Improving Bounds for FPGA Logic Minimization

Abstract

We present a methodology for improving the bounds of combinational designs implemented on networks of lookup tables, moving them closer to the theoretical minimum. Our work effectively extends optimality to span logic minimization and technology mapping. We obtain a proof of optimality by restricting ourselves to 4-input look-up tables (LUTs) and generating all possible circuits up to a certain area or latency depending on the optimization mode. Since simple-minded generation would take a long time, we develop levels of abstraction (steps) and techniques to restrict and order the search space, and produce results in practical time. We use logic decomposition to break up large designs, using the resulting trees to guide our search and prune the search space. The price of this optimality is that we are limited to small blocks; however, such blocks can be used to build larger designs.