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Why is checking a proof easier than finding one?

  • A.The checker may assume the prover has already done the work correctly
  • B.Each step need only be matched against a rule
  • C.Proofs are always much shorter than the searches that produced them
  • D.Checking requires no knowledge of the domain the proof concerns

Answer: B

Verification examines each step in turn and confirms it instantiates an inference rule, which is linear in the proof's length, while finding the proof required searching an enormous space. Proof length varies, domain knowledge is not needed by either, and assuming correctness would defeat the purpose. An asymmetry between constructing and verifying is what allows a complex tool to be trusted through a simple one.

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