Data Conversion Method between a Natural Number and a Binary Tree for an Inductive Proof and Its Application

Kazuko Takahashi; Shizuo Yoshimaru; Mizuki Goto

doi:10.29007/w5xk

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Data Conversion Method between a Natural Number and a Binary Tree for an Inductive Proof and Its Application

15 pages•Published: June 19, 2013

Kazuko Takahashi, Shizuo Yoshimaru and Mizuki Goto

Abstract

This paper presents modeling of
a binary tree that represents a natural number
and gives an inductive proof for its properties
using theorem provers.
We define a function for converting data from a natural number
into a binary tree
and give an inductive proof for its well-definedness.
We formalize this method, develop a computational model based on it,
and apply it to an electronic cash protocol.
We also define the payment function on the binary tree
and go on to prove the divisibility of electronic cash
using the theorem provers Isabelle/HOL and Coq, respectively.
Furthermore, we discuss the effectiveness of this method.

Keyphrases: computational model, elecronic cash protocol, induction scheme, theorem proving methods

In: Laura Kovács and Temur Kutsia (editors). SCSS 2013. 5th International Symposium on Symbolic Computation in Software Science, vol 15, pages 93--107

Links:	https://easychair.org/publications/paper/zfm
	https://doi.org/10.29007/w5xk

BibTeX entry

@inproceedings{SCSS2013:Data_Conversion_Method_between,
  author    = {Kazuko Takahashi and Shizuo Yoshimaru and Mizuki Goto},
  title     = {Data Conversion Method between a Natural Number and a Binary Tree for an Inductive Proof and Its Application},
  booktitle = {SCSS 2013. 5th International Symposium on Symbolic Computation in Software Science},
  editor    = {Laura Kovacs and Temur Kutsia},
  series    = {EPiC Series in Computing},
  volume    = {15},
  pages     = {93--107},
  year      = {2013},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {https://easychair.org/publications/paper/zfm},
  doi       = {10.29007/w5xk}}

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