On thinking probabilistically

An Historical Note on the Origins of Probabilistic Indexing

The motivation behind ‘‘Probabilistic Indexing’’ was to replace two-valued thinking about information retrieval with probabilistic notions. This involved a new view of the information retrieval problem – viewing it as problem of inference and prediction, and introducing probabilistically weighted indexes and probabilistically ranked output. These ideas were first formulated and written up in Au...

Educating Children in Stochastic Modeling: Games with Stochastic Urns and Colored Tinker-cubes

It is an established opinion that young children have good probabilistic intuitions although their mental framework for reasoning probabilistically may be fragmentary and even contain inconsistencies. We join the camp of mathematics educators who advocate an early training in stochastic thinking. We recognize, however, that such early training can only be based on a heuristic approach to stocha...

On Dinur’s Proof of the Pcp Theorem

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 dramatical...

Probabilistically Checkable Proofs the Easy Way

Probabilistically Checkable Proofs: A Primer

Probabilistically checkable proofs are proofs that can checked probabilistically by reading very few bits of the proof. Roughly ten years back it was shown that proofs could be made probabilistically checkable with a modest increase in their size. While the initial proofs were a little too complex, a recent proof due to Irit Dinur gives a dramatically simple (and radically new) construction of ...