{"title":"通过正则分解证明几乎肯定终止","authors":"Jianhui Chen, Fei He","doi":"10.1145/3385412.3386002","DOIUrl":null,"url":null,"abstract":"Almost-sure termination is the most basic liveness property of probabilistic programs. We present a novel decomposition-based approach for proving almost-sure termination of probabilistic programs with complex control-flow structure and non-determinism. Our approach automatically decomposes the runs of the probabilistic program into a finite union of ω-regular subsets and then proves almost-sure termination of each subset based on the notion of localized ranking supermartingales. Compared to the lexicographic methods and the compositional methods, our approach does not require a lexicographic order over the ranking supermartingales as well as the so-called unaffecting condition. Thus it has high generality. We present the algorithm of our approach and prove its soundness, as well as its relative completeness. We show that our approach can be applied to some hard cases and the evaluation on the benchmarks of previous works shows the significant efficiency of our approach.","PeriodicalId":20580,"journal":{"name":"Proceedings of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation","volume":"17 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":"{\"title\":\"Proving almost-sure termination by omega-regular decomposition\",\"authors\":\"Jianhui Chen, Fei He\",\"doi\":\"10.1145/3385412.3386002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Almost-sure termination is the most basic liveness property of probabilistic programs. We present a novel decomposition-based approach for proving almost-sure termination of probabilistic programs with complex control-flow structure and non-determinism. Our approach automatically decomposes the runs of the probabilistic program into a finite union of ω-regular subsets and then proves almost-sure termination of each subset based on the notion of localized ranking supermartingales. Compared to the lexicographic methods and the compositional methods, our approach does not require a lexicographic order over the ranking supermartingales as well as the so-called unaffecting condition. Thus it has high generality. We present the algorithm of our approach and prove its soundness, as well as its relative completeness. We show that our approach can be applied to some hard cases and the evaluation on the benchmarks of previous works shows the significant efficiency of our approach.\",\"PeriodicalId\":20580,\"journal\":{\"name\":\"Proceedings of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation\",\"volume\":\"17 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-06-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3385412.3386002\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3385412.3386002","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Proving almost-sure termination by omega-regular decomposition
Almost-sure termination is the most basic liveness property of probabilistic programs. We present a novel decomposition-based approach for proving almost-sure termination of probabilistic programs with complex control-flow structure and non-determinism. Our approach automatically decomposes the runs of the probabilistic program into a finite union of ω-regular subsets and then proves almost-sure termination of each subset based on the notion of localized ranking supermartingales. Compared to the lexicographic methods and the compositional methods, our approach does not require a lexicographic order over the ranking supermartingales as well as the so-called unaffecting condition. Thus it has high generality. We present the algorithm of our approach and prove its soundness, as well as its relative completeness. We show that our approach can be applied to some hard cases and the evaluation on the benchmarks of previous works shows the significant efficiency of our approach.