1. NP ⊆ PCP(n 3, 1) Theory of Computation

2. NP ⊆ PCP(n 3,1) What is that? NP ⊆ PCP(n 3,1) What is that?

3. Before discussing COMPLEX COMPUTATION… we will clarify & classify first the NP & PCP

4. NP ⊆ PCP (n 3,1) In computational complexity theory, NP is one of the most fundamental complexity classes. The abbreviation NP refers to "nondeterministic polynomial time.“ Intuitively, NP is the set of all decision problems for which the instances where the answer is "yes" have efficiently verifiable proofs of the fact that the answer is indeed "yes".

5. More precisely, these proofs have to be verifiable in polynomial time by a deterministic Turing machine. In an equivalent formal definition, NP is the set of decision problems where the "yes"-instances can be accepted in polynomial time by a non-deterministic Turing machine. NP ⊆ PCP (n 3,1)

6. In computational complexity theory, a probabilistically checkable proof (PCP) is a type of proof that can be checked by a randomized algorithm using a bounded amount of randomness and reading a bounded number of bits of the proof.

7. The algorithm is then required to accept correct proofs and reject incorrect proofs with very high probability. A standard proof (or certificate), as used in the verifier-based definition of the complexity class NP, also satisfies these requirements, since the checking procedure deterministically reads the whole proof, always accepts correct proofs and rejects incorrect proofs.

12. How can the verifier be convinced of this fact after only a constant number of queries to the prover?

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23. End.. Prepared by: Jaypee B. Julve