Complexity of the combinator reduction machine

AbstractThe complexity of the computation of recursive programs by the combinator reduction machine is studied. The number of the reduction steps in compared between the two models of computation. The main theorem states that the time required by the reduction machine is linear in that of the program scheme. The coefficient of the linearity was shown to be O(n2), where n is the maximal number of variables of the functions being used. For the analysis of the combinator codes, the notion of extended combinator code is introduced