NP-Completeness and Physical Zero-Knowledge Proofs for Sumplete, a Puzzle Generated by ChatGPT

Author:

Hatsugai Kyosuke,Ruangwises Suthee,Asano Kyoichi,Abe Yoshiki

Abstract

AbstractSumplete is a logic puzzle generated by ChatGPT in March 2023. The puzzle consists of a rectangular grid, with each cell containing an integer. Each row and column also has an integer called target value assigned to it. The objective of this puzzle is to cross out some numbers in the grid such that the sum of uncrossed numbers in each row and column is equal to the corresponding target value. In this paper, we prove that Sumplete is NP-complete. We also propose a physical zero-knowledge proof protocol for the puzzle using physical cards.

Funder

Japan Society for the Promotion of Science

Publisher

Springer Science and Business Media LLC

Reference21 articles.

1. Hatsugai, K., Asano, K., Abe, Y.: A physical zero-knowledge proof for Sumplete, a puzzle generated by chatgpts. In: COCOON (2023)

2. OpenAI: GPT-4 Technical Report (2023)

3. Puzzled Penguin: ChatGPT invented its own puzzle game. https://puzzledpenguin.substack.com/p/chatgpt-invented-its-own-puzzle-game (2023)

4. Hey, Good Game: Sumplete. https://sumplete.com/

5. Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof systems. SIAM J. Comput. 18(1), 186–208 (1989)

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