Enumeration of cryptarithms using deterministic finite automata

研究成果: Conference contribution

抜粋

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.

元の言語English
ホスト出版物のタイトルImplementation and Application of Automata - 23rd International Conference, CIAA 2018, Proceedings
編集者Cezar Campeanu
出版者Springer Verlag
ページ286-298
ページ数13
ISBN(印刷物)9783319948119
DOI
出版物ステータスPublished - 2018 1 1
イベント23rd International Conference on Implementation and Application of Automata, CIAA 2018 - Charlottetown, Canada
継続期間: 2018 7 302018 8 2

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
10977 LNCS
ISSN(印刷物)0302-9743
ISSN(電子版)1611-3349

Other

Other23rd International Conference on Implementation and Application of Automata, CIAA 2018
Canada
Charlottetown
期間18/7/3018/8/2

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

フィンガープリント Enumeration of cryptarithms using deterministic finite automata' の研究トピックを掘り下げます。これらはともに一意のフィンガープリントを構成します。

  • これを引用

    Nozaki, Y., Hendrian, D., Yoshinaka, R., & Shinohara, A. (2018). Enumeration of cryptarithms using deterministic finite automata. : C. Campeanu (版), Implementation and Application of Automata - 23rd International Conference, CIAA 2018, Proceedings (pp. 286-298). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); 巻数 10977 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-94812-6_24