A polynomial-time algorithm for a promise problem that takes one of these constructs as input would imply “NP equals RP,” according to the Valiant–Vazirani theorem. The DPLL algorithm takes one of these constructs as input. In 1972, Richard Karp exhibited chains of polynomial-time reductions stemming from a problem taking one of these constructs as input, which was shown by the Cook–Levin theorem to be NP-complete. These constructs can be placed in conjunctive normal form by applying De Morgan’s laws. These constructs’ clauses are restricted to contain at most three literals in a problem abbreviated 3SAT (“THREE-sat”), which asks if there is an input for which these constructs output “true.” For 10 points, name these constructs built by using operators like “AND” and “OR” to link variables that take the value true or false. ■END■
ANSWER: Boolean formulas [or Boolean expressions; accept Boolean formulas in conjunctive normal form; accept Boolean functions; accept Boolean sentences; accept Boolean statements; accept Boolean clauses until “clauses” is read; accept Boolean well-formed formulas or Boolean wffs; accept propositional formulas or propositional expressions or propositional sentences; accept logical formulas or logical expressions; prompt on formulas or expressions or functions or sentences or statements or well-formed formulas or wffs; prompt on clauses until read; prompt on booleans or bools; reject “Boolean circuits” or “Boolean variables”]
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= Average correct buzz position