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On the complexity of nonuniform wavelength-based machine

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Abstract

The wavelength-based machine, or simply w-machine, is an optical computational model, which is designed based on simultaneous movement of several wavelengths in a single light ray, and simultaneous effect of simple optical devices on them. In this paper, we investigate nonuniform complexity classes of w-machine, based on three complexity measures, namely, size, time, and word length. We show that the class of languages which can be generated by constant size nonuniform w-machines contain infinitely many Turing undecidable languages. Also, we show that polynomial size nonuniform w-machines generate all NP languages, and every NP-hard language requires at least polynomial time and polynomial size nonuniform w-machines to be generated. We prove that the class of languages which can be generated by polynomial size nonuniform w-machines is equal to NP/poly, and almost all languages require exponential size and polynomial time nonuniform w-machines to be generated.

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Authors and Affiliations

  1. University of Tehran, Tehran, Iran

    Sama Goliaei & Mohammad-Hadi Foroughmand-Araabi

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  1. Sama Goliaei
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  2. Mohammad-Hadi Foroughmand-Araabi
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Correspondence to Sama Goliaei.

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Goliaei, S., Foroughmand-Araabi, MH. On the complexity of nonuniform wavelength-based machine. Nat Comput 13, 269–283 (2014). https://doi.org/10.1007/s11047-014-9412-2

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  • DOI: https://doi.org/10.1007/s11047-014-9412-2

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