Year: 2024
Type: article
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.
Source: Mathematics
DOI: 10.3390/math12182881
Author: Vladimir A. Kulyukin
Institution: Utah State University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,955
OpenAlex ID: W4402793944