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2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)最新文献

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Smart Choices and the Selection Monad 智能选择和选择单子
2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2020-07-17 DOI: 10.1109/LICS52264.2021.9470641
M. Abadi, G. Plotkin
{"title":"Smart Choices and the Selection Monad","authors":"M. Abadi, G. Plotkin","doi":"10.1109/LICS52264.2021.9470641","DOIUrl":"https://doi.org/10.1109/LICS52264.2021.9470641","url":null,"abstract":"Describing systems in terms of choices and their resulting costs and rewards promises to free algorithm designers and programmers from specifying how to make those choices. In implementations, the choices can be realized by optimization or machine-learning methods.We study this approach from a programming-language perspective. We define a small language that supports decision-making abstraction, rewards, and probabilities. We give a globally optimizing operational semantics, and, using the selection monad for decision-making, three denotational semantics with auxiliary monads for reward and probability; the three model various correlations between returned values and expected rewards. We show the two kinds of semantics coincide by proving adequacy theorems; we show that observational equivalence is characterized by semantic equality (at basic types) by proving full abstraction theorems; and we discuss program equations.","PeriodicalId":174663,"journal":{"name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"10 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129217625","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: 3
Fusible numbers and Peano Arithmetic 易熔数和皮亚诺算术
2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2020-03-31 DOI: 10.1109/LICS52264.2021.9470703
Jeff Erickson, Gabriel Nivasch, Junyan Xu
{"title":"Fusible numbers and Peano Arithmetic","authors":"Jeff Erickson, Gabriel Nivasch, Junyan Xu","doi":"10.1109/LICS52264.2021.9470703","DOIUrl":"https://doi.org/10.1109/LICS52264.2021.9470703","url":null,"abstract":"Inspired by a mathematical riddle involving fuses, we define the fusible numbers as follows: 0 is fusible, and whenever x, y are fusible with |y − x| < 1, the number (x + y + 1)/2 is also fusible. We prove that the set of fusible numbers, ordered by the usual order on ℝ, is well-ordered, with order type ε0. Furthermore, we prove that the density of the fusible numbers along the real line grows at an incredibly fast rate: Letting g(n) be the largest gap between consecutive fusible numbers in the interval [n, ∞), we have $g{(n)^{ - 1}} geq {F_{{varepsilon _0}}}(n - c)$ for some constant c, where Fα denotes the fast-growing hierarchy.Finally, we derive some true statements that can be formulated but not proven in Peano Arithmetic, of a different flavor than previously known such statements: PA cannot prove the true statement \"For every natural number n there exists a smallest fusible number larger than n.\" Also, consider the algorithm \"M(x): if x < 0 return −x, else return M(x − M(x − 1))/2.\" Then M terminates on real inputs, although PA cannot prove the statement \"M terminates on all natural inputs.\"","PeriodicalId":174663,"journal":{"name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"196 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127774978","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
No-Rainbow Problem and the Surjective Constraint Satisfaction Problem 无彩虹问题与满射约束满足问题
2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2020-03-26 DOI: 10.1109/LICS52264.2021.9470632
Dmitriy Zhuk
{"title":"No-Rainbow Problem and the Surjective Constraint Satisfaction Problem","authors":"Dmitriy Zhuk","doi":"10.1109/LICS52264.2021.9470632","DOIUrl":"https://doi.org/10.1109/LICS52264.2021.9470632","url":null,"abstract":"The Surjective Constraint Satisfaction Problem (SCSP) is the problem of deciding whether there exists a surjective assignment to a set of variables subject to some specified constraints, where a surjective assignment is an assignment containing all elements of the domain. In this paper we show that the most famous SCSP, called No-Rainbow Problem, is NP-Hard. Additionally, we disprove the conjecture saying that the SCSP over a constraint language Γ and the CSP over the same language with constants have the same computational complexity up to poly-time reductions. Our counter-example also shows that the complexity of the SCSP cannot be described in terms of polymorphisms of the constraint language.","PeriodicalId":174663,"journal":{"name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130717973","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: 3
Intersection Type Distributors 交集型分配器
2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2020-02-04 DOI: 10.1109/LICS52264.2021.9470617
Federico Olimpieri
{"title":"Intersection Type Distributors","authors":"Federico Olimpieri","doi":"10.1109/LICS52264.2021.9470617","DOIUrl":"https://doi.org/10.1109/LICS52264.2021.9470617","url":null,"abstract":"We study a family of distributors-induced bicategorical models of λ-calculus, proving that they can be syntactically presented via intersection type systems. We first introduce a class of 2-monads whose algebras are monoidal categories modelling resource management. We lift these monads to distributors and define a parametric Kleisli bicategory, giving a sufficient condition for its cartesian closure. In this framework we define a proof-relevant semantics: the interpretation of a term associates to it the set of its typing derivations in appropriate systems. We prove that our model characterize solvability, adapting reducibility techniques to our setting. We conclude by describing two examples of our construction.","PeriodicalId":174663,"journal":{"name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127312875","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: 13
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