{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T21:01:54Z","timestamp":1725483714892},"reference-count":0,"publisher":"EasyChair","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>This paper presents modeling of<\/jats:p><jats:p>a binary tree that represents a natural number<\/jats:p><jats:p>and gives an inductive proof for its properties<\/jats:p><jats:p>using theorem provers.<\/jats:p><jats:p>We define a function for converting data from a natural number<\/jats:p><jats:p>into a binary tree<\/jats:p><jats:p>and give an inductive proof for its well-definedness.<\/jats:p><jats:p>We formalize this method, develop a computational model based on it,<\/jats:p><jats:p>and apply it to an electronic cash protocol.<\/jats:p><jats:p>We also define the payment function on the binary tree<\/jats:p><jats:p>and go on to prove the divisibility of electronic cash<\/jats:p><jats:p>using the theorem provers Isabelle\/HOL and Coq, respectively.<\/jats:p><jats:p>Furthermore, we discuss the effectiveness of this method.<\/jats:p>","DOI":"10.29007\/w5xk","type":"proceedings-article","created":{"date-parts":[[2018,1,23]],"date-time":"2018-01-23T17:59:06Z","timestamp":1516730346000},"page":"93-77","source":"Crossref","is-referenced-by-count":0,"title":["Data Conversion Method between a Natural Number and a Binary Tree for an Inductive Proof and Its Application"],"prefix":"10.29007","volume":"15","author":[{"given":"Kazuko","family":"Takahashi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shizuo","family":"Yoshimaru","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mizuki","family":"Goto","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"11545","event":{"name":"SCSS 2013. 5th International Symposium on Symbolic Computation in Software Science"},"container-title":["EPiC Series in Computing"],"original-title":[],"deposited":{"date-parts":[[2018,1,23]],"date-time":"2018-01-23T17:59:09Z","timestamp":1516730349000},"score":1,"resource":{"primary":{"URL":"https:\/\/easychair.org\/publications\/paper\/zfm"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"references-count":0,"URL":"https:\/\/doi.org\/10.29007\/w5xk","relation":{},"ISSN":["2398-7340"],"issn-type":[{"type":"print","value":"2398-7340"}],"subject":[]}}