Introductions for the “Weizmann Distinguished Lectures Day” by Oded Goldreich

Boaz Barak (MSR) [WIS’04] Pioneering non-black-box proofs of security (e.g., for zero-knowledge): Standard proofs of security are via reductions that use the hypothetical adversary as a black-box, and it was believed that limitations of such proofs represent real limitations. Work on randomness extraction (from few independent sources). Work on the Unique Game Conjecture.

Irit Dinur (WIS) [TAU’01] Focus: A proof of the PCP THM by (gradual) Gap Amplification. PCP THM = Every NP-proof can be efficiently transformed to one that can be verified probabilistically by inspecting a constant number of bits in it. Prior proofs of the PCP theorem combined two extremely complex PCP systems. Irit’s proof starts with a trivial PCP system and obtains the final one by a long sequence of gradual amplifications of the detection probability. Along the way she resolves a problem that would have taken a decade to resolve otherwise: Obtaining PCP systems of almost linear length.

Johan Hastad (KTH) [MIT’86] (relatively tight) Lower Bounds for AC0. Pseudorandom Generators based on any One-Way Function. Leading 2 nd generation of PCP constructions, culminating with (relatively tight) non- approximability results for several central optimization problems including MaxClique and MaxSAT. Tight: OWF are necessary.

Salil Vadhan (Harvard) [MIT’99] Unconditional studies of ZK, culminating in SZKA based on any OWF. N.B.: Dual result to CZKIP based on OWF. Major player in 2 nd generation of constructions of randomness extractors (from T’99 to GUV’07). The Zig-Zag product (see its application to UCONN in L).

Richard Karp (UCB) [Harvard’59] One of the founding fathers of Computer Science. NP-Completeness ["Reducibility Among Combinatorial Problems", 1972] Classical algorithms for optimization problems, including max-flow [w. Edmonds, 1971] and matching in bipartite graphs [w. Hopcroft, 1973]. And much more…