{"title":"高阶可达性游戏vs低阶可达性游戏","authors":"Kazuyuki Asada, H. Katsura, N. Kobayashi","doi":"10.48550/arXiv.2203.08416","DOIUrl":null,"url":null,"abstract":"We consider the reachability problem for higher-order functional programs and study the relationship between reachability games (i.e., the reachability problem for programs with angelic and demonic nondeterminism) and may-reachability (i.e., the reachability problem for programs with only angelic nondeterminism). We show that reachability games for order-n programs can be reduced to may-reachability problems for order(n + 1) programs, and vice versa. We formalize the reductions by using higher-order fixpoint logic and prove their correctness. We also discuss applications of the reductions to higher-order program verification.","PeriodicalId":404583,"journal":{"name":"Reachability Problems","volume":"72 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"On Higher-Order Reachability Games vs May Reachability\",\"authors\":\"Kazuyuki Asada, H. Katsura, N. Kobayashi\",\"doi\":\"10.48550/arXiv.2203.08416\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the reachability problem for higher-order functional programs and study the relationship between reachability games (i.e., the reachability problem for programs with angelic and demonic nondeterminism) and may-reachability (i.e., the reachability problem for programs with only angelic nondeterminism). We show that reachability games for order-n programs can be reduced to may-reachability problems for order(n + 1) programs, and vice versa. We formalize the reductions by using higher-order fixpoint logic and prove their correctness. We also discuss applications of the reductions to higher-order program verification.\",\"PeriodicalId\":404583,\"journal\":{\"name\":\"Reachability Problems\",\"volume\":\"72 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-03-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Reachability Problems\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.48550/arXiv.2203.08416\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Reachability Problems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.48550/arXiv.2203.08416","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On Higher-Order Reachability Games vs May Reachability
We consider the reachability problem for higher-order functional programs and study the relationship between reachability games (i.e., the reachability problem for programs with angelic and demonic nondeterminism) and may-reachability (i.e., the reachability problem for programs with only angelic nondeterminism). We show that reachability games for order-n programs can be reduced to may-reachability problems for order(n + 1) programs, and vice versa. We formalize the reductions by using higher-order fixpoint logic and prove their correctness. We also discuss applications of the reductions to higher-order program verification.
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