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

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A Quantum Interpretation of Bunched Logic & Quantum Separation Logic 聚束逻辑的量子解释&量子分离逻辑
2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2021-01-30 DOI: 10.1109/LICS52264.2021.9470673
Li Zhou, G. Barthe, Justin Hsu, M. Ying, Nengkun Yu
{"title":"A Quantum Interpretation of Bunched Logic & Quantum Separation Logic","authors":"Li Zhou, G. Barthe, Justin Hsu, M. Ying, Nengkun Yu","doi":"10.1109/LICS52264.2021.9470673","DOIUrl":"https://doi.org/10.1109/LICS52264.2021.9470673","url":null,"abstract":"We propose a model of the substructural logic of Bunched Implications (BI) that is suitable for reasoning about quantum states. In our model, the separating conjunction of BI describes separable quantum states. We develop a program logic where pre- and post-conditions are BI formulas describing quantum states—the program logic can be seen as a counterpart of separation logic for imperative quantum programs. We exercise the logic for proving the security of quantum one-time pad and secret sharing, and we show how the program logic can be used to discover a flaw in Google Cirq’s tutorial on the Variational Quantum Algorithm (VQA).","PeriodicalId":174663,"journal":{"name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130554326","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
Continuous One-Counter Automata 连续单计数器自动机
2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2021-01-28 DOI: 10.1109/LICS52264.2021.9470525
Michael Blondin, Tim Leys, Filip Mazowiecki, Philip Offtermatt, G. Pérez
{"title":"Continuous One-Counter Automata","authors":"Michael Blondin, Tim Leys, Filip Mazowiecki, Philip Offtermatt, G. Pérez","doi":"10.1109/LICS52264.2021.9470525","DOIUrl":"https://doi.org/10.1109/LICS52264.2021.9470525","url":null,"abstract":"We study the reachability problem for continuous one-counter automata, COCA for short. In such automata, transitions are guarded by upper and lower bound tests against the counter value. Additionally, the counter updates associated with taking transitions can be (non-deterministically) scaled down by a nonzero factor between zero and one. Our three main results are as follows: (1) We prove that the reachability problem for COCA with global upper and lower bound tests is in NC2; (2) that, in general, the problem is decidable in polynomial time; and (3) that it is decidable in the polynomial hierarchy for COCA with parametric counter updates and bound tests.","PeriodicalId":174663,"journal":{"name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"116 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128035833","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: 1
Alignment Completeness for Relational Hoare Logics 关系Hoare逻辑的对齐完整性
2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2021-01-28 DOI: 10.1109/LICS52264.2021.9470690
Ramana Nagasamudram, D. Naumann
{"title":"Alignment Completeness for Relational Hoare Logics","authors":"Ramana Nagasamudram, D. Naumann","doi":"10.1109/LICS52264.2021.9470690","DOIUrl":"https://doi.org/10.1109/LICS52264.2021.9470690","url":null,"abstract":"Relational Hoare logics (RHL) provide rules for reasoning about relations between programs. Several RHLs include a rule we call sequential product that infers a relational correctness judgment from judgments of ordinary Hoare logic (HL). Other rules embody sensible patterns of reasoning and have been found useful in practice, but sequential product is relatively complete on its own (with HL). As a more satisfactory way to evaluate RHLs, a notion of alignment completeness is introduced, in terms of the inductive assertion method and product automata. Alignment completeness results are given to account for several different sets of rules. The notion may serve to guide the design of RHLs and relational verifiers for richer programming languages and alignment patterns.","PeriodicalId":174663,"journal":{"name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"122 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128032696","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: 4
Normalization for Cubical Type Theory 三次型理论的规范化
2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2021-01-27 DOI: 10.1109/LICS52264.2021.9470719
Jonathan Sterling, C. Angiuli
