Abstract: Developing a software is actually a transformation from the "problem space" to the "solution space". The representations of the "problem space" and "solution space" were abstracted from their characteristics, and the limitations of the programming were discussed from several typical problems. The reached conclusion shows that no matter how advanced the programming language is, if the real computer is based on the model of "Turing machine", the ability of the program will always be limited, i.e. there are many undecidable programs. Therefore, the cryptosystem which based on the uncomputability is feasible, and an idea of such cryptosystem was proposed.

Key words: computer science, problem space, solution space, computability(decidability), cryptosystem