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Bounded honest-verifier simulator and unbounded prover

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I have a honest-verifier zero knowledge simulator $M$. The conversation between prover and verifier has the usual $(a, b, z)$ form. How can the bounded model $M$ generate $a$ and $z$ is the prover is probably unbounded? I know that I have to use the fact, that the verifier is honest, but I just cannot figure it out how.

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