Various types of probabilistic proof systems have played a central role in the development of computer science in the last couple of decades. These proof systems deviate from the traditional concept of a proof by introducing randomization and interaction into the verification process. Probabilistic proof systems carry an error probability (which is explicitly bounded and can be decreased by repetitions), but they offer various advantages over deterministic proof systems.
In the the lecture series, I will concentrate on three types of probabilistic proof systems:
interactive proofs, zero-knowledge proofs, and probabilistically checkable proofs. Surveying the basic results regarding these proof systems, I will stress the essential role of randomness in each of them. If time permits, I will also discuss recent developments and current challenges regarding each of these proof systems.