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Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science最新文献

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Smooth approximations and CSPs over finitely bounded homogeneous structures 有限有界齐次结构上的光滑逼近与csp
Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2020-11-08 DOI: 10.1145/3531130.3533353
A. Mottet, M. Pinsker
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引用次数: 14
A Type Theory for Strictly Unital ∞-Categories 严格酉∞范畴的类型论
Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2020-07-16 DOI: 10.1145/3531130.3533363
Eric Finster, David J. Reutter, J. Vicary
{"title":"A Type Theory for Strictly Unital ∞-Categories","authors":"Eric Finster, David J. Reutter, J. Vicary","doi":"10.1145/3531130.3533363","DOIUrl":"https://doi.org/10.1145/3531130.3533363","url":null,"abstract":"We use type-theoretic techniques to present an algebraic theory of ∞-categories with strict units. Starting with a known type-theoretic presentation of fully weak ∞-categories, in which terms denote valid operations, we extend the theory with a non-trivial definitional equality. This forces some operations to coincide strictly in any model, yielding the strict unit behaviour. We make a detailed investigation of the meta-theoretic properties of this theory. We give a reduction relation that generates definitional equality, and prove that it is confluent and terminating, thus yielding the first decision procedure for equality in a strictly-unital setting. Moreover, we show that our definitional equality relation identifies all terms in a disc context, providing a point comparison with a previously proposed definition of strictly unital ∞-category. We also prove a conservativity result, showing that every operation of the strictly unital theory indeed arises from a valid operation in the fully weak theory. From this, we infer that strict unitality is a property of an ∞-category rather than additional structure.","PeriodicalId":373589,"journal":{"name":"Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125490024","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
Quantum Weakest Preconditions for Reasoning about Expected Runtimes of Quantum Programs 量子程序预期运行时间推理的量子最弱前提
Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2019-11-28 DOI: 10.1145/3531130.3533327
Junyi Liu, Li Zhou, G. Barthe, M. Ying
{"title":"Quantum Weakest Preconditions for Reasoning about Expected Runtimes of Quantum Programs","authors":"Junyi Liu, Li Zhou, G. Barthe, M. Ying","doi":"10.1145/3531130.3533327","DOIUrl":"https://doi.org/10.1145/3531130.3533327","url":null,"abstract":"We study expected runtimes for quantum programs. Inspired by recent work on probabilistic programs, we first define expected runtime as a generalisation of quantum weakest precondition. Then, we show that the expected runtime of a quantum program can be represented as the expectation of an observable (in physics). A method for computing the expected runtimes of quantum programs in finite-dimensional state spaces is developed. Several examples are provided as applications of this method, including computing the expected runtime of quantum Bernoulli Factory – a quantum algorithm for generating random numbers. In particular, using our new method, an open problem of computing the expected runtime of quantum random walks introduced by Ambainis et al. (STOC 2001) is solved.","PeriodicalId":373589,"journal":{"name":"Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134623237","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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