Parallel processors with bit-serial processing elements (PE's) usually implement arithmetic functions by a sequence of word-level arithmetic operations; however, basic operations must be specified at the bit level. In this correspondence the possibility of more efficiently implementing a function with a special tailored sequence of bit-serial operations is considered. A general scheme is described for generating efficient programs to implement arbitrary functions on bit-serial-arithmetic processors. This scheme is based on logic design methodology and involves designing a logic network to realize a desired function. The parallel processor is then used to efficiently simulate a set of these networks. Heuristic design algorithms are used to generate the logic networks; several algorithms are described and compared with some benchmark functions. Several efficient PE designs are described and analyzed.