{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T08:57:30Z","timestamp":1775465850963,"version":"3.50.1"},"reference-count":79,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T00:00:00Z","timestamp":1559088000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T00:00:00Z","timestamp":1559088000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["2018-04118"],"award-info":[{"award-number":["2018-04118"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Theory Comput Syst"],"published-print":{"date-parts":[[2020,4]]},"DOI":"10.1007\/s00224-019-09929-9","type":"journal-article","created":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T09:25:57Z","timestamp":1559121957000},"page":"542-567","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Additive Number Theory via Automata Theory"],"prefix":"10.1007","volume":"64","author":[{"given":"Aayush","family":"Rajasekaran","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1197-3820","authenticated-orcid":false,"given":"Jeffrey","family":"Shallit","sequence":"additional","affiliation":[]},{"given":"Tim","family":"Smith","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,5,29]]},"reference":[{"key":"9929_CR1","doi-asserted-by":"publisher","first-page":"2795","DOI":"10.1016\/j.tcs.2009.02.006","volume":"410","author":"J-P Allouche","year":"2009","unstructured":"Allouche, J.-P., Rampersad, N., Shallit, J.: Periodicity, repetitions, and orbits of an automatic sequence. Theoret. Comput. Sci. 410, 2795\u20132803 (2009)","journal-title":"Theoret. Comput. Sci."},{"key":"9929_CR2","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1007\/s10474-017-0688-4","volume":"151","author":"K Aloui","year":"2017","unstructured":"Aloui, K., Mauduit, C., Mkaouar, M.: Somme des chiffres et r\u00e9partition dans les classes de congruence pour les palindromes ellips\u00e9phiques. Acta Math. Hung. 151, 409\u2013455 (2017)","journal-title":"Acta Math. Hung."},{"key":"9929_CR3","doi-asserted-by":"crossref","unstructured":"Alur, R., Madhusudan, P.: Visibly Pushdown Languages. In: Proc. Thirty-Sixth Ann. ACM Symp. Theor. Comput. (STOC), pp. 202\u2013211, ACM (2004)","DOI":"10.1145\/1007352.1007390"},{"key":"9929_CR4","unstructured":"Alur, R., Madhusudan, P.: Adding nested structure to words. J. Assoc. Comput. Mach. 56 (2009), Art. 16"},{"key":"9929_CR5","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1215\/ijm\/1256049011","volume":"21","author":"K Appel","year":"1977","unstructured":"Appel, K., Haken, W.: Every planar map is four colorable. I. Discharging Illinois J. Math. 21, 429\u2013490 (1977)","journal-title":"I. Discharging Illinois J. Math."},{"key":"9929_CR6","doi-asserted-by":"publisher","first-page":"491","DOI":"10.1215\/ijm\/1256049012","volume":"21","author":"K Appel","year":"1977","unstructured":"Appel, K., Haken, W., Koch, J.: Every planar map is four colorable. II. Reducibility Illinois J. Math. 21, 491\u2013567 (1977)","journal-title":"II. Reducibility Illinois J. Math."},{"key":"9929_CR7","first-page":"133","volume":"22","author":"C Ashbacher","year":"1990","unstructured":"Ashbacher, C.: More on palindromic squares. J. Recreat. Math. 22, 133\u2013135 (1990)","journal-title":"J. Recreat. Math."},{"key":"9929_CR8","unstructured":"Banks, W.D.: Every natural number is the sum of forty-nine palindromes. INTEGERS \u2014 Electronic J. Combinat. Number Theory 16 (2016), #A3 (electronic)"},{"key":"9929_CR9","doi-asserted-by":"publisher","first-page":"853","DOI":"10.4310\/MRL.2004.v11.n6.a10","volume":"11","author":"WD Banks","year":"2004","unstructured":"Banks, W.D., Hart, D.N., Sakata, M.: Almost all palindromes are composite. Math. Res. Lett. 11, 853\u2013868 (2004)","journal-title":"Math. Res. Lett."