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Why does theorem proving often outperform model checking?

  • A.Theorem proving requires fewer symbols to be declared
  • B.A proof may be short even when the model count is enormous
  • C.Theorem proving is guaranteed to terminate more quickly
  • D.Model checking cannot handle any formulas containing negation

Answer: B

A conclusion following from three of a thousand premises can be proved in three steps while enumeration would examine two to the thousand models. The proof ignores everything irrelevant. Termination guarantees run the other way, negation is handled by both, and symbol counts are fixed by the problem. That the length of a proof bears no relation to the size of the model space is what makes syntactic methods worth developing at all.

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