Year: 2025
Type: article
Abstract: In this paper, we discuss canonical number systems (CNSs), which are generalizations of positional number systems to polynomials over the integers. We defined the information quantity of a polynomial relative to the base of the CNS and proved that it has a strong relation with the length of the representation in the number system. Based on this result, we showed that for every CNS polynomial, there exists a finite transducer automaton executing the addition operation of polynomials in canonical representation of a certain base. Finally, we observed the size -- i.e., the number of states -- of such automata.
Source: Algorithms
DOI: 10.3390/a18030122
Authors: Tamás Herendi, Viktória Padányi
Institution: University of Debrecen
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,930
Funder: Debreceni Egyetem
OpenAlex ID: W4407766888