Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science最新文献_第2页

A Theory of Register Monitors 寄存器监视器理论

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-07-09 DOI: 10.1145/3209108.3209194

Thomas Ferrère, T. Henzinger, N. Saraç

{"title":"A Theory of Register Monitors","authors":"Thomas Ferrère, T. Henzinger, N. Saraç","doi":"10.1145/3209108.3209194","DOIUrl":"https://doi.org/10.1145/3209108.3209194","url":null,"abstract":"The task of a monitor is to watch, at run-time, the execution of a reactive system, and signal the occurrence of a safety violation in the observed sequence of events. While finite-state monitors have been studied extensively, in practice, monitoring software also makes use of unbounded memory. We define a model of automata equipped with integer-valued registers which can execute only a bounded number of instructions between consecutive events, and thus can form the theoretical basis for the study of infinite-state monitors. We classify these register monitors according to the number k of available registers, and the type of register instructions. In stark contrast to the theory of computability for register machines, we prove that for every k ≥ 1, monitors with k + 1 counters (with instruction set ⟨+1, =⟩) are strictly more expressive than monitors with k counters. We also show that adder monitors (with instruction set ⟨1, +, =⟩) are strictly more expressive than counter monitors, but are complete for monitoring all computable safety ω-languages for k = 6. Real-time monitors are further required to signal the occurrence of a safety violation as soon as it occurs. The expressiveness hierarchy for counter monitors carries over to real-time monitors. We then show that 2 adders cannot simulate 3 counters in real-time. Finally, we show that real-time adder monitors with inequalities are as expressive as real-time Turing machines.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"97 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122344194","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: 12

On computability and tractability for infinite sets 关于无穷集的可计算性和可跟踪性

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-07-09 DOI: 10.1145/3209108.3209190

M. Bojanczyk, Szymon Toruńczyk

引用次数: 5

A Logical Account for Linear Partial Differential Equations 线性偏微分方程的逻辑解释

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-07-09 DOI: 10.1145/3209108.3209192

M. Kerjean

{"title":"A Logical Account for Linear Partial Differential Equations","authors":"M. Kerjean","doi":"10.1145/3209108.3209192","DOIUrl":"https://doi.org/10.1145/3209108.3209192","url":null,"abstract":"Differential Linear Logic (DiLL), introduced by Ehrhard and Regnier, extends linear logic with a notion of linear approximation of proofs. While DiLL is classical logic, i.e. has an involutive negation, classical denotational models of it in which this notion of differentiation corresponds to the usual one, defined on any smooth function, were missing. We solve this issue by constructing a model of it based on nuclear topological vector spaces and distributions with compact support. This interpretation sheds a new light on the rules of DiLL, as we are able to understand them as the computational principles for the resolution of Linear Partial Differential Equations. We thus introduce D-DiLL, a deterministic refinement of DiLL with a D-exponential, for which we exhibit a cut-elimination procedure, and a categorical semantics. When D is a Linear Partial Differential Operator with constant coefficients, then the D-exponential is interpreted as the space of generalised functions ψ solutions to Dψ = φ. The logical inference rules represents the computational steps for the construction of the solution φ. We recover linear logic and its differential extension DiLL particular case.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127028565","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

Two complete axiomatisations of pure-state qubit quantum computing 纯态量子比特量子计算的两个完全公理化

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-07-09 DOI: 10.1145/3209108.3209128

Amar Hadzihasanovic, K. Ng, Quanlong Wang

{"title":"Two complete axiomatisations of pure-state qubit quantum computing","authors":"Amar Hadzihasanovic, K. Ng, Quanlong Wang","doi":"10.1145/3209108.3209128","DOIUrl":"https://doi.org/10.1145/3209108.3209128","url":null,"abstract":"Categorical quantum mechanics places finite-dimensional quantum theory in the context of compact closed categories, with an emphasis on diagrammatic reasoning. In this framework, two equational diagrammatic calculi have been proposed for pure-state qubit quantum computing: the ZW calculus, developed by Coecke, Kissinger and the first author for the purpose of qubit entanglement classification, and the ZX calculus, introduced by Coecke and Duncan to give an abstract description of complementary observables. Neither calculus, however, provided a complete axiomatisation of their model. In this paper, we present extended versions of ZW and ZX, and show their completeness for pure-state qubit theory, thus solving two major open problems in categorical quantum mechanics. First, we extend the original ZW calculus to represent states and linear maps with coefficients in an arbitrary commutative ring, and prove completeness by a strategy that rewrites all diagrams into a normal form. We then extend the language and axioms of the original ZX calculus, and show their completeness for pure-state qubit theory through a translation between ZX and ZW specialised to the field of complex numbers. This translation expands the one used by Jeandel, Perdrix, and Vilmart to derive an axiomatisation of the approximately universal Clifford+T fragment; restricting the field of complex numbers to a suitable subring, we obtain an alternative axiomatisation of the same theory.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127050012","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: 81

A Simple and Optimal Complementation Algorithm for Büchi Automata <s:1> chi自动机的一种简单最优补算法

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-07-09 DOI: 10.1145/3209108.3209138

Joël Allred, U. Ultes-Nitsche

引用次数: 14

Probabilistic Böhm Trees and Probabilistic Separation 概率Böhm树和概率分离

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-07-09 DOI: 10.1145/3209108.3209126

