{"title":"简单随机对策中能量平价目标值的逼近","authors":"Mohan Dantam, Richard Mayr","doi":"10.48550/arXiv.2307.05762","DOIUrl":null,"url":null,"abstract":"We consider simple stochastic games $\\mathcal G$ with energy-parity objectives, a combination of quantitative rewards with a qualitative parity condition. The Maximizer tries to avoid running out of energy while simultaneously satisfying a parity condition. We present an algorithm to approximate the value of a given configuration in 2-NEXPTIME. Moreover, $\\varepsilon$-optimal strategies for either player require at most $O(2EXP(|{\\mathcal G}|)\\cdot\\log(\\frac{1}{\\varepsilon}))$ memory modes.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"11 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Approximating the Value of Energy-Parity Objectives in Simple Stochastic Games\",\"authors\":\"Mohan Dantam, Richard Mayr\",\"doi\":\"10.48550/arXiv.2307.05762\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider simple stochastic games $\\\\mathcal G$ with energy-parity objectives, a combination of quantitative rewards with a qualitative parity condition. The Maximizer tries to avoid running out of energy while simultaneously satisfying a parity condition. We present an algorithm to approximate the value of a given configuration in 2-NEXPTIME. Moreover, $\\\\varepsilon$-optimal strategies for either player require at most $O(2EXP(|{\\\\mathcal G}|)\\\\cdot\\\\log(\\\\frac{1}{\\\\varepsilon}))$ memory modes.\",\"PeriodicalId\":369104,\"journal\":{\"name\":\"International Symposium on Mathematical Foundations of Computer Science\",\"volume\":\"11 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-07-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Symposium on Mathematical Foundations of Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.48550/arXiv.2307.05762\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Symposium on Mathematical Foundations of Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.48550/arXiv.2307.05762","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Approximating the Value of Energy-Parity Objectives in Simple Stochastic Games
We consider simple stochastic games $\mathcal G$ with energy-parity objectives, a combination of quantitative rewards with a qualitative parity condition. The Maximizer tries to avoid running out of energy while simultaneously satisfying a parity condition. We present an algorithm to approximate the value of a given configuration in 2-NEXPTIME. Moreover, $\varepsilon$-optimal strategies for either player require at most $O(2EXP(|{\mathcal G}|)\cdot\log(\frac{1}{\varepsilon}))$ memory modes.
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