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A semantic logic for CAST related to Zuse, Deutsch and McCulloch and Pitts computing principles

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Computer Aided Systems Theory — EUROCAST '95 (EUROCAST 1995)

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Abstract

The goal of CAST research and development is to provide modelling tools for formal systems design in the field of information and systems engineering. This paper deals with such modelling tools for formal systems related to Zuse, Deutsch and McCulloch and Pitts computing principles. The semantic logic of such systems can be exhibited in replacing the differential equations by digital cellular automata. K. Zuse proposed such a method for representing physical systems by a computing space. I show that the digital wave equation exhibits waves by digital particles with interference effects. The logical table of the wave equation shows the conservation of the parity related to exclusive OR. The Fractal Machine proposed by the author deals with a cellular automata based on incursion, an inclusive recursion, with exclusive OR. In this machine, the superimposition of states is related to the Deutsch quantum computer. Finally, it is shown that the exclusive OR can be modelled by a fractal non-linear equation and a new method to design digital equations is proposed to create McCulloch and Pitts formal neurons.

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Authors and Affiliations

  1. Institut de Mathématique, Université de Liège, Avenue des Tilleuls 15, B-4000, Liege, Belgium

    Daniel M. Dubois

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  1. Daniel M. Dubois
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Franz Pichler Roberto Moreno Díaz Rudolf Albrecht

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© 1996 Springer-Verlag Berlin Heidelberg

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Dubois, D.M. (1996). A semantic logic for CAST related to Zuse, Deutsch and McCulloch and Pitts computing principles. In: Pichler, F., Díaz, R.M., Albrecht, R. (eds) Computer Aided Systems Theory — EUROCAST '95. EUROCAST 1995. Lecture Notes in Computer Science, vol 1030. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0034784

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  • DOI: https://doi.org/10.1007/BFb0034784

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  • Print ISBN: 978-3-540-60748-9

  • Online ISBN: 978-3-540-49358-7

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