The verifier performs actions according to the input, according to the proof but also according to the random bits. And at the end he will give an answer YES or NOT, but this answer will not be certainly correct, it will be only probably correct.
Now the question is. Can we trade the number of random bits with the number of bits that we have to read in the proof still preserving a low error probability?
To formulate this result I have to introduce the formal model of PCP theorem.
