Verification of a brick Wang tiling algorithm

Toshiaki Matsushima; Yoshihiro Mizoguchi; Alexandre Derouet-Jourdan

doi:10.29007/2m5f

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Verification of a brick Wang tiling algorithm

10 pages•Published: March 27, 2016

Toshiaki Matsushima, Yoshihiro Mizoguchi and Alexandre Derouet-Jourdan

Abstract

We have implemented a certified Wang tiling program for tiling a rectangle region using a brick corner Wang tile set. A brick corner Wang tile set is a special Wang tile set introduced by A. Derouet-Jourdan et al. in computer graphics in 2015 to model wall patterns texture. We have implemented a tiling algorithm using Coq proof assistant and proved its correctness. This correctness assures the existence of a tiling of any brick corner Wang tile set for any size of rectangle. The essential points of our proof are the existence of a tiling for a $2 \times 2$ rectangle and a simple induction process. Since the brick corner Wang tile is a class of infinite kinds of tile sets, it is not straightforward and there are many conditional branches to prove the correctness. The certification with Coq assures that there are no lack of conditions.

Keyphrases: Coq, program verification, Wang tiling

In: James H. Davenport and Fadoua Ghourabi (editors). SCSS 2016. 7th International Symposium on Symbolic Computation in Software Science, vol 39, pages 107--116

Links:	https://easychair.org/publications/paper/4mz
	https://doi.org/10.29007/2m5f

BibTeX entry

@inproceedings{SCSS2016:Verification_of_brick_Wang,
  author    = {Toshiaki Matsushima and Yoshihiro Mizoguchi and Alexandre Derouet-Jourdan},
  title     = {Verification of a brick Wang tiling algorithm},
  booktitle = {SCSS 2016. 7th International Symposium on  Symbolic Computation in Software Science},
  editor    = {James H. Davenport and Fadoua Ghourabi},
  series    = {EPiC Series in Computing},
  volume    = {39},
  pages     = {107--116},
  year      = {2016},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {https://easychair.org/publications/paper/4mz},
  doi       = {10.29007/2m5f}}

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