},{"key":"9929_CR10","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10998-005-0016-6","volume":"51","author":"WD Banks","year":"2005","unstructured":"Banks, W.D., Shparlinski, I.E.: Prime divisors of palindromes. Period. Math Hung. 51, 1\u201310 (2005)","journal-title":"Period. Math Hung."},{"key":"9929_CR11","doi-asserted-by":"publisher","first-page":"95","DOI":"10.4064\/ba54-2-1","volume":"54","author":"WD Banks","year":"2006","unstructured":"Banks, W.D., Shparlinski, I.E.: Average value of the Euler function on binary palindromes. Bull. Pol. Acad. Sci Math. 54, 95\u2013101 (2006)","journal-title":"Bull. Pol. Acad. Sci Math."},{"issue":"1","key":"9929_CR12","first-page":"13","volume":"23","author":"JKR Barnett","year":"1991","unstructured":"Barnett, J.K.R.: Tables of square palindromes in bases 2 and 10. J. Recreat. Math. 23(1), 13\u201318 (1991)","journal-title":"J. Recreat. Math."},{"key":"9929_CR13","doi-asserted-by":"publisher","first-page":"1387","DOI":"10.1142\/S1793042112500819","volume":"8","author":"B Basi\u0107","year":"2012","unstructured":"Basi\u0107, B. : On d-digit palindromes in different bases: the number of bases is unbounded. Internat. J. Number Theory 8, 1387\u20131390 (2012)","journal-title":"Internat. J. Number Theory"},{"key":"9929_CR14","doi-asserted-by":"publisher","first-page":"765","DOI":"10.4134\/JKMS.2015.52.4.765","volume":"52","author":"B Basi\u0107","year":"2015","unstructured":"Basi\u0107, B.: On \u201cvery palindromic\u201d sequences. J. Korean Math. Soc. 52, 765\u2013780 (2015)","journal-title":"J. Korean Math. Soc."},{"key":"9929_CR15","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1090\/bproc\/37","volume":"5","author":"J Bell","year":"2018","unstructured":"Bell, J., Hare, K., Shallit, J.: When is an automatic set an additive basis. Proc. Amer. Math. Soc. Ser. B 5, 50\u201363 (2018)","journal-title":"Proc. Amer. Math. Soc. Ser. B"},{"key":"9929_CR16","doi-asserted-by":"crossref","unstructured":"Bell, J.P., Lidbetter, T.F., Shallit, J.: Additive number theory via approximation by regular languages. In: Hoshi, M., Seki, S. (eds.) DLT Vol. 11088 of Lecture Notes in Computer Science, pp 121\u2013132. Springer, Berlin (2018)","DOI":"10.1007\/978-3-319-98654-8_10"},{"key":"9929_CR17","first-page":"37","volume":"6","author":"A B\u00e9rczes","year":"2014","unstructured":"B\u00e9rczes, A., Ziegler, V.: On simultaneous palindromes. J. Combin. Number Theory 6, 37\u201349 (2014)","journal-title":"J. Combin. Number Theory"},{"key":"9929_CR18","volume-title":"Winning Ways for your Mathematical Plays, Vol. 2 Games in Particular","author":"ER Berlekamp","year":"1982","unstructured":"Berlekamp, E.R., Conway, J.H., Guy, R.K.: Winning Ways for your Mathematical Plays, Vol. 2 Games in Particular. Academic Press, Cambridge (1982)"},{"key":"9929_CR19","unstructured":"Berstel, J.: Axel Thue\u2019s Papers on Repetitions in Words: a Translation. Number 20 in Publications Du Laboratoire De Combinatoire Et d\u2019Informatique Math\u00e9matique. Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al (1995)"},{"key":"9929_CR20","doi-asserted-by":"crossref","unstructured":"von Braunm\u00fchl, B., Verbeek, R.: Input-driven languages are recognized in n space. In: Karpinski, M. (ed.) Foundations of Computation Theory, FCT 83, Vol. 158 of Lecture Notes in Computer Science, pp 40\u201351. Springer, Berlin (1983)","DOI":"10.1007\/3-540-12689-9_92"},{"key":"9929_CR21","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1016\/S0304-3975(96)00260-5","volume":"181","author":"V Bruy\u00e8re","year":"1997","unstructured":"Bruy\u00e8re, V., Hansel, G.: Bertrand numeration systems and recognizability. Theoret. Comput. Sci. 181, 17\u201343 (1997)","journal-title":"Theoret. Comput. Sci."