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**1 - 2**of**2**### Time Indeterminacy, Non-Universality in Computation, and the Demise of the Church-Turing Thesis †

, 2011

"... 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 compu ..."

Abstract
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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 (for example, 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. A 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

### Computations with Uncertain Time Constraints: Effects on Parallelism and Universality

, 2008

"... 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 compu ..."

Abstract
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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 (for example, 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. 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.