@inproceedings{894c10ff08624c16acbff0264aef7935,

title = "Enumeration of cryptarithms using deterministic finite automata",

abstract = "A cryptarithm is a mathematical puzzle where given an arithmetic equation written with letters rather than numerals, a player must discover an assignment of numerals on letters that makes the equation hold true. In this paper, we propose a method to construct a DFA that accepts cryptarithms that admit (unique) solutions for each base. We implemented the method and constructed a DFA for bases k≤ 7. Those DFAs can be used as complete catalogues of cryptarithms, whose applications include enumeration of and counting the exact numbers Gk(n) of cryptarithm instances with n digits that admit base-k solutions. Moreover, explicit formulas for G2(n) and G3(n) are given.",

keywords = "Alphametics, Automaton, Cryptartihms, DFA, Enumeration",

author = "Yuki Nozaki and Diptarama Hendrian and Ryo Yoshinaka and Ayumi Shinohara",

note = "Publisher Copyright: {\textcopyright} 2018, Springer International Publishing AG, part of Springer Nature.; 23rd International Conference on Implementation and Application of Automata, CIAA 2018 ; Conference date: 30-07-2018 Through 02-08-2018",

year = "2018",

doi = "10.1007/978-3-319-94812-6_24",

language = "English",

isbn = "9783319948119",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "286--298",

editor = "Cezar Campeanu",

booktitle = "Implementation and Application of Automata - 23rd International Conference, CIAA 2018, Proceedings",

}