{"title":"Normalization for Cubical Type Theory","authors":"Jonathan Sterling, C. Angiuli","doi":"10.1109/LICS52264.2021.9470719","DOIUrl":"https://doi.org/10.1109/LICS52264.2021.9470719","url":null,"abstract":"We prove normalization for (univalent, Cartesian) cubical type theory, closing the last major open problem in the syntactic metatheory of cubical type theory. Our normalization result is reduction-free, in the sense of yielding a bijection between equivalence classes of terms in context and a tractable language of β/η-normal forms. As corollaries we obtain both decidability of judgmental equality and the injectivity of type constructors.","PeriodicalId":174663,"journal":{"name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116606820","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: 33
Compositional Semantics for Probabilistic Programs with Exact Conditioning 具有精确条件的概率规划的组合语义
2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2021-01-27 DOI: 10.1109/LICS52264.2021.9470552
Dario Stein, S. Staton
{"title":"Compositional Semantics for Probabilistic Programs with Exact Conditioning","authors":"Dario Stein, S. Staton","doi":"10.1109/LICS52264.2021.9470552","DOIUrl":"https://doi.org/10.1109/LICS52264.2021.9470552","url":null,"abstract":"We define a probabilistic programming language for Gaussian random variables with a first-class exact conditioning construct. We give operational, denotational and equational semantics for this language, establishing convenient properties like exchangeability of conditions. Conditioning on equality of continuous random variables is nontrivial, as the exact observation may have probability zero; this is Borel’s paradox. Using categorical formulations of conditional probability, we show that the good properties of our language are not particular to Gaussians, but can be derived from universal properties, thus generalizing to wider settings. We define the Cond construction, which internalizes conditioning as a morphism, providing general compositional semantics for probabilistic programming with exact conditioning.","PeriodicalId":174663,"journal":{"name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122296103","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: 18
The Smash Product of Monoidal Theories 单一性理论的粉碎产物
2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2021-01-25 DOI: 10.1109/LICS52264.2021.9470575
Amar Hadzihasanovic
{"title":"The Smash Product of Monoidal Theories","authors":"Amar Hadzihasanovic","doi":"10.1109/LICS52264.2021.9470575","DOIUrl":"https://doi.org/10.1109/LICS52264.2021.9470575","url":null,"abstract":"The tensor product of props was defined by Hackney and Robertson as an extension of the Boardman–Vogt product of operads to more general monoidal theories. Theories that factor as tensor products include the theory of commutative monoids and the theory of bialgebras. We give a topological interpretation (and vast generalisation) of this construction as a low-dimensional projection of a \"smash product of pointed directed spaces\". Here directed spaces are embodied by combinatorial structures called diagrammatic sets, while Gray products replace cartesian products. The correspondence is mediated by a web of adjunctions relating diagrammatic sets, pros, probs, props, and Gray-categories. The smash product applies to presentations of higher-dimensional theories and systematically produces higher-dimensional coherence data.","PeriodicalId":174663,"journal":{"name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126430715","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: 4
Finite Model Theory of the Triguarded Fragment and Related Logics 三角片段的有限模型理论及相关逻辑
2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2021-01-21 DOI: 10.1109/LICS52264.2021.9470734
Emanuel Kiero'nski, S. Rudolph
{"title":"Finite Model Theory of the Triguarded Fragment and Related Logics","authors":"Emanuel Kiero'nski, S. Rudolph","doi":"10.1109/LICS52264.2021.9470734","DOIUrl":"https://doi.org/10.1109/LICS52264.2021.9470734","url":null,"abstract":"The Triguarded Fragment (TGF) is among the most expressive decidable fragments of first-order logic, subsuming both its two-variable and guarded fragments without equality. We show that the TGF has the finite model property (providing a tight doubly exponential bound on the model size) and hence finite satisfiability coincides with satisfiability known to be N2ExpTime-complete. Using similar constructions, we also establish 2ExpTime-completeness for finite satisfiability of the constant-free (tri)guarded fragment with transitive guards.","PeriodicalId":174663,"journal":{"name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123386346","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: 7
SD-Regular Transducer Expressions for Aperiodic Transformations 非周期变换的sd -正则换能器表达式