},{"key":"9929_CR22","doi-asserted-by":"crossref","first-page":"191","DOI":"10.36045\/bbms\/1103408547","volume":"1","author":"V Bruy\u00e8re","year":"1994","unstructured":"Bruy\u00e8re, V., Hansel, G., Michaux, C., Villemaire, R.: Logic and p-recognizable sets of integers. Bull. Belgian Math. Soc. 1, 191\u2013238 (1994). Corrigendum, Bull. Belg. Math. Soc. 1 (1994) 577","journal-title":"Bull. Belgian Math. Soc."},{"key":"9929_CR23","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1002\/malq.19600060105","volume":"6","author":"JR B\u00fcchi","year":"1960","unstructured":"B\u00fcchi, J.R.: Weak secord-order arithmetic and finite automata. Zeitschrift fur\u0308 mathematische Logik und Grundlagen der Mathematik 6, 66\u201392 (1960). Reprinted in S. Mac Lane and D. Siefkes, eds., The Collected Works of J. Richard Buchi\u0308, Springer, 1990, pp.398\u2013424","journal-title":"Zeitschrift fur\u0308 mathematische Logik und Grundlagen der Mathematik"},{"key":"9929_CR24","doi-asserted-by":"publisher","first-page":"1035","DOI":"10.1142\/S0129054112400448","volume":"23","author":"E Charlier","year":"2012","unstructured":"Charlier, E., Rampersad, N., Shallit, J.: Enumeration and decidable properties of automatic sequences. Internat. J. Found. Comp. Sci. 23, 1035\u20131066 (2012)","journal-title":"Internat. J. Found. Comp. Sci."},{"key":"9929_CR25","unstructured":"Cilleruelo, J., Luca, F.: Every positive integer is a sum of three palindromes. arXiv:\n1602.06208v1\n\n (2016)"},{"key":"9929_CR26","doi-asserted-by":"publisher","first-page":"3023","DOI":"10.1090\/mcom\/3221","volume":"87","author":"J Cilleruelo","year":"2018","unstructured":"Cilleruelo, J., Luca, F., Baxter, L.: Every positive integer is a sum of three palindromes. Math. Comput. 87, 3023\u20133055 (2018)","journal-title":"Math. Comput."},{"key":"9929_CR27","first-page":"101","volume":"1","author":"J Cilleruelo","year":"2009","unstructured":"Cilleruelo, J., Luca, F., Shparlinski, I.E.: Power values of palindromes. J Combin. Number Theory 1, 101\u2013107 (2009)","journal-title":"J Combin. Number Theory"},{"key":"9929_CR28","doi-asserted-by":"publisher","first-page":"433","DOI":"10.1007\/s00605-013-0477-2","volume":"171","author":"J Cilleruelo","year":"2013","unstructured":"Cilleruelo, J., Tesoro, R., Luca, F.: Palindromes in linear recurrence sequences. Monatsh. Math. 171, 433\u2013442 (2013)","journal-title":"Monatsh. Math."},{"key":"9929_CR29","doi-asserted-by":"publisher","first-page":"1","DOI":"10.4064\/aa137-1-1","volume":"137","author":"S Col","year":"2009","unstructured":"Col, S.: Palindromes dans les progressions arithm\u00e9tiques. Acta Arith. 137, 1\u201341 (2009)","journal-title":"Acta Arith."},{"key":"9929_CR30","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1016\/j.tcs.2016.10.005","volume":"657","author":"CF Du","year":"2017","unstructured":"Du, C.F., Mousavi, H., Rowland, E., Schaeffer, L.: J. Shallit. Decision algorithms for Fibonacci-automatic words II: related sequences and avoidability. Theoret. Comput. Sci. 657, 146\u2013162 (2017)","journal-title":"Theoret. Comput. Sci."},{"key":"9929_CR31","doi-asserted-by":"publisher","first-page":"943","DOI":"10.1142\/S0129054116500386","volume":"27","author":"CF Du","year":"2016","unstructured":"Du, C.F., Mousavi, H., Schaeffer, L., Shallit, J.: Decision algorithms for Fibonacci-automatic words III: enumeration and abelian properties. Internat. J. Found. Comp. Sci. 27, 943\u2013963 (2016)","journal-title":"Internat. J. Found. Comp. Sci."},{"key":"9929_CR32","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1016\/0020-0190(88)90148-2","volume":"26","author":"PW Dymond","year":"1988","unstructured":"Dymond, P.W.: Input-driven languages are in n depth. Inform. Process. Lett. 26, 247\u2013250 (1988)","journal-title":"Inform. Process. Lett."