On Dinur’s proof of the PCP theorem
Jaikumar Radhakrishnan, Madhu Sudan · Bulletin of the American Mathematical Society · 2006
Probabilistically checkable proofs are proofs that can be checked probabilistically by reading very few bits of the proof. In the early 1990s, it was shown that proofs could be transformed into probabilistically checkable ones with only a modest increase in their length. The initial transformations, though elementary, were a little too complex. A recent work due to Irit Dinur gives a dramatically simple (and radically new) construction of probabilistically checkable proofs. This article explains the notion of a probabilistically checkable proof, presents the formal definition and then introduces the reader to Dinur’s work along with some of the context.