{"title":"令人烦恼的逻辑学","authors":"Kyle Burke, Craig Tennenhouse","doi":"10.1007/s00182-024-00899-y","DOIUrl":null,"url":null,"abstract":"<p>We define a new impartial combinatorial game, FLAG COLORING, based on flood filling, and find some values and outcome classes for some game positions. We then generalize FLAG COLORING to a graph game, re-imagining the game on two colors as an edge-reduction game on graphs, and find values for many positions represented as graph families on two colors. We demonstrate that the generalized game is PSPACE-complete for two or more colors via a reduction from AVOID TRUE. Finally, remaining open problems are discussed.</p>","PeriodicalId":14155,"journal":{"name":"International Journal of Game Theory","volume":"130 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Vexing vexillological logic\",\"authors\":\"Kyle Burke, Craig Tennenhouse\",\"doi\":\"10.1007/s00182-024-00899-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We define a new impartial combinatorial game, FLAG COLORING, based on flood filling, and find some values and outcome classes for some game positions. We then generalize FLAG COLORING to a graph game, re-imagining the game on two colors as an edge-reduction game on graphs, and find values for many positions represented as graph families on two colors. We demonstrate that the generalized game is PSPACE-complete for two or more colors via a reduction from AVOID TRUE. Finally, remaining open problems are discussed.</p>\",\"PeriodicalId\":14155,\"journal\":{\"name\":\"International Journal of Game Theory\",\"volume\":\"130 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-05-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Game Theory\",\"FirstCategoryId\":\"96\",\"ListUrlMain\":\"https://doi.org/10.1007/s00182-024-00899-y\",\"RegionNum\":4,\"RegionCategory\":\"经济学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"ECONOMICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Game Theory","FirstCategoryId":"96","ListUrlMain":"https://doi.org/10.1007/s00182-024-00899-y","RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ECONOMICS","Score":null,"Total":0}
引用次数: 0
摘要
我们定义了一种新的基于洪水填充的公正组合博弈--FLAG COLORING，并为一些博弈位置找到了一些值和结果类别。然后，我们将 FLAG COLORING 广义为图博弈，将双色图博弈重新想象为图上的边还原博弈，并为许多位置找到了双色图族的值。我们证明，对于两种或更多种颜色，通过从 "避免真实"（AVOID TRUE）的还原，广义游戏是 PSPACE 完备的。最后，我们还讨论了剩余的未决问题。
We define a new impartial combinatorial game, FLAG COLORING, based on flood filling, and find some values and outcome classes for some game positions. We then generalize FLAG COLORING to a graph game, re-imagining the game on two colors as an edge-reduction game on graphs, and find values for many positions represented as graph families on two colors. We demonstrate that the generalized game is PSPACE-complete for two or more colors via a reduction from AVOID TRUE. Finally, remaining open problems are discussed.
期刊介绍：
International Journal of Game Theory is devoted to game theory and its applications. It publishes original research making significant contributions from a methodological, conceptual or mathematical point of view. Survey articles may also be considered if especially useful for the field.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
