Making Branching Programs Oblivious Requires Superlogarithmic Overhead

Paul Beame, Widad Machmouchi
2011 2011 IEEE 26th Annual Conference on Computational Complexity  
We prove a time-space tradeoff lower bound of T = Ω'n log( n S ) log log( n S )´for randomized oblivious branching programs to compute 1GAP , also known as the pointer jumping problem, a problem for which there is a simple deterministic time n and space O(log n) RAM (random access machine) algorithm. We give a similar time-space tradeoff of T = Ω'n log( n S ) log log( n S )´for Boolean randomized oblivious branching programs computing GIP -M AP , a variation of the generalized inner product
more » ... lem that can be computed in time n and space O(log 2 n) by a deterministic Boolean branching program. These are also the first lower bounds for randomized oblivious branching programs computing explicit functions that apply for T = ω(n log n). They also show that any simulation of general branching programs by randomized oblivious ones requires either a superlogarithmic increase in time or an exponential increase in space.
doi:10.1109/ccc.2011.35 dblp:conf/coco/BeameM11 fatcat:llp2k6z6g5gwxhql6d3vwgz5qa