Simpler and Faster Dictionaries on the AC0 RAM

We consider the static dictionary problem of using O(n) w-bit words to store n w- bit keys for fast retrieval on a w-bit AC0 RAM, i.e., on a RAM with a word length of w bits whose instruction set is arbitrary, except that each instruction must be realizable through an unbounded-fanin circuit of constant depth and wO(1) size. We improve the best known upper bound for moderate values of w relative to n. If w/log n = (log log n)O(1), query time (log log log n)O(1) is achieved, and if additionally w/log n ≥ (log log n)1+e for some fixed e > 0, the query time is constant. For both of these special cases, the best previous upper bound was O(log log n). A new lower bound is also observed.

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