We present a general approach to the FPGA technology mapping problem that applies to any logic block composed of lookup tables LUTs and can yield optimal solutions. The connections between LUTs of a logic block are modeled by virtual switches, which de ne a set of multiple-LUT blocks MLBs called an MLB-basis. We identify the MLB-bases for various commercial logic blocks. Given an MLB-basis, we formulate FPGA mapping as a mixed integer linear programming MILP problem to achieve both the generality and the optimality objectives. We solve the MILP models using a general-purpose MILP solver, and present the results of mapping some ISCAS-85 benchmark circuits with a variety of commercial FPGAs. Circuits of a few hundred gates can be mapped in reasonable time using the MILP approach directly. Larger circuits can be handled by partitioning them prior to technology mapping. We show that optimal or provably near-optimal solutions can be obtained for the large ISCAS-85 benchmark circuits ...
Amit Chowdhary, John P. Hayes