The essential idea in the fast parallel computation of division and
related problems is that of Chinese remainder representation
(CRR) -- storing a number in the form of its residues modulo many
small primes. Integer division provides one of the few natural
examples of problems for which ...
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Integer division has been known to lie in P-uniform TC^0 since
the mid-1980's, and recently this was improved to DLOG-uniform
TC^0. At the time that the results in this paper were proved and
submitted for conference presentation, it was unknown whether division
lay in DLOGTIME-uniform TC^0 (also known as ...
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We present improved uniform TC$^0$ circuits for division, matrix powering, and related problems, where the improvement is in terms of ``majority depth'' (initially studied by Maciel and Therien). As a corollary, we obtain improved bounds on the complexity of certain problems involving arithmetic circuits, which are known to lie in ... more >>>
We investigate the complexity of languages that correspond to algebraic real numbers, and we present improved upper bounds on the complexity of these languages. Our key technical contribution is the presentation of improved uniform TC^0 circuits
for division, matrix powering, and related problems, where the improvement is in terms of ...
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