Computing with uncertainty and its implications to universality

It is known that there exist computational problems that can be solved on a parallel computer, yet are impossible to be solved sequentially. Specifically, no general purpose sequential model of computation, such as the Turing machine or the random access machine, can simulate a large family of computations (e.g. solutions to certain real-time problems), each of which is capable of being carried out readily by a particular parallel computer. We extend the scope of such problems to the class of problems with uncertain time constraints. The first type of time constraints refers to uncertain time requirements on the input data, that is when and for how long are the input data available. The second type of time constraints refers to uncertain deadlines on when outputs are to be produced. Our main objective is to exhibit computational problems in which it is very difficult to find out (read ‘compute’) what to do and when to do it. Furthermore, problems with uncertain time constraints, as described here, prove once more that it is impossible to define a ‘universal computer’, that is a computer able to perform (through simulation or otherwise) all computations that are executable on other computers. Finally, one of the contributions of this paper is to promote the study of a topic, conspicuously absent to date from theoretical computer science, namely the role of physical time and physical space in computation. The focus of our work is to analyse the effect of external natural phenomena on the various components of a computational process, namely the input phase, the calculation phase (including the algorithm and the computing agents themselves) and the output phase.