Abstract
Interval-valued computing is a kind of massively parallel computing. It operates on specific subsets of the interval [0,1) – unions of subintervals. They serve as basic data units and are called interval-values. It was established that this system (in its unrestricted version) has computing power equivalent to Turing machines, by a rather simple observation. However, this equivalence involves an infinite number of interval-valued variables. In this paper, a more refined equivalence is established using only a fixed number of interval-valued variables. This fixed number depends only on the number of states of the Turing machine – logarithmically. This method makes it also possible to extend interval-valued computations into infinite length to capture the computing power of red-green Turing machines.
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Nagy, B., Vályi, S. (2018). An Extension of Interval-Valued Computing Equivalent to Red-Green Turing Machines. In: Durand-Lose, J., Verlan, S. (eds) Machines, Computations, and Universality. MCU 2018. Lecture Notes in Computer Science(), vol 10881. Springer, Cham. https://doi.org/10.1007/978-3-319-92402-1_8
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DOI: https://doi.org/10.1007/978-3-319-92402-1_8
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