It is known that there exists a PCP characterization of NP where the verifier makes 3 queries and has a one-sided error that is bounded away from 1; and also that 2 queries do not suffice for such a characterization. Thus PCPs with 3 queries possess non-trivial verification power and motivate the task of determining the lowest error that can be achieved with a 3-query PCP. Recently, Håstad [11] has shown a tight characterization of NP by constructing a 3-query PCP verifier with "error"

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... ly close to 1=2. Unfortunately, this verifier makes two-sided error and Håstad makes essential use of this feature. One-sided error, on the other hand, is a natural notion to associate with a proof system, since it has the desirable property that every rejected proof has a short counterexample. The question of determining the smallest error for which there exists a 3-query PCP verifier making onesided error and accepting an NP-complete language, however, remained open. We resolve this question by showing that NP has a 3-query PCP with a one-sided error that is arbitrarily close to 1=2. This characterization is tight, i.e., the error cannot be lower. This result is in seeming contradiction with the results of Trevisan [15] and Zwick [17] who show that in order to recognize an NP-complete language, the error probability of a PCP verifier making 3 non-adaptive queries and having one-sided error must be at least 5=8. We get around this bottleneck by designing an adaptive 3-query PCP for NP. Our result yields the first tight analysis of an adaptive PCP; and reveals a previously unsuspected separation between the powers of adaptive and non-adaptive PCPs. Our design and analysis of adaptive PCPs can be extended to higher number of queries as well and we give an example of such a proof system with 5 queries. Our adaptive verifiers yield proof systems whose error probabilities match those of previous constructions, while also achieving one-sidedness in the error. This raises new questions about the power of adaptive PCPs, which deserve further study.