{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T02:05:57Z","timestamp":1776305157322,"version":"3.50.1"},"reference-count":14,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2020,9]]},"abstract":"<jats:p> We prove some new theorems in additive number theory, using novel techniques from automata theory and formal languages. As an example of our method, we prove that every natural number [Formula: see text] is the sum of at most three natural numbers whose base-[Formula: see text] representation has an equal number of [Formula: see text]\u2019s and [Formula: see text]\u2019s. <\/jats:p>","DOI":"10.1142\/s0129054120410014","type":"journal-article","created":{"date-parts":[[2020,10,12]],"date-time":"2020-10-12T15:24:03Z","timestamp":1602516243000},"page":"667-687","source":"Crossref","is-referenced-by-count":1,"title":["Additive Number Theory via Approximation by Regular Languages"],"prefix":"10.1142","volume":"31","author":[{"given":"Jason","family":"Bell","sequence":"first","affiliation":[{"name":"Department of Pure Mathematics, University of Waterloo, Waterloo, ON N2L 3G1, Canada"}]},{"given":"Thomas F.","family":"Lidbetter","sequence":"additional","affiliation":[{"name":"School of Computer Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada"}]},{"given":"Jeffrey","family":"Shallit","sequence":"additional","affiliation":[{"name":"School of Computer Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada"}]}],"member":"219","published-online":{"date-parts":[[2020,10,10]]},"reference":[{"key":"S0129054120410014BIB001","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511546563","volume-title":"Automatic Sequences: Theory, Applications, Generalizations","author":"Allouche J.-P.","year":"2003"},{"key":"S0129054120410014BIB002","first-page":"#A3","volume":"16","author":"Banks W. D.","year":"2016","journal-title":"INTEGERS: Elect. J. Combin. Number Theory"},{"key":"S0129054120410014BIB003","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1090\/bproc\/37","volume":"5","author":"Bell J.","year":"2018","journal-title":"Proc. Amer. Math. Soc. Ser. B"},{"key":"S0129054120410014BIB004","series-title":"Lecture Notes in Comput. Sci.","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1007\/978-3-319-98654-8_10","volume-title":"Developments in Language Theory (DLT 2018)","volume":"11088","author":"Bell J.","year":"2018"},{"key":"S0129054120410014BIB005","doi-asserted-by":"crossref","first-page":"3023","DOI":"10.1090\/mcom\/3221","volume":"87","author":"Cilleruelo J.","year":"2018","journal-title":"Math. Comp."},{"key":"S0129054120410014BIB006","doi-asserted-by":"publisher","DOI":"10.1142\/S0129054110007441"},{"key":"S0129054120410014BIB007","doi-asserted-by":"crossref","first-page":"382","DOI":"10.1145\/321466.321470","volume":"15","author":"Hartmanis J.","year":"1968","journal-title":"J. Assoc. Comput. Mach."},{"key":"S0129054120410014BIB008","volume-title":"Introduction to Automata Theory, Languages, and Computation","author":"Hopcroft J. E.","year":"1979"},{"key":"S0129054120410014BIB009","first-page":"441","volume":"23","author":"Horv\u00e1th S.","year":"1987","journal-title":"J. Inf. Process. Cybern. EIK"},{"key":"S0129054120410014BIB012","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-3845-2","volume-title":"Additive Number Theory: The Classical Bases","author":"Nathanson M. B.","year":"1996"},{"key":"S0129054120410014BIB013","volume-title":"Elementary Methods in Number Theory","author":"Nathanson M. B.","year":"2000"},{"key":"S0129054120410014BIB014","series-title":"Leibniz International Proceedings in Informatics","first-page":"54:1","volume-title":"35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)","author":"Rajasekaran A.","year":"2018"},{"key":"S0129054120410014BIB015","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1006\/jsco.1994.1023","volume":"17","author":"Raymond D. R.","year":"1994","journal-title":"J. Symbolic Comput."},{"key":"S0129054120410014BIB016","doi-asserted-by":"crossref","first-page":"24","DOI":"10.7146\/math.scand.a-11990","volume":"52","author":"Shorey T. N.","year":"1983","journal-title":"Math. Scand."}],"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129054120410014","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,13]],"date-time":"2020-11-13T08:59:57Z","timestamp":1605257997000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129054120410014"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9]]},"references-count":14,"journal-issue":{"issue":"06","published-print":{"date-parts":[[2020,9]]}},"alternative-id":["10.1142\/S0129054120410014"],"URL":"https:\/\/doi.org\/10.1142\/s0129054120410014","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"value":"0129-0541","type":"print"},{"value":"1793-6373","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,9]]}}}