We present a simple example that disproves the universality principle. Unlike previous counter-examples to computational universality, it does not rely on extraneous phenomena, such as the availability of input variab...
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We present a simple example that disproves the universality principle. Unlike previous counter-examples to computational universality, it does not rely on extraneous phenomena, such as the availability of input variables that are time varying, computationalcomplexity that changes with time or order of execution, physical variables that interact with each other, uncertain deadlines, or mathematical conditions among the variables that must be obeyed throughout the computation. In the most basic case of the new example, all that is used is a single pre-existing global variable whose value is modified by the computation itself. In addition, our example offers a new dimension for separating the computable from the uncomputable, while illustrating the power of parallelism in computation.
rank-varying computational complexity describes those computations in which the complexity of executing each step is not a constant, but evolves throughout the computation as a function of the order of execution of ea...
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rank-varying computational complexity describes those computations in which the complexity of executing each step is not a constant, but evolves throughout the computation as a function of the order of execution of each step [2]. This paper identifies practical instances of this computational paradigm in the procedures for computing the quantum Fourier transform and its inverse. It is shown herein that under the constraints imposed by quantum decoherence, only a parallel approach can guarantee a reliable solution or, alternatively, improve scalability.
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