Three problems in computer science

We describe three problems that each have a history of research that goes back to the early days of computer science. These past efforts, which we do not review here, have succeeded in uncovering some the essence of these otherwise elusive challenges, and make it possible to focus on these questions more clearly now. Difficult as they may appear to be, they are well-posed scientific questions, we believe, and therefore will be solved eventually. While their solutions can be expected to have mathematical content, the problems as we state them are not purely mathematical. In each case, a part of the solution would be the emergence of some consensus on the nature of the right mathematical formulation.