Approximate logic synthesis under general error magnitude and frequency constraints

Recent interest in approximate circuit design is driven by its potential for large energy savings. In this paper, we address the problem of approximate logic synthesis (ALS). ALS is concerned with formally synthesizing a minimum-cost approximate Boolean network whose behavior deviates in a well-defined manner from a specified exact Boolean function, where in this work, we allow the deviation to be constrained by both the magnitude and frequency of the error. We make two contributions in solving this general ALS problem: The first contribution is to establish that the approximate synthesis problem un-constrained by the frequency of errors is isomorphic with the Boolean relations (BR) minimization problem. That equivalence allows us to exploit recently developed fast algorithms for BR problems to solve the error magnitude-only constrained ALS problem. The second contribution is an efficient heuristic algorithm for iteratively refining the magnitude-constrained solution to arrive at a solution also satisfying the error frequency constraint. Our combined greedy approximate logic synthesis (GALS) approach is able to operate on any Boolean network for which the deviation measures can be specified and is most immediately applicable to arithmetic blocks. Experiments on adder and multiplier blocks demonstrate literal count reductions of up to 60% under tight error frequency and magnitude constraints.