(a) Stingy SAT is the following problem: given a set of clauses (each a disjunction of literals) and an integer k, find a satisfying assignment in which at most k variables are true, if such an assignment exists. Prove that stingy SAT is NP-hard. (b) The Double SAT problem asks whether a given satisfiability problem has at least two different satisfying assignments. For example, the problem {{V1, V2}, {V1, V2}, {V1, V2}} is satisfiable, but has only one solution (v₁ = F, v₂ = T). In contrast, {{V1, V2}, {V1, V2}} has exactly two solutions. Show that Double-SAT is NP-hard.
(a) Stingy SAT is the following problem: given a set of clauses (each a disjunction of literals) and an integer k, find a satisfying assignment in which at most k variables are true, if such an assignment exists. Prove that stingy SAT is NP-hard. (b) The Double SAT problem asks whether a given satisfiability problem has at least two different satisfying assignments. For example, the problem {{V1, V2}, {V1, V2}, {V1, V2}} is satisfiable, but has only one solution (v₁ = F, v₂ = T). In contrast, {{V1, V2}, {V1, V2}} has exactly two solutions. Show that Double-SAT is NP-hard.
Related questions
Question
Transcribed Image Text:(a) Stingy SAT is the following problem: given a set of clauses (each a disjunction of
literals) and an integer k, find a satisfying assignment in which at most k variables
are true, if such an assignment exists. Prove that stingy SAT is NP-hard.
(b) The Double SAT problem asks whether a given satisfiability problem has at least two
different satisfying assignments. For example, the problem {{V1, V2}, {V1, V2}, {V1, V2}}
is satisfiable, but has only one solution (v₁ = F, v₂ = T). In contrast, {{V1, V2}, {V1, V2}}
has exactly two solutions. Show that Double-SAT is NP-hard.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
