Quantitative multi-objective verification for probabilistic systems

We present a verification framework for analysing multiple quantitative objectives of systems that exhibit both nondeterministic and stochastic behaviour. These systems are modelled as probabilistic automata, enriched with cost or reward structures that capture, for example, energy usage or performance metrics. Quantitative properties of these models are expressed in a specification language that incorporates probabilistic safety and liveness properties, expected total cost or reward, and supports multiple objectives of these types. We propose and implement an efficient verification framework for such properties and then present two distinct applications of it: firstly, controller synthesis subject to multiple quantitative objectives; and, secondly, quantitative compositional verification. The practical applicability of both approaches is illustrated with experimental results from several large case studies

Entanglement consumption of instantaneous nonlocal quantum measurements

Relativistic causality has dramatic consequences on the measurability of nonlocal variables and poses the fundamental question of whether it is physically meaningful to speak about the value of nonlocal variables at a particular time. Recent work has shown that by weakening the role of the measurement in preparing eigenstates of the variable it is in fact possible to measure all nonlocal observables instantaneously by exploiting entanglement. However, for these measurement schemes to succeed with certainty an infinite amount of entanglement must be distributed initially and all this entanglement is necessarily consumed. In this work we sharpen the characterisation of instantaneous nonlocal measurements by explicitly devising schemes in which only a finite amount of the initially distributed entanglement is ever utilised. This enables us to determine an upper bound to the average consumption for the most general cases of nonlocal measurements. This includes the tasks of state verification, where the measurement verifies if the system is in a given state, and verification measurements of a general set of eigenstates of an observable. Despite its finiteness the growth of entanglement consumption is found to display an extremely unfavourable exponential of an exponential scaling with either the number of qubits needed to contain the Schmidt rank of the target state or total number of qubits in the system for an operator measurement. This scaling is seen to be a consequence of the combination of the generic exponential scaling of unitary decompositions combined with the highly recursive structure of our scheme required to overcome the no-signalling constraint of relativistic causality.Comment: 32 pages and 14 figures. Updated to published versio

Using Project Management Techniques to Design a PMP Mathematics Study App for the Windows Universal Platform

Background As a late comer to the smartphone market, Microsoft has fallen behind the Apple and Google app ecosystems in the quantity and quality of apps offered. To attract developer talent, Microsoft released the Universal Windows Platform which enables apps to run across Windows devices with few additional modifications. Although the Windows app ecosystem has realized an increased number of available apps, few apps related to project management are currently available. About the project This project will design a PMP Certification Mathematics Study App for the Universal Windows Platform which will serve as a reference and study aid for the PMP certification exam. The app will be available to mobile and PC users who are utilizing the Microsoft Windows 10 and Windows 8 operating systems. Features of the app will include project management formula lookup, formula flashcards, and practice problems. At the completion of the project, the app will be submitted to the Windows Store for review and publishing to the Windows 10 application ecosystem. Approach The project scope will include the design of the app from requirements gathering to completion. Project deliverables will be aligned with Windows store applications evaluation criteria for responsiveness, reliability, and style. This project will conclude with submission of a completed application design to the project sponsor.Title Page / Table of Contents / List of Exhibits / Abstract / Background / About the project / Approach / Keywords / Introduction / Project Purpose / Project Approach / Research and Analysis / Research Approach / Research Analysis / Application Design Rating Verification / Research Objective 1: Investigate the preferred learning style of potential users / Research Objective 1: Design Conclusions and Implications / Flashcards Module / Formula Builder Module / Formula Reference Module / Research Objective 2: Investigate the most important aspect of user satisfaction / Research Objective 2: Design Conclusions and Implications / Research Conclusions / Requirements Gathering / User Interface Design / Project Deliverable Design / ViTech CORE / Input Application Requirements / Identify Application Components / Identify Component Functions / Identify Use Cases and Test Activities / Project Deliverables / Application Design Documents / Application Hierarchy / Conclusions and Recommendations / ViTech CORE Software Con/ lusions / Graphing Capabilities / Diagnostics Capabilities / Requirements Mapping and Verification / Final Project Deliverables / Recommendations for Further Research and Development / Application Publishing / Further Development and Product Updates / User Feedback Collection / Application Update Opportunities / Application Expansion Opportunitie

Formal Verification of an Iterative Low-Power x86 Floating-Point Multiplier with Redundant Feedback

We present the formal verification of a low-power x86 floating-point multiplier. The multiplier operates iteratively and feeds back intermediate results in redundant representation. It supports x87 and SSE instructions in various precisions and can block the issuing of new instructions. The design has been optimized for low-power operation and has not been constrained by the formal verification effort. Additional improvements for the implementation were identified through formal verification. The formal verification of the design also incorporates the implementation of clock-gating and control logic. The core of the verification effort was based on ACL2 theorem proving. Additionally, model checking has been used to verify some properties of the floating-point scheduler that are relevant for the correct operation of the unit.Comment: In Proceedings ACL2 2011, arXiv:1110.447