Methoden und Beschreibungssprachen zur Modellierung und Verifikation vonSchaltungen und Systemen: MBMV 2015 - Tagungsband, Chemnitz, 03. - 04. März 2015

Der Workshop Methoden und Beschreibungssprachen zur Modellierung und Verifikation von Schaltungen und Systemen (MBMV 2015) findet nun schon zum 18. mal statt. Ausrichter sind in diesem Jahr die Professur Schaltkreis- und Systementwurf der Technischen Universität Chemnitz und das Steinbeis-Forschungszentrum Systementwurf und Test. Der Workshop hat es sich zum Ziel gesetzt, neueste Trends, Ergebnisse und aktuelle Probleme auf dem Gebiet der Methoden zur Modellierung und Verifikation sowie der Beschreibungssprachen digitaler, analoger und Mixed-Signal-Schaltungen zu diskutieren. Er soll somit ein Forum zum Ideenaustausch sein. Weiterhin bietet der Workshop eine Plattform für den Austausch zwischen Forschung und Industrie sowie zur Pflege bestehender und zur Knüpfung neuer Kontakte. Jungen Wissenschaftlern erlaubt er, ihre Ideen und Ansätze einem breiten Publikum aus Wissenschaft und Wirtschaft zu präsentieren und im Rahmen der Veranstaltung auch fundiert zu diskutieren. Sein langjähriges Bestehen hat ihn zu einer festen Größe in vielen Veranstaltungskalendern gemacht. Traditionell sind auch die Treffen der ITGFachgruppen an den Workshop angegliedert. In diesem Jahr nutzen zwei im Rahmen der InnoProfile-Transfer-Initiative durch das Bundesministerium für Bildung und Forschung geförderte Projekte den Workshop, um in zwei eigenen Tracks ihre Forschungsergebnisse einem breiten Publikum zu präsentieren. Vertreter der Projekte Generische Plattform für Systemzuverlässigkeit und Verifikation (GPZV) und GINKO - Generische Infrastruktur zur nahtlosen energetischen Kopplung von Elektrofahrzeugen stellen Teile ihrer gegenwärtigen Arbeiten vor. Dies bereichert denWorkshop durch zusätzliche Themenschwerpunkte und bietet eine wertvolle Ergänzung zu den Beiträgen der Autoren. [... aus dem Vorwort

Reachability Analysis for Neural Feedback Systems Using Regressive Polynomial Rule Inference

We present an approach to construct reachable set overapproxi- mations for continuous-time dynamical systems controlled using neural network feedback systems. Feedforward deep neural net- works are now widely used as a means for learning control laws through techniques such as reinforcement learning and data-driven predictive control. However, the learning algorithms for these net- works do not guarantee correctness properties on the resulting closed-loop systems. Our approach seeks to construct overapproxi- mate reachable sets by integrating a Taylor model-based flowpipe construction scheme for continuous differential equations with an approach that replaces the neural network feedback law for a small subset of inputs by a polynomial mapping. We generate the polynomial mapping using regression from input-output sam- ples. To ensure soundness, we rigorously quantify the gap between the output of the network and that of the polynomial model. We demonstrate the effectiveness of our approach over a suite of bench- mark examples ranging from 2 to 17 state variables, comparing our approach with alternative ideas based on range analysis

Optimization of Lyapunov invariants in analysis and implementation of safety-critical software systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2008.Includes bibliographical references (leaves 168-176).This dissertation contributes to two major research areas in safety-critical software systems, namely, software analysis, and software implementation. In reference to the software analysis problem, the main contribution of the dissertation is the development of a novel framework, based on Lyapunov invariants and convex optimization, for verification of various safety and performance specifications for software systems. The enabling elements of the framework for software