1. CW Concurrent Write CR Concurrent Read EW Exclusive Write ER Exclusive Read P=N 1  i  N 1  j  M P=1 1  j  M

2.  i, P i  m j CW  i, P i  m j CR Pi  mjPi  mj P1  mjP1  mj EW Pi  mjPi  mj P1  mjP1  mj ER P=N 1  i  N 1  j  M P=1 1  j  M

3. BSR- Broadcast. Each P i broadcasts a datum & tag, d i & g i, respectively, to all M memory locations. So,  i  j, P i sends to U j, 1  i  N, 1  j  M

4. BSR- Selection. Each U j uses a “limit”, l j, with a selection rule, , to test g i. So, evaluate g i  l j where  : , , , , ,  If g i  l j is TRUE, then d i is selected (accepted) for the reduction phase, else it is rejected by U j.

5. BSR- Reduction. All d i ’s selected by U j are combined (or reduced) into one datum using a binary associative reduction operator, R, with R being SUM, PRODUCT, AND, OR, XOR, MAX, MIN   V    Result is stored in U j.

7. Always question, never blindly accept (things are not always what they seem!). Further, there are always implications... If all memory accesses take log(M) time, is there any such thing as a constant time operation/algorithm? Does this somehow imply that it is possible to break O(1)?