Various types of probabilistic proof systems have played a central role in the development of computer science in the last decade. In this exposition, we concentrate on three such proof systems -- interactive proofs, zero-knowledge proofs, and probabilistic checkable proofs -- stressing the essential role of randomness in each of them.<br /> <br />This exposition is an expanded version of a survey written for the proceedings of the International Congress of Mathematicians (ICM94) held in Zurich

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... in 1994. It is hope that this exposition may be accessible to a broad audience of computer scientists and mathematians.