Thomas Leventis

引用次数: 13

An Algebraic Theory of Markov Processes 马尔可夫过程的代数理论

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-07-09 DOI: 10.1145/3209108.3209177

G. Bacci, R. Mardare, P. Panangaden, G. Plotkin

引用次数: 22

Extensional and Intensional Semantic Universes: A Denotational Model of Dependent Types 外延和内延语义世界:依赖类型的指称模型

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-07-09 DOI: 10.1145/3209108.3209206

Valentin Blot, J. Laird

{"title":"Extensional and Intensional Semantic Universes: A Denotational Model of Dependent Types","authors":"Valentin Blot, J. Laird","doi":"10.1145/3209108.3209206","DOIUrl":"https://doi.org/10.1145/3209108.3209206","url":null,"abstract":"We describe a dependent type theory, and a denotational model for it, that incorporates both intensional and extensional semantic universes. In the former, terms and types are interpreted as strategies on certain graph games, which are concrete data structures of a generalized form, and in the latter as stable functions on event domains. The concrete data structures themselves form an event domain, with which we may interpret an (extensional) universe type of (intensional) types. A dependent game corresponds to a stable function into this domain; we use its trace to define dependent product and sum constructions as it captures precisely how unfolding moves combine with the dependency to shape the possible interaction in the game. Since each strategy computes a stable function on CDS states, we can lift typing judgements from the intensional to the extensional setting, giving an expressive type theory with recursively defined type families and type operators. We define an operational semantics for intensional terms, giving a functional programming language based on our type theory, and prove that our semantics for it is computationally adequate. By extending it with a simple non-local control operator on intensional terms, we can precisely characterize behaviour in the intensional model. We demonstrate this by proving full abstraction and full completeness results.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125258736","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

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-07-09 DOI: 10.1145/3209108.3209119

Andreas Nuyts, Dominique Devriese

{"title":"Degrees of Relatedness: A Unified Framework for Parametricity, Irrelevance, Ad Hoc Polymorphism, Intersections, Unions and Algebra in Dependent Type Theory","authors":"Andreas Nuyts, Dominique Devriese","doi":"10.1145/3209108.3209119","DOIUrl":"https://doi.org/10.1145/3209108.3209119","url":null,"abstract":"Dependent type theory allows us to write programs and to prove properties about those programs in the same language. However, some properties do not require much proof, as they are evident from a program's implementation, e.g. if a polymorphic program is not ad hoc but relationally parametric, then we get parametricity theorems for free. If we want to safely shortcut proofs by relying on the evident good behaviour of a program, then we need a type-level guarantee that the program is indeed well-behaved. This can be achieved by annotating function types with a modality describing the behaviour of functions. We consider a dependent type system with modalities for relational parametricity, irrelevance (i.e. type-checking time erasability of an argument) and ad hoc polymorphism. The interplay of three modalities and dependent types raises a number of questions. For example: If a term depends on a variable with a given modality, then how should its type depend on it? Are all modalities always applicable, e.g. should we consider parametric functions from the booleans to the naturals? Do we need any further modalities in order to properly reason about these three? We develop a type system, based on a denotational presheaf model, that answers these questions. The core idea is to equip every type with a number of relations --- just equality for small types, but more for larger types --- and to describe function behaviour by saying how functions act on those relations. The system has modality-aware equality judgements (ignoring irrelevant parts) and modality-aware proving operators (for proving free theorems) which are even self-applicable. It also supports sized types, some form of intersection and union types, and parametric quantification over algebraic structures. We prove soundness in a denotational presheaf model.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122196413","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: 28

Syntax and Semantics for Operations with Scopes 具有作用域的操作的语法和语义

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-07-09 DOI: 10.1145/3209108.3209166

Maciej Piróg, T. Schrijvers, Nicolas Wu, Mauro Jaskelioff

{"title":"Syntax and Semantics for Operations with Scopes","authors":"Maciej Piróg, T. Schrijvers, Nicolas Wu, Mauro Jaskelioff","doi":"10.1145/3209108.3209166","DOIUrl":"https://doi.org/10.1145/3209108.3209166","url":null,"abstract":"Motivated by the problem of separating syntax from semantics in programming with algebraic effects and handlers, we propose a categorical model of abstract syntax with so-called scoped operations. As a building block of a term, a scoped operation is not merely a node in a tree, as it can also encompass a whole part of the term (a scope). Some examples from the area of programming are given by the operation catch for handling exceptions, in which the part in the scope is the code that may raise an exception, or the operation once, which selects a single solution from a nondeterministic computation. A distinctive feature of such operations is their behaviour under program composition, that is, syntactic substitution. Our model is based on what Ghani et al. call the monad of explicit substitutions, defined using the initial-algebra semantics in the category of endofunctors. We also introduce a new kind of multi-sorted algebras, called scoped algebras, which serve as interpretations of syntax with scopes. In generality, scoped algebras are given in the style of the presheaf formalisation of syntax with binders of Fiore et al. As the main technical result, we show that our monad indeed arises from free objects in the category of scoped algebras. Importantly, we show that our results are immediately applicable. In particular, we show a Haskell implementation together with practical, real-life examples.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"40 9","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120907305","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: 21