Efficient optimistic concurrency control using loosely synchronized clocks
SIGMOD '95 Proceedings of the 1995 ACM SIGMOD international conference on Management of data
Providing Persistent Objects in Distributed Systems
ECOOP '99 Proceedings of the 13th European Conference on Object-Oriented Programming
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We present computationally efficient error-correcting codes and holographic proofs. Our error-correcting codes are asymptotically good and can be encoded and decoded in linear time. Our construction of holographic proofs provide, for every proof of any theorem, a slightly larger ``holographic'''' proof whose accuracy can be probabilistically checked by an algorithm that only reads a constant number of the bits of the holographic proof and runs in poly-logarithmic time (such proofs have also been called ``transparent proofs'''' and ``probabilistically checkable proofs''''). We explain how these constructions are related and how improvements of these constructions should result in a strengthening of this relationship. For every constant $r$ such that $0 r 0$ and a linear-time decoding algorithm for these codes that maps every word of relative distance at most $\epsilon $ from a codeword to that codeword. The encoding circuits have logarithmic depth. The decoding algorithm can be implemented as a circuit with $\O{n \log n}$ wires and logarithmic depth. These constructions make use of explicit constructions of expander graphs and superconcentrators. Our constructions of holographic proofs improve on the theorem $PCP(\log n, 1) = NP$, proved by Arora, Lund, Motwani, Sudan, and Szegedy, by providing, for every $\epsilon