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Quadratic Time-Space Lower Bounds for Computing Natural Functions with a Random Oracle

2018
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Innovations in Theoretical Computer Science
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We define a model of size-S R-way branching programs with oracles that can make up to S distinct oracle queries over all of their possible inputs, and generalize a lower bound proof strategy of Beame [SICOMP 1991] to apply in the case of random oracles. Through a series of succinct reductions, we prove that the following problems require randomized algorithms where the product of running time and space usage must be Ω(n 2 /poly(log n)) to obtain correct answers with constant nonzero

doi:10.4230/lipics.itcs.2019.56
dblp:conf/innovations/McKayW19
fatcat:prlyjqud5vgujafxl7vtbkaco4