},{"key":"9929_CR33","doi-asserted-by":"crossref","unstructured":"Go\u010d, D., Henshall, D., Shallit, J.: Automatic theorem-proving in combinatorics on words. In: Moreira, N., Reis, R. (eds.) CIAA 2012, Vol. 7381 of Lecture Notes in Computer Science, pp 180\u2013191. Springer, Berlin (2012)","DOI":"10.1007\/978-3-642-31606-7_16"},{"key":"9929_CR34","doi-asserted-by":"crossref","unstructured":"Go\u010d, D., Mousavi, H., Shallit, J.: On the number of unbordered factors. In: Dediu, A.-H., Martin-Vide, C., Truthe, B. (eds.) LATA 2013, Vol. 7810 of Lecture Notes in Computer Science, pp 299\u2013310. Springer, Berlin (2013)","DOI":"10.1007\/978-3-642-37064-9_27"},{"key":"9929_CR35","doi-asserted-by":"crossref","unstructured":"Go\u010d, D., Saari, K., Shallit, J.: Primitive words and Lyndon words in automatic and linearly recurrent sequences. In: Dediu, A.-H., Martin-Vide, C., Truthe, B. (eds.) LATA 2013, Primitive Vol. 7810 of Lecture Notes in Computer Science, pp 311\u2013322. Springers, Berlin (2013)","DOI":"10.1007\/978-3-642-37064-9_28"},{"key":"9929_CR36","doi-asserted-by":"crossref","unstructured":"Go\u010d, D., Schaeffer, L., Shallit, J.: The subword complexity of k-automatic sequences is k-synchronized. In: B\u00e9al, M.-P., Carton, O. (eds.) DLT 2013, Vol. 7907 of Lecture Notes in Computer Science, pp 252\u2013263. Springer, Berlin (2013)","DOI":"10.1007\/978-3-642-38771-5_23"},{"key":"9929_CR37","first-page":"725","volume":"9","author":"EH Goins","year":"2009","unstructured":"Goins, E.H.: Palindromes in different bases: a conjecture of J. Ernest Wilkins. INTEGERS \u2014 Electronic J. Combinat. Number Theory 9, 725\u2013734 (2009). Paper #A55, (electronic)","journal-title":"INTEGERS \u2014 Electronic J. Combinat. Number Theory"},{"key":"9929_CR38","doi-asserted-by":"publisher","first-page":"2961","DOI":"10.1016\/j.tcs.2009.01.004","volume":"410","author":"Y-S Han","year":"2009","unstructured":"Han, Y.-S., Salomaa, K.: Nondeterministic state complexity of nested word automata. Theoret. Comput. Sci. 410, 2961\u20132971 (2009)","journal-title":"Theoret. Comput. Sci."},{"key":"9929_CR39","first-page":"A76","volume":"16","author":"S Haque","year":"2016","unstructured":"Haque, S., Shallit, J.: Discriminators and k-regular sequences. INTEGERS \u2014 Electronic J. Combinat. Number Theory 16, A76 (2016). (electronic)","journal-title":"INTEGERS \u2014 Electronic J. Combinat. Number Theory"},{"key":"9929_CR40","unstructured":"Hardy, G.H., Wright, E.M.: An Introduction to the Theory of Numbers, 5th edn. Oxford University Press, Oxford (1985)"},{"key":"9929_CR41","first-page":"259","volume":"36","author":"M Harminc","year":"1998","unstructured":"Harminc, M., Sot\u00e1k, R.: Palindromic numbers in arithmetic progressions. Fibonacci Quart. 36, 259\u2013262 (1998)","journal-title":"Fibonacci Quart."},{"key":"9929_CR42","doi-asserted-by":"crossref","unstructured":"Heizmann, M., Hoenicke, J., Podelski, A.: Software model checking for people who love automata. In: Sharygina, N., Veith, H. (eds.) Computer Aided Verification \u2014 25th International Conference, CAV 2013, vol. 8044 of Lecture Notes in Computer Science, pp 36\u201352. Springer, Berlin (2013)","DOI":"10.1007\/978-3-642-39799-8_2"},{"key":"9929_CR43","doi-asserted-by":"crossref","unstructured":"Heizmann, M., Dietsch, D., Greitschus, M., Leike, J., Musa, B., Sch\u00e4tzle, C., Podelski, A.: Ultimate automizer with two-track proofs. In: Chechik, M., Raskin, J.