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检索条件"任意字段=Proceedings of the 34th Annual ACM/IEEE Symposium on Logic in Computer Science"

共 360 条记录，以下是91-100 订阅

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A Near-Minimal Axiomatisation of ZX-Calculus for Pure Qubit Quantum Mechanics 34

A Near-Minimal Axiomatisation of ZX-Calculus for Pure Qubit ...

引用

34th annual acm/ieee symposium on logic in computer science (LICS)

作者： Vilmart, Renaud Univ Lorraine INRIA CNRS LORIA F-54000 Nancy France

ISBN: (纸本)9781728136080

Recent developments in the ZX-Calculus have resulted in complete axiomatisations first for an approximately universal restriction of the language, and then for the whole language. the main drawbacks were that the axioms that were added to achieve completeness were numerous, tedious to manipulate and lacking a physical interpretation. We present in this paper two complete axiomatisations for the general ZX-Calculus, that we believe are optimal, in that all their equations are necessary and moreover have a nice physical interpretation. To do so, we introduce the singular-value decomposition of a ZX-diagram, and use it to show that all the rules of the former axiomatisation are provable with the new one.

关键词： Standards Qubit Quantum mechanics Calculus Transforms logic gates

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Quantum Hoare logic with Ghost Variables 34

Quantum Hoare Logic with Ghost Variables

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34th annual acm/ieee symposium on logic in computer science (LICS)

作者： Unruh, Dominique Univ Tartu Tartu Estonia

ISBN: (纸本)9781728136080

Quantum Hoare logic allows us to reason about quantum programs. We present an extension of quantum Hoare logic that introduces "ghost variables" to extend the expressive power of pre-/postconditions. Ghost variables are variables that do not actually occur in the program and are allowed to have arbitrary quantum states (in a sense, they are existentially quantified), and be entangled with program variables. Ghost variables allow us to express properties such as the distribution of a program variable or the fact that a variable has classical content. And as a case study, we show how quantum Hoare logic with ghost variables can be used to prove the security of the quantum one-time pad.

关键词： Quantum entanglement Quantum computing Probabilistic logic computers Cryptography Semantics

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No-Go theorems for Distributive Laws 34

No-Go Theorems for Distributive Laws

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34th annual acm/ieee symposium on logic in computer science (LICS)

作者： Zwart, Maaike Marsden, Dan Univ Oxford Oxford England

ISBN: (纸本)9781728136080

Monads are commonplace in computer science, and can be composed using Beck's distributive laws. Unfortunately, finding distributive laws can be extremely difficult and error-prone. the literature contains some principles for constructing distributive laws. However, until now there have been no general techniques for establishing when no such law exists. We present two families of theorems for showing when there can be no distributive law for two monads. the first widely generalizes a counterexample attributed to Plotkin. It covers all the previous known no-go results for specific pairs of monads, and includes many new results. the second family is entirely novel, encompassing various new practical situations. For example, it negatively resolves the open question of whether the list monad distributes over itself, and also reveals a previously unobserved error in the literature.

关键词： Mathematical model Probability distribution computer science Standards Algebra Tools Semantics

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Timed systems through the lens of logic 19

Timed systems through the lens of logic

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proceedings of the 34th annual acm/ieee symposium on logic in computer science

作者： S. Akshay Paul Gastin Vincent Jugé Shankara Narayanan Krishna IIT Bombay Université Paris-Saclay Université Paris-Est Marne-la-Vallée

In this paper, we analyze timed systems with data structures. We start by describing behaviors of timed systems using graphs with timing constraints. Such a graph is called realizable if we can assign time-stamps to nodes or events so that they are consistent with the timing constraints. the logical definability of several graph properties [20], [10] has been a challenging problem, and we show, using a highly non-trivial argument, that the realizability property for collections of graphs with strict timing constraints is logically definable in a class of propositional dynamic logic (EQ-ICPDL), which is strictly contained in MSO. Using this result, we propose a novel, algorithmically efficient and uniform proof technique for the analysis of timed systems enriched with auxiliary data structures, like stacks and queues. Our technique unravels new results (for emptiness checking as well as model checking) for timed systems with richer features than considered so far, while also recovering existing results.

关键词： timed systems propositional dynamic logic logical definability efficient algorithms graphs

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Matching μ-logic 34

Matching μ-Logic

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34th annual acm/ieee symposium on logic in computer science (LICS)

作者： Chen, Xiaohong Rosu, Grigore Univ Illinois Dept Comp Sci Urbana IL 61801 USA

ISBN: (纸本)9781728136080

Matching logic is a logic for specifying and reasoning about structure by means of patterns and pattern matching. this paper makes two contributions. First, it proposes a sound and complete proof system for matching logic in its full generality. Previously, sound and complete deduction for matching logic was known only for particular theories providing equality and membership. Second, it proposes matching mu-logic, an extension of matching logic with a least fixpoint mu-binder. It is shown that matching mu-logic captures as special instances many important logics in mathematics and computer science, including first-order logic with least fixpoints, modal mu-logic as well as dynamic logic and various temporal logics such as infinite/finite-trace linear temporal logic and computation tree logic, and notably reachability logic, the underlying logic of the K framework for programming language semantics and formal analysis. Matching mu-logic therefore serves as a unifying foundation for specifying and reasoning about fixpoints and induction, programming languages and program specification and verification.

关键词： Pattern matching Semantics Syntactics Cognition computer languages Standards

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Type-Based Complexity Analysis of Probabilistic Functional Programs 34

Type-Based Complexity Analysis of Probabilistic Functional P...

