{"title":"论模型检查知识与时间的复杂性","authors":"Laura Bozzelli, Bastien Maubert, Aniello Murano","doi":"10.1145/3637212","DOIUrl":null,"url":null,"abstract":"<p>We establish the precise complexity of the model-checking problem for the main logics of knowledge and time. While this problem was known to be non-elementary for agents with perfect recall, with a number of exponentials that increases with the alternation of knowledge operators, the precise complexity of the problem when the maximum alternation is fixed has been an open problem for twenty years. We close it by establishing improved upper bounds for CTL<sup>*</sup> with knowledge, and providing matching lower bounds that also apply for epistemic extensions of <sans-serif>LTL</sans-serif> and <sans-serif>CTL</sans-serif>. We also study the model-checking problem for these logics on systems satisfying the “no learning” property, introduced by Halpern and Vardi in their taxonomy of logics of knowledge and time, and we settle the complexity in almost all cases.</p>","PeriodicalId":50916,"journal":{"name":"ACM Transactions on Computational Logic","volume":"143 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On The Complexity of Model Checking Knowledge and Time\",\"authors\":\"Laura Bozzelli, Bastien Maubert, Aniello Murano\",\"doi\":\"10.1145/3637212\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We establish the precise complexity of the model-checking problem for the main logics of knowledge and time. While this problem was known to be non-elementary for agents with perfect recall, with a number of exponentials that increases with the alternation of knowledge operators, the precise complexity of the problem when the maximum alternation is fixed has been an open problem for twenty years. We close it by establishing improved upper bounds for CTL<sup>*</sup> with knowledge, and providing matching lower bounds that also apply for epistemic extensions of <sans-serif>LTL</sans-serif> and <sans-serif>CTL</sans-serif>. We also study the model-checking problem for these logics on systems satisfying the “no learning” property, introduced by Halpern and Vardi in their taxonomy of logics of knowledge and time, and we settle the complexity in almost all cases.</p>\",\"PeriodicalId\":50916,\"journal\":{\"name\":\"ACM Transactions on Computational Logic\",\"volume\":\"143 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-12-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACM Transactions on Computational Logic\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.1145/3637212\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACM Transactions on Computational Logic","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1145/3637212","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
On The Complexity of Model Checking Knowledge and Time
We establish the precise complexity of the model-checking problem for the main logics of knowledge and time. While this problem was known to be non-elementary for agents with perfect recall, with a number of exponentials that increases with the alternation of knowledge operators, the precise complexity of the problem when the maximum alternation is fixed has been an open problem for twenty years. We close it by establishing improved upper bounds for CTL* with knowledge, and providing matching lower bounds that also apply for epistemic extensions of LTL and CTL. We also study the model-checking problem for these logics on systems satisfying the “no learning” property, introduced by Halpern and Vardi in their taxonomy of logics of knowledge and time, and we settle the complexity in almost all cases.
期刊介绍：
TOCL welcomes submissions related to all aspects of logic as it pertains to topics in computer science. This area has a great tradition in computer science. Several researchers who earned the ACM Turing award have also contributed to this field, namely Edgar Codd (relational database systems), Stephen Cook (complexity of logical theories), Edsger W. Dijkstra, Robert W. Floyd, Tony Hoare, Amir Pnueli, Dana Scott, Edmond M. Clarke, Allen E. Emerson, and Joseph Sifakis (program logics, program derivation and verification, programming languages semantics), Robin Milner (interactive theorem proving, concurrency calculi, and functional programming), and John McCarthy (functional programming and logics in AI).
Logic continues to play an important role in computer science and has permeated several of its areas, including artificial intelligence, computational complexity, database systems, and programming languages.
The Editorial Board of this journal seeks and hopes to attract high-quality submissions in all the above-mentioned areas of computational logic so that TOCL becomes the standard reference in the field.
Both theoretical and applied papers are sought. Submissions showing novel use of logic in computer science are especially welcome.
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