{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:56:28Z","timestamp":1760057788787,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,2,20]],"date-time":"2025-02-20T00:00:00Z","timestamp":1740009600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"University of Debrecen, Hungary","award":["TKP2021-NKTA-34","TKP2021-NKTA-34"],"award-info":[{"award-number":["TKP2021-NKTA-34","TKP2021-NKTA-34"]}]},{"name":"Ministry of Culture and Innovation of Hungary from the National Research, Development and Innovation Fund","award":["TKP2021-NKTA-34","TKP2021-NKTA-34"],"award-info":[{"award-number":["TKP2021-NKTA-34","TKP2021-NKTA-34"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>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 A\u2208Z[x] 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 P, there exists a finite transducer automaton executing the addition operation of polynomials in canonical representation of base P. Finally, we observed the size\u2014i.e., the number of states\u2014of such automata.<\/jats:p>","DOI":"10.3390\/a18030122","type":"journal-article","created":{"date-parts":[[2025,2,20]],"date-time":"2025-02-20T11:03:37Z","timestamp":1740049417000},"page":"122","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Automata and Arithmetics in Canonical Number Systems"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-5527-4241","authenticated-orcid":false,"given":"Tam\u00e1s","family":"Herendi","sequence":"first","affiliation":[{"name":"Department of Computer Science, Faculty of Informatics, University of Debrecen, Kassai Str. 26, 4028 Debrecen, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vikt\u00f3ria","family":"Pad\u00e1nyi","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Faculty of Informatics, University of Debrecen, Kassai Str. 26, 4028 Debrecen, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,20]]},"reference":[{"key":"ref_1","unstructured":"Knuth, D.E. 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Semirings, Automata, Languages, Springer.","DOI":"10.1007\/978-3-642-69959-7"},{"key":"ref_18","first-page":"19","article-title":"On a generalization of the radix representation\u2014A survey","volume":"41","author":"Akiyama","year":"2004","journal-title":"Fields Inst. Commun."},{"key":"ref_19","unstructured":"Berth\u00e9, V., and Rigo, M. (2015). Combinatorics, Automata and Number Theory, Cambridge University Press."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/18\/3\/122\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:39:00Z","timestamp":1760027940000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/18\/3\/122"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,20]]},"references-count":19,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,3]]}},"alternative-id":["a18030122"],"URL":"https:\/\/doi.org\/10.3390\/a18030122","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2025,2,20]]}}}