Problem statement: The goal of automatic programming system is to create, in an automated way, a computer program that enables a computer to solve a problem. It is difficult to build an automatic programming system: They require carefully designed specification languages and an intimate knowledge base. Determine the relevance of mathematical system theory to the problems of automatic programming and find automatic programming methodology, where a computer program evolved to solve problem by using problem’s input output specifications only. Approach: Problem behavior was described as a finite state automata based on its meaning, also problem’s input-output specifications were described in theoretical manner, based on its input and output trajectories information, then a program was evolved to solve the problem. Different implementation languages can be used without significantly affecting existing problem specification. Evolutionary process adapts ant colony optimization algorithm to find good finite state automata that efficiently satisfies input-output specifications. Results: By moving from state to states, each ant incrementally constructs sub-solution in an iterative process. The algorithm converged to the optimal final solution, by accumulating most effective sub-solutions; main problem will appeared in solving problem with little input-output specifications. Fixed and dynamic input-output specifications were used to mimic chaotic behavior of real world. Conclusion: These results indicated that theoretical bases can enhance efficiency and performance of automatic programming system, leading to an increase in the system productivity and letting the concentrate to be done on problem specification only. Also, the collective behavior emerging from the interaction of the different ants had proved effective in solving problem; finally, in dynamic input-output specification chaos theory, especially “butterfly effect”, can be used to control the sensitivity to initial configuration of trajectory information.
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