10.5 Summary One of the main focal points of computer science is the study of algorithms. The limits of computer science are determined largely by our success in finding tractable algorithms and programs. Occasionally we are able to prove that certain problems do not have a computable solution. An example of such a problem is the Halting problem. Given a programming language, P, it has been proved that it is not possible to write a P program which will determine whether or not any given P program halts with an answer after a finite amount of time.
Many problems remain for which only intractable solutions have been found.
Such problems provide exciting and challanging research experiences for computer scientists.