Editing Interactive proof system (section)

=== NP ===

The complexity class [[NP (complexity)|NP]] may be viewed as a very simple proof system. In this system, the verifier is a deterministic, polynomial-time machine (a [[P (complexity)|P]] machine). The protocol is:
* The prover looks at the input and computes the solution using its unlimited power and returns a polynomial-size proof certificate.
* The verifier verifies that the certificate is valid in deterministic polynomial time. If it is valid, it accepts; otherwise, it rejects.

In the case where a valid proof certificate exists, the prover is always able to make the verifier accept by giving it that certificate. In the case where there is no valid proof certificate, however, the input is not in the language, and no prover, however malicious it is, can convince the verifier otherwise, because any proof certificate will be rejected.