Computations with Uncertain Time Constraints: Effects on Parallelism and Universality

Abstract

We introduce the class of problems with uncertain time constraints. The first type of time constraints refers to uncertain time requirements on the input, that is, when and for how long are the input data available. A second type of time constraints refers to uncertain deadlines for tasks. 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 compute all computable functions. 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 analyze 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.