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What does a satisfiability solver return when a formula is satisfiable?

  • A.A satisfying assignment
  • B.A proof that no contradiction can be derived from the clause set
  • C.The number of distinct assignments satisfying the whole formula
  • D.A simplified version of the formula with the variables eliminated

Answer: A

The solver returns a model, which can be checked independently in linear time, so a positive answer is easy to verify. A negative answer requires a refutation proof, which good solvers can also emit. Counting models and eliminating variables are different problems, the first being considerably harder. That a yes answer is cheaply checkable while a no answer needs a proof is an asymmetry worth exploiting whenever a tool's output must be trusted. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.

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