Asynchronous Parallel Preex Computation

The preex problem is to compute all the products x 1 x 2 x k , for 1 k n, where is an associative binary operation. We start with an asynchronous circuit to solve this problem with O(log n) latency and O(n log n) circuit size, with O(n)-operations in the circuit. Our contributions are: (i) A modiication to the circuit that improves its average-case latency from O(log n) to O(log log n) time; and (ii) A further modiication that allows the circuit to run at full-throughput i.e., with constant response time. The construction can be used to obtain a asynchronous adder with O(log n) worst-case latency and O(log log n) average-case latency.