Conclusions

Program development involves several basic phases:

This talk has focused on elements of the phases 1-4.

At each stage, we have identified both theoretical and practical constraints that limit the possibilities of program solutions.

Theoretical Limitations

Some problems (e.g., the Halting Problem) have no solution.
Some problems (e.g., the Satisfiability Problem) have solutions, but they are not feasible for reasonable data sets.

Practical Limitations

Cannot tell when specifications are complete, consistent, and unambiguous.
Testing most solutions completely is not feasible.
Program Verification cannot be automated to give a mathematical proof of correctness (even assuming we have sufficiently precise specifications).

created: 3 January 2007
last revised: 7 January 2007 previous