{"title":"NP-Completeness and Physical Zero-Knowledge Proofs for Sumplete, a Puzzle Generated by ChatGPT","authors":"Kyosuke Hatsugai, Suthee Ruangwises, Kyoichi Asano, Yoshiki Abe","doi":"10.1007/s00354-024-00267-0","DOIUrl":null,"url":null,"abstract":"<p>Sumplete 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 <i>target value</i> 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.</p>","PeriodicalId":54726,"journal":{"name":"New Generation Computing","volume":"214 1","pages":""},"PeriodicalIF":2.0000,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"New Generation Computing","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1007/s00354-024-00267-0","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, HARDWARE & ARCHITECTURE","Score":null,"Total":0}
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Abstract
Sumplete 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.
期刊介绍：
The journal is specially intended to support the development of new computational and cognitive paradigms stemming from the cross-fertilization of various research fields. These fields include, but are not limited to, programming (logic, constraint, functional, object-oriented), distributed/parallel computing, knowledge-based systems, agent-oriented systems, and cognitive aspects of human embodied knowledge. It also encourages theoretical and/or practical papers concerning all types of learning, knowledge discovery, evolutionary mechanisms, human cognition and learning, and emergent systems that can lead to key technologies enabling us to build more complex and intelligent systems. The editorial board hopes that New Generation Computing will work as a catalyst among active researchers with broad interests by ensuring a smooth publication process.
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