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-A New and efficient Genetic Algorithm (GA) based approach is presented to minimise the number of terms of Mixed Polarity Reed Muller (MPRM) single and multi output incompletely specified Boolean functions. The algorithm determines the allocation of don't care terms for the given function resulting in optimal MPRM expansions. For an n-variable function with β unspecified minterms there are (3 n × 2 β ) distinct MPRM expansions. A minimum MPRM is one with the fewest products. The algorithm is implemented in C++ and fully tested using standard benchmark examples. For the benchmark examples tested, the number of terms is reduced, on average, by 49% if "don't care" terms are included.