-F. (eds.) Tools and Algorithms for the Construction and Analysis of Systems \u2014 22nd International Conference, TACAS 2016, vol. 9636 of Lecture Notes in Computer Science, pp 950\u2013953. Springer, Berlin (2016)","DOI":"10.1007\/978-3-662-49674-9_68"},{"key":"9929_CR44","first-page":"81","volume":"40","author":"S Hern\u00e1ndez","year":"2006","unstructured":"Hern\u00e1ndez, S., Luca, F.: Palindromic powers. Rev. Colombiana Mat. 40, 81\u201386 (2006)","journal-title":"Rev. Colombiana Mat."},{"key":"9929_CR45","volume-title":"Introduction to Automata Theory, Languages, and Computation","author":"JE Hopcroft","year":"1979","unstructured":"Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Boston (1979)"},{"key":"9929_CR46","unstructured":"Kane, D.M., Sanna, C., Shallit, J.: Waring\u2019s Theorem for Binary Powers. arXiv:\n1801.04483\n\n. To appear, Combinatorica (2018)"},{"issue":"2","key":"9929_CR47","first-page":"124","volume":"22","author":"M Keith","year":"1990","unstructured":"Keith, M.: Classification and enumeration of palindromic squares. J. Recreat. Math. 22(2), 124\u2013132 (1990)","journal-title":"J. Recreat. Math."},{"key":"9929_CR48","first-page":"299","volume":"36","author":"P Kidder","year":"2007","unstructured":"Kidder, P., Kwong, H.: Remarks on integer palindromes. J. Recreat. Math. 36, 299\u2013306 (2007)","journal-title":"J. Recreat. Math."},{"key":"9929_CR49","first-page":"261","volume":"41","author":"I Korec","year":"1991","unstructured":"Korec, I.: Palindromic squares for various number system bases. Math. Slovaca 41, 261\u2013276 (1991)","journal-title":"Math. Slovaca"},{"issue":"\/43","key":"9929_CR50","first-page":"293","volume":"42","author":"H Kresov\u00e1","year":"1984","unstructured":"Kresov\u00e1, H., Sa\u030cl\u00e1t, T.: On palindromic numbers. Acta Math. Univ Comenian. 42(\/43), 293\u2013298 (1984)","journal-title":"Acta Math. Univ Comenian."},{"key":"9929_CR51","doi-asserted-by":"crossref","unstructured":"La Torre, S., Napoli, M., Parente, M.: On the membership problem for visibly pushdown languages. In: Graf, S., Zhang, W. (eds.) ATVA 2006, vol. 4218 of Lecture Notes in Computer Science, pp. 96\u2013109, Springer (2006)","DOI":"10.1007\/11901914_10"},{"key":"9929_CR52","first-page":"190","volume":"29","author":"CG Lekkerkerker","year":"1952","unstructured":"Lekkerkerker, C.G.: Voorstelling van natuurlijke getallen door een som van getallen van Fibonacci. Simon Stevin 29, 190\u2013195 (1952)","journal-title":"Simon Stevin"},{"key":"9929_CR53","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1007\/s00605-002-0490-3","volume":"138","author":"F Luca","year":"2003","unstructured":"Luca, F.: Palindromes in Lucas sequences. Monatsh. Math. 138, 209\u2013223 (2003)","journal-title":"Monatsh. Math."},{"key":"9929_CR54","doi-asserted-by":"publisher","first-page":"487","DOI":"10.1016\/j.crma.2008.03.015","volume":"346","author":"F Luca","year":"2008","unstructured":"Luca, F., Togb\u00e9, A.: On binary palindromes of the form 10n1. C. R. Acad. Sci. Paris 346, 487\u2013489 (2008)","journal-title":"C. R. Acad. Sci. Paris"},{"key":"9929_CR55","unstructured":"Luca, F., Young, P.T.: On the Binary Expansion of the Odd Catalan Numbers. In: Proc. 14Th Int. Conf. on Fibonacci Numbers and Their Applications, pp. 185\u2013190. Soc. Mat. Mexicana (2011)"},{"key":"9929_CR56","unstructured":"Madhusudan, P., Nowotka, D., Rajasekaran, A., Shallit, J.: Lagrange\u2019s theorem for binary squares. In: Potapov, I., Spirakis, P., Worrell, J. (eds.) 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018), Leibniz International Proceedings in Informatics, pp. 18:1\u201318:14. Schloss Dagstuhl\u2014Leibniz-Zentrum f\u00fcr Informatik, Germany (2018)"},{"issue":"3","key":"9929_CR57","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1023\/A:1005843212881","volume":"19","author":"W McCune","year":"1997","unstructured":"McCune, W.: Solution of the Robbins problem. J. Autom. Reason. 