r) such that all formulas in (r,f(r))-CNF are satisfiable, but (r,f(r)+1)-SAT is already NP-Complete. It is open whether or not the function f is computable. One can only estimate some bounds of f(r) except for f(3)=3 and f(4)=4. In this paper, the applications of minimal unsatisfiable formulas are described for transformations between CNF formulas. A new algorithm is presented to introduce less new variables in transformation from CNF to 3-CNF, which for clauses with length l(3) only ???2l ??? new variables are introduced. The principle and method for transforming CNF to (r,s)-CNF and constructing unsatisfiable formulas in (r,s)-CNF are presented." @default.
- W2567850168 created "2017-01-13" @default.
- W2567850168 creator A5080025285 @default.
- W2567850168 date "2006-01-01" @default.
- W2567850168 modified "2023-09-23" @default.
- W2567850168 title "Applications of Minimal Unsatisfiable Formulas to Polynomially Reduction for Formulas" @default.
- W2567850168 hasPublicationYear "2006" @default.
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