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Toward simulated evolution of machine-language iteration

We use a simulated evolution search (genetic programming) for the automatic synthesis of small iterative machine-language programs. For an integer register machine with an addition instruction as its sole arithmetic operator, we show that genetic programming can produce exact and general multiplication routines by synthesizing the necessary iterative control structures from primitive machine-language instructions. Our program representation is a virtual register machine that admits arbitrary control flow. Our evolution strategy furthermore does not artificially restrict the synthesis of any control structure; we only place an upper bound on program evaluation time. A program's fitness is the distance between the output produced by a test case and the desired output (multiplication). The test cases exhaustively cover multiplication over a finite subset of the natural numbers (N10); yet the derived solutions constitute general multiplication for the positive integers. For this problem, simulated evolution with a two-point crossover operator examines significantly fewer individuals in finding a solution than random search. Introduction of a small rate of mutation further increases the number of solutions.