19(3), 263\u2013276 (1997)","journal-title":"J. Autom. Reason."},{"key":"9929_CR58","doi-asserted-by":"crossref","unstructured":"Mehlhorn, K.: Pebbling Mountain Ranges and Its Application of DCFL-Recognition. In: Proc. 7Th Int\u2019l Conf. on Automata, Languages, and Programming (ICALP), Vol. 85 of Lecture Notes in Computer Science, pp. 422\u2013435. Springer (1980)","DOI":"10.1007\/3-540-10003-2_89"},{"key":"9929_CR59","unstructured":"Mousavi, H.: Automatic theorem proving in Walnut. arXiv:\n1603.06017\n\n (2016)"},{"key":"9929_CR60","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1051\/ita\/2016010","volume":"50","author":"H Mousavi","year":"2016","unstructured":"Mousavi, H., Schaeffer, L., Shallit, J.: Decision algorithms for Fibonacci-automatic words, I Basic results. RAIRO Inform. Th\u00e9or. App. 50, 39\u201366 (2016)","journal-title":"RAIRO Inform. Th\u00e9or. App."},{"key":"9929_CR61","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3845-2","volume-title":"Additive Number Theory: The Classical Bases","author":"MB Nathanson","year":"1996","unstructured":"Nathanson, M.B.: Additive Number Theory: The Classical Bases. Springer, Berlin (1996)"},{"key":"9929_CR62","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1007\/BF01694004","volume":"2","author":"W Ogden","year":"1968","unstructured":"Ogden, W.: A helpful result for proving inherent ambiguity. Math. Systems Theory 2, 191\u2013194 (1968)","journal-title":"Math. Systems Theory"},{"key":"9929_CR63","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1016\/j.jcss.2017.02.001","volume":"86","author":"A Okhotin","year":"2017","unstructured":"Okhotin, A., Salomaa, K.: State complexity of operations on input-driven pushdown automata. J Comput. System Sci. 86, 207\u2013228 (2017)","journal-title":"J Comput. System Sci."},{"key":"9929_CR64","doi-asserted-by":"publisher","first-page":"3290","DOI":"10.1016\/j.tcs.2009.05.002","volume":"410","author":"X Piao","year":"2009","unstructured":"Piao, X., Salomaa, K.: Operational state complexity of nested word automata. Theoret. Comput. Sci. 410, 3290\u20133302 (2009)","journal-title":"Theoret. Comput. Sci."},{"key":"9929_CR65","first-page":"Paper #A13 (ele","volume":"15A","author":"P Pollack","year":"2015","unstructured":"Pollack, P.: Palindromic sums of proper divisors. INTEGERS \u2014 Electronic J. Combinat. Number Theory 15A, Paper #A13 (electronic) (2015)","journal-title":"INTEGERS \u2014 Electronic J. Combinat. Number Theory"},{"key":"9929_CR66","unstructured":"Rajasekaran, A.: Using automata theory to solve problems in additive number theory. Master\u2019s thesis, School of Computer Science, University of Waterloo, 2018. Available at \nhttps:\/\/uwspace.uwaterloo.ca\/handle\/10012\/13202"},{"key":"9929_CR67","unstructured":"Rajasekaran, A., Smith, T., Shallit, J.: Sums of palindromes: an approach via automata. In: Niedermeier, R., Vall\u00e9e, B. (eds.) 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018), Leibniz International Proceedings in Informatics, pp. 54:1\u201354:12. Schloss Dagstuhl \u2014 Leibniz-Zentrum fur\u0308 Informatik (2018)"},{"key":"9929_CR68","doi-asserted-by":"publisher","first-page":"580","DOI":"10.1016\/j.ic.2010.11.021","volume":"209","author":"K Salomaa","year":"2011","unstructured":"Salomaa, K.: Limitations of lower bound methods for deterministic nested word automata. Inform. Comput. 209, 580\u2013589 (2011)","journal-title":"Inform. Comput."