Speeding up random access machines by few processors
Sequential and parallel random access machines (RAMs, PRAMs) with arithmetic operations + and − are considered. PRAMs may also multiply with constants. These machines work on integer inputs. It is shown that, in contrast to bit orientated models as Turing machines or log-cost RAMs, one can in many cases speed up RAMs by PRAMs with few processors. More specifically, a RAM without indirect addressing can be uniformly sped up by a PRAM with q processors by a factor (loglogq)2/logq. A similar result holds for nonuniform speed ups of RAMs with indirect addressing. Furthermore, certain networks of RAMs (such as k-dimensional grids) with q processors can be sped up significantly with only q1+τ processors. Nonuniformly, the above speed up can even be achieved for arbitrary bounded degree networks (including powerful networks such as permutation networks or Cube-Connected Cycles), if only few input variables are allowed. It is previously shown by the author, that the speed ups for RAMs are almost best possible.
KeywordsTuring Machine Parallel Random Access Machine Storage Access Algebraic Circuit Algebraic Computation Tree
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