9,999 research outputs found

    Verification and Synthesis of Symmetric Uni-Rings for Leads-To Properties

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    This paper investigates the verification and synthesis of parameterized protocols that satisfy leadsto properties R⇝QR \leadsto Q on symmetric unidirectional rings (a.k.a. uni-rings) of deterministic and constant-space processes under no fairness and interleaving semantics, where RR and QQ are global state predicates. First, we show that verifying R⇝QR \leadsto Q for parameterized protocols on symmetric uni-rings is undecidable, even for deterministic and constant-space processes, and conjunctive state predicates. Then, we show that surprisingly synthesizing symmetric uni-ring protocols that satisfy R⇝QR \leadsto Q is actually decidable. We identify necessary and sufficient conditions for the decidability of synthesis based on which we devise a sound and complete polynomial-time algorithm that takes the predicates RR and QQ, and automatically generates a parameterized protocol that satisfies R⇝QR \leadsto Q for unbounded (but finite) ring sizes. Moreover, we present some decidability results for cases where leadsto is required from multiple distinct RR predicates to different QQ predicates. To demonstrate the practicality of our synthesis method, we synthesize some parameterized protocols, including agreement and parity protocols

    Beyond Reuse Distance Analysis: Dynamic Analysis for Characterization of Data Locality Potential

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    Emerging computer architectures will feature drastically decreased flops/byte (ratio of peak processing rate to memory bandwidth) as highlighted by recent studies on Exascale architectural trends. Further, flops are getting cheaper while the energy cost of data movement is increasingly dominant. The understanding and characterization of data locality properties of computations is critical in order to guide efforts to enhance data locality. Reuse distance analysis of memory address traces is a valuable tool to perform data locality characterization of programs. A single reuse distance analysis can be used to estimate the number of cache misses in a fully associative LRU cache of any size, thereby providing estimates on the minimum bandwidth requirements at different levels of the memory hierarchy to avoid being bandwidth bound. However, such an analysis only holds for the particular execution order that produced the trace. It cannot estimate potential improvement in data locality through dependence preserving transformations that change the execution schedule of the operations in the computation. In this article, we develop a novel dynamic analysis approach to characterize the inherent locality properties of a computation and thereby assess the potential for data locality enhancement via dependence preserving transformations. The execution trace of a code is analyzed to extract a computational directed acyclic graph (CDAG) of the data dependences. The CDAG is then partitioned into convex subsets, and the convex partitioning is used to reorder the operations in the execution trace to enhance data locality. The approach enables us to go beyond reuse distance analysis of a single specific order of execution of the operations of a computation in characterization of its data locality properties. It can serve a valuable role in identifying promising code regions for manual transformation, as well as assessing the effectiveness of compiler transformations for data locality enhancement. We demonstrate the effectiveness of the approach using a number of benchmarks, including case studies where the potential shown by the analysis is exploited to achieve lower data movement costs and better performance.Comment: Transaction on Architecture and Code Optimization (2014

    Generalised Compositional Theories and Diagrammatic Reasoning

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    This chapter provides an introduction to the use of diagrammatic language, or perhaps more accurately, diagrammatic calculus, in quantum information and quantum foundations. We illustrate the use of diagrammatic calculus in one particular case, namely the study of complementarity and non-locality, two fundamental concepts of quantum theory whose relationship we explore in later part of this chapter. The diagrammatic calculus that we are concerned with here is not merely an illustrative tool, but it has both (i) a conceptual physical backbone, which allows it to act as a foundation for diverse physical theories, and (ii) a genuine mathematical underpinning, permitting one to relate it to standard mathematical structures.Comment: To appear as a Springer book chapter chapter, edited by G. Chirabella, R. Spekken

    The ZX-calculus is complete for stabilizer quantum mechanics

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    The ZX-calculus is a graphical calculus for reasoning about quantum systems and processes. It is known to be universal for pure state qubit quantum mechanics, meaning any pure state, unitary operation and post-selected pure projective measurement can be expressed in the ZX-calculus. The calculus is also sound, i.e. any equality that can be derived graphically can also be derived using matrix mechanics. Here, we show that the ZX-calculus is complete for pure qubit stabilizer quantum mechanics, meaning any equality that can be derived using matrices can also be derived pictorially. The proof relies on bringing diagrams into a normal form based on graph states and local Clifford operations.Comment: 26 page

    Improving Usability of Interactive Graphics Specification and Implementation with Picking Views and Inverse Transformations

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    Specifying and programming graphical interactions are difficult tasks, notably because designers have difficulties to express the dynamics of the interaction. This paper shows how the MDPC architecture improves the usability of the specification and the implementation of graphical interaction. The architecture is based on the use of picking views and inverse transforms from the graphics to the data. With three examples of graphical interaction, we show how to express them with the architecture, how to implement them, and how this improves programming usability. Moreover, we show that it enables implementing graphical interaction without a scene graph. This kind of code prevents from errors due to cache consistency management

    Postcondition-preserving fusion of postorder tree transformations

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    Tree transformations are commonly used in applications such as program rewriting in compilers. Using a series of simple transformations to build a more complex system can make the resulting software easier to understand, maintain, and reason about. Fusion strategies for combining such successive tree transformations promote this modularity, whilst mitigating the performance impact from increased numbers of tree traversals. However, it is important to ensure that fused transformations still perform their intended tasks. Existing approaches to fusing tree transformations tend to take an informal approach to soundness, or be too restrictive to consider the kind of transformations needed in a compiler. We use postconditions to define a more useful formal notion of successful fusion, namely postcondition-preserving fusion. We also present criteria that are sufficient to ensure postcondition-preservation and facilitate modular reasoning about the success of fusion

    Depicting qudit quantum mechanics and mutually unbiased qudit theories

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    We generalize the ZX calculus to quantum systems of dimension higher than two. The resulting calculus is sound and universal for quantum mechanics. We define the notion of a mutually unbiased qudit theory and study two particular instances of these theories in detail: qudit stabilizer quantum mechanics and Spekkens-Schreiber toy theory for dits. The calculus allows us to analyze the structure of qudit stabilizer quantum mechanics and provides a geometrical picture of qudit stabilizer theory using D-toruses, which generalizes the Bloch sphere picture for qubit stabilizer quantum mechanics. We also use our framework to describe generalizations of Spekkens toy theory to higher dimensional systems. This gives a novel proof that qudit stabilizer quantum mechanics and Spekkens-Schreiber toy theory for dits are operationally equivalent in three dimensions. The qudit pictorial calculus is a useful tool to study quantum foundations, understand the relationship between qubit and qudit quantum mechanics, and provide a novel, high level description of quantum information protocols.Comment: In Proceedings QPL 2014, arXiv:1412.810
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