The Complexity of Parallel Prefix Problems on Small Domains

India jaikumar~tcs.tifr.res.in We show non-triviallower bounds for several prefix problems in the CReW PRAM model. Our main result is an O( a( n)) lower bound for the chaining problem, matching the previously known upper bound. We give a reduction to show that the same lower bound applies to a parenthesis matching problem, again matching the previously known upper bound. We also give reductions to show that similar lower bounds hold for the prefix maxima and the range maxima problems.