A polynomial time exact solution to the bit-aware register binding problem

Finding the minimum register bank is an optimization problem related to the synthesis of hardware. Given a program, the problem asks for the minimum number of registers plus their minimum size, in bits, that suffices to compile said program. This problem is NP-complete; hence, usually solved via heuristics. In this paper, we show that this problem has an optimal solution in polynomial time, as long as swaps can be inserted in the program to move variables across registers. This observation sets a lower bound to heuristics that minimize the size of register banks. We have compared the optimal algorithm with two classic heuristics. Our approach uses, on average, 6 to 10% less bits than that previous work.