},{"key":"9929_CR69","doi-asserted-by":"crossref","unstructured":"Shallit, J.: Decidability and enumeration for automatic sequences: a survey. In: Bulatov, A.A., Shur, A.M. (eds.) CSR 2013, vol. 7913 of Lecture Notes in Computer Science, pp 49\u201363. Springer, Berlin (2013)","DOI":"10.1007\/978-3-642-38536-0_5"},{"key":"9929_CR70","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1016\/1385-7258(86)90020-X","volume":"48","author":"TN Shorey","year":"1986","unstructured":"Shorey, T.N.: On the equation zq = (xn \u2212 1)\/(x \u2212 1). Indag. Math. 48, 345\u2013351 (1986)","journal-title":"Indag. Math."},{"key":"9929_CR71","unstructured":"Sigg, M.: On a conjecture of John Hoffman regarding sums of palindromic numbers. arXiv:\n1510.07507\n\n (2015)"},{"issue":"1","key":"9929_CR72","first-page":"11","volume":"5","author":"GJ Simmons","year":"1972","unstructured":"Simmons, G.J.: On palindromic squares of non-palindromic numbers. J. Recreat. Math. 5(1), 11\u201319 (1972)","journal-title":"J. Recreat. Math."},{"key":"9929_CR73","doi-asserted-by":"crossref","unstructured":"Sloane, N.J.A., et al.: The on-line encyclopedia of integer sequences Available at \nhttps:\/\/oeis.org\n\n (2019)","DOI":"10.1515\/9780691197944-009"},{"key":"9929_CR74","first-page":"1","volume":"1","author":"A Thue","year":"1912","unstructured":"Thue, A.: \u00dcBer die gegenseitige Lage gleicher Teile gewisser Zeichenreihen. Norske vid. Selsk. Skr. Mat. Nat. Kl. 1, 1\u201367 (1912). Reprinted in Selected Mathematical Papers of Axel Thue, T. Nagell, editor, Universitetsforlaget, Oslo, 1977, 413\u2013478","journal-title":"Norske vid. Selsk. Skr. Mat. Nat. Kl."},{"key":"9929_CR75","first-page":"209","volume":"12","author":"C Trigg","year":"1974","unstructured":"Trigg, C.: Infinite sequences of palindromic triangular numbers. Fibonacci Quart. 12, 209\u2013212 (1974)","journal-title":"Fibonacci Quart."},{"issue":"2","key":"9929_CR76","doi-asserted-by":"publisher","first-page":"57","DOI":"10.2307\/2025976","volume":"76","author":"T Tymoczko","year":"1979","unstructured":"Tymoczko, T.: The four-color problem and its philosophical significance. J. Philosophy 76(2), 57\u201383 (1979)","journal-title":"J. Philosophy"},{"key":"9929_CR77","unstructured":"Vaughan, R.C., Wooley, T.: Number Theory for the Millennium. III, pp. 301\u2013340. A. K. Peters. In: Bennett, M.A., Berndt, B.C., Boston, N., Diamond, H.G., Hildebrand, A.J., Philipp, W. (eds.) (2002)"},{"key":"9929_CR78","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1080\/0025570X.1978.11976671","volume":"51","author":"S Yates","year":"1978","unstructured":"Yates, S.: The mystique of repunits. Math. Mag. 51, 22\u201328 (1978)","journal-title":"Math. Mag."},{"key":"9929_CR79","first-page":"179","volume":"41","author":"E Zeckendorf","year":"1972","unstructured":"Zeckendorf, E.: Repr\u00e9sentation des nombres naturels par une somme de nombres de Fibonacci ou de nombres de Lucas. Bull. Soc. Roy. Li\u00e9ge 41, 179\u2013182 (1972)","journal-title":"Bull. Soc. Roy. Li\u00e9ge"}],"container-title":["Theory of Computing Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00224-019-09929-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00224-019-09929-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00224-019-09929-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,27]],"date-time":"2020-05-27T23:21:05Z","timestamp":1590621665000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00224-019-09929-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,29]]},"references-count":79,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2020,4]]}},"alternative-id":["9929"],"URL":"https:\/\/doi.org\/10.1007\/s00224-019-09929-9","relation":{},"ISSN":["1432-4350","1433-0490"],"issn-type":[{"value":"1432-4350","type":"print"},{"value":"1433-0490","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,5,29]]},"assertion":[{"value":"29 May 2019","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}