The paper introduces a new characterization of the complexity class NP, stating that NP consists of languages for which membership proofs can be verified probabilistically in polynomial time using a logarithmic number of random bits and reading sublogarithmic bits from the proof. This characterization has significant implications, including the NP-hardness of approximating the clique number within any constant factor. The authors use techniques from interactive proofs and verifier composition to achieve this result, providing a detailed proof and discussing the broader context of complexity theory, including the hardness of approximation and the power of interaction in computational problems.The paper introduces a new characterization of the complexity class NP, stating that NP consists of languages for which membership proofs can be verified probabilistically in polynomial time using a logarithmic number of random bits and reading sublogarithmic bits from the proof. This characterization has significant implications, including the NP-hardness of approximating the clique number within any constant factor. The authors use techniques from interactive proofs and verifier composition to achieve this result, providing a detailed proof and discussing the broader context of complexity theory, including the hardness of approximation and the power of interaction in computational problems.