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34th annual acm/ieee symposium on logic in computer science (LICS)

作者： Avanzini, Martin Dal Lago, Ugo Ghyselen, Alexis INRIA Sophia Antipolis Valbonne France Univ Bologna Bologna Italy Univ Lyon EnsL UCBL CNRSLIP Lyon France

ISBN: (纸本)9781728136080

We show that complexity analysis of probabilistic higher-order functional programs can be carried out compositionally by way of a type system. the introduced type system is a significant extension of refinement types. On the one hand, the presence of probabilistic effects requires adopting a form of dynamic distribution type, subject to a coupling-based subtyping discipline. On the other hand, recursive definitions are proved terminating by way of Lyapunov ranking functions. We prove not only that the obtained type system, called lRPCF, provides a sound methodology for average case complexity analysis, but also that it is extensionally complete, in the sense that any average case polytime Turing machines can be encoded as a term typable in lRPCF.

关键词： Complexity theory Probabilistic logic computer languages Indexes Testing Cognition Turing machines

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Quantum channels as a categorical completion 34

Quantum channels as a categorical completion

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34th annual acm/ieee symposium on logic in computer science (LICS)

作者： Huot, Mathieu Staton, Sam Univ Oxford Oxford England

ISBN: (纸本)9781728136080

We propose a categorical foundation for the connection between pure and mixed states in quantum information and quantum computation. the foundation is based on distributive monoidal categories. First, we prove that the category of all quantum channels is a canonical completion of the category of pure quantum operations (with ancilla preparations). More precisely, we prove that the category of completely positive trace-preserving maps between finite-dimensional C*-algebras is a canonical completion of the category of finite-dimensional vector spaces and isometries. Second, we extend our result to give a foundation to the topological relationships between quantum channels. We do this by generalizing our categorical foundation to the topologically-enriched setting. In particular, we show that the operator norm topology on quantum channels is the canonical topology induced by the norm topology on isometries.

关键词： Quantum mechanics Topology logic gates Qubit Matrices Calculus

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the theory of Traces for Systems with Nondeterminism and Probability 34

The Theory of Traces for Systems with Nondeterminism and Pro...

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34th annual acm/ieee symposium on logic in computer science (LICS)

作者： Bonchi, Filippo Sokolova, Ana Vignudelli, Valeria Univ Pisa Pisa Italy Univ Salzburg Salzburg Austria Univ Lyon CNRS ENS Lyon UCB Lyon 1LIP Lyon France

ISBN: (纸本)9781728136080

this paper studies trace-based equivalences for systems combining nondeterministic and probabilistic choices. We show how trace semantics for such processes can be recovered by instantiating a coalgebraic construction known as the generalised powerset construction. We characterise and compare the resulting semantics to known definitions of trace equivalences appearing in the literature. Most of our results are based on the exciting interplay between monads and their presentations via algebraic theories.

关键词： Semantics Probabilistic logic Algebra Automata Standards Artificial intelligence Europe

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Walk refinement, walk logic, and the iteration number of the Weisfeiler-Leman algorithm 34

Walk refinement, walk logic, and the iteration number of the...

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34th annual acm/ieee symposium on logic in computer science (LICS)

作者： Lichter, Moritz Ponomarenko, Ilia Schweitzer, Pascal TU Kaiserslautern Kaiserslautern Germany Russian Acad Sci St Petersburg Dept Steklov Math Inst Moscow Russia

ISBN: (纸本)9781728136080

We show that the 2-dimensional Weisfeiler-Leman algorithm stabilizes n-vertex graphs after at most O(n log n) iterations. this implies that if such graphs are distinguishable in 3-variable first order logic with counting, then they can also be distinguished in this logic by a formula of quantifier depth at most O(n log n). For this we exploit a new refinement based on counting walks and argue that its iteration number differs from the classic Weisfeiler-Leman refinement by at most a logarithmic factor. We then prove matching linear upper and lower bounds on the number of iterations of the walk refinement. this is achieved with an algebraic approach by exploiting properties of semisimple matrix algebras. We also define a walk logic and a bijective walk pebble game that precisely correspond to the new walk refinement.

关键词： first order logic counting quantifiers quantifier depth Weisfeiler-Leman algorithm

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HoCHC: A Refutationally Complete and Semantically Invariant System of Higher-order logic Modulo theories 34

HoCHC: A Refutationally Complete and Semantically Invariant ...

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34th annual acm/ieee symposium on logic in computer science (LICS)

作者： Ong, C-H Luke Wagner, Dominik Univ Oxford Oxford England

ISBN: (纸本)9781728136080

We present a simple resolution proof system for higher-order constrained Horn clauses (HoCHC)-a system of higher-order logic modulo theories-and prove its soundness and refutational completeness w.r.t. both standard and Henkin semantics. As corollaries, we obtain the compactness theorem and semi-decidability of HoCHC for semi-decidable background theories, and we prove that HoCHC satisfies a canonical model property. Moreover a variant of the well-known translation from higher-order to 1st-order logic is shown to be sound and complete for HoCHC in both semantics. We illustrate how to transfer decidability results for (fragments of) 1st-order logic modulo theories to our higher-order setting, using as example the Bernays-Schonfinkel-Ramsey fragment of HoCHC modulo a restricted form of Linear Integer Arithmetic.

关键词： Semantics Standards Cost accounting Syntactics Adaptation models Safety Model checking

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