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On Signifiable Computability: Part I: Signification of Real Numbers, Sequences, and Types

Author

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  • Vladimir A. Kulyukin

    (Department of Computer Science, Utah State University, Logan, UT 84322, USA)

Abstract

Signifiable computability aims to separate what is theoretically computable from what is computable through performable processes on computers with finite amounts of memory. Real numbers and sequences thereof, data types, and instances are treated as finite texts, and memory limitations are made explicit through a requirement that the texts be stored in the available memory on the devices that manipulate them. In Part I of our investigation, we define the concepts of signification and reference of real numbers. We extend signification to number tuples, data types, and data instances and show that data structures representable as tuples of discretely finite numbers are signifiable. From the signification of real tuples, we proceed to the constructive signification of multidimensional matrices and show that any data structure representable as a multidimensional matrix of discretely finite numbers is signifiable.

Suggested Citation

  • Vladimir A. Kulyukin, 2024. "On Signifiable Computability: Part I: Signification of Real Numbers, Sequences, and Types," Mathematics, MDPI, vol. 12(18), pages 1-17, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:18:p:2881-:d:1478878
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    References listed on IDEAS

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    1. Vladimir A. Kulyukin, 2023. "On Correspondences between Feedforward Artificial Neural Networks on Finite Memory Automata and Classes of Primitive Recursive Functions," Mathematics, MDPI, vol. 11(12), pages 1-25, June.
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    1. Vladimir A. Kulyukin, 2023. "On the Computability of Primitive Recursive Functions by Feedforward Artificial Neural Networks," Mathematics, MDPI, vol. 11(20), pages 1-16, October.

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