2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2021-01-18 DOI: 10.1109/LICS52264.2021.9470738
L. Dartois, P. Gastin, S. Krishna
{"title":"SD-Regular Transducer Expressions for Aperiodic Transformations","authors":"L. Dartois, P. Gastin, S. Krishna","doi":"10.1109/LICS52264.2021.9470738","DOIUrl":"https://doi.org/10.1109/LICS52264.2021.9470738","url":null,"abstract":"FO transductions, aperiodic deterministic two-way transducers, as well as aperiodic streaming string transducers are all equivalent models for first order definable functions. In this paper, we solve the problem of expressions capturing first order definable functions, thereby generalizing the seminal SF=AP (star-free expressions = aperiodic languages) result of Schützenberger. Our result also generalizes a lesser known characterization by Schutzenberger of aperiodic languages by SD-regular expressions (SD=AP). We show that every first order definable function over finite words captured by an aperiodic deterministic two-way transducer can be described with an SD-regular transducer expression (SDRTE). An SDRTE is a regular expression where Kleene stars are used in a restricted way: they can appear only on aperiodic languages which are prefix codes of bounded synchronization delay. SDRTEs are constructed from simple functions using the combinators unambiguous sum (deterministic choice), Hadamard product, and unambiguous versions of the Cauchy product and the fc-chained Kleene-star, where the star is restricted as mentioned. In order to construct an SDRTE associated with an aperiodic deterministic two-way transducer, (i) we concretize Schutzenberger’s SD=AP result, by proving that aperiodic languages are captured by SD-regular expressions which are unambiguous and stabilising; (ii) by structural induction on the unambiguous, stabilising SD-regular expressions describing the domain of the transducer, we construct SDRTEs. Finally, we also look at various formalisms equivalent to SDRTEs which use the function composition, allowing to trade the fc-chained star for a 1-star.","PeriodicalId":174663,"journal":{"name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133131882","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: 4
Categories of Nets 网的分类
2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2021-01-11 DOI: 10.1109/LICS52264.2021.9470566
J. Baez, F. Genovese, J. Master, Michael Shulman
{"title":"Categories of Nets","authors":"J. Baez, F. Genovese, J. Master, Michael Shulman","doi":"10.1109/LICS52264.2021.9470566","DOIUrl":"https://doi.org/10.1109/LICS52264.2021.9470566","url":null,"abstract":"We present a unified framework for Petri nets and various variants, such as pre-nets and Kock’s whole-grain Petri nets. Our framework is based on a less well-studied notion that we call Σ-nets, which allow fine-grained control over whether each transition behaves according to the collective or individual token philosophy. We describe three forms of execution semantics in which pre-nets generate strict monoidal categories, Σ-nets (including whole-grain Petri nets) generate symmetric strict monoidal categories, and Petri nets generate commutative monoidal categories, all by left adjoint functors. We also construct adjunctions relating these categories of nets to each other, in particular showing that all kinds of net can be embedded in the unifying category of Σ-nets, in a way that commutes coherently with their execution semantics.","PeriodicalId":174663,"journal":{"name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125582000","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: 15
Positive First-order Logic on Words 词的正一阶逻辑
2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2021-01-06 DOI: 10.1109/LICS52264.2021.9470602
Denis Kuperberg
{"title":"Positive First-order Logic on Words","authors":"Denis Kuperberg","doi":"10.1109/LICS52264.2021.9470602","DOIUrl":"https://doi.org/10.1109/LICS52264.2021.9470602","url":null,"abstract":"We study FO+, a fragment of first-order logic on finite words, where monadic predicates can only appear positively. We show that there is an FO-definable language that is monotone in monadic predicates but not definable in FO+. This provides a simple proof that Lyndon’s preservation theorem fails on finite structures. We additionally show that given a regular language, it is undecidable whether it is definable in FO+.","PeriodicalId":174663,"journal":{"name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114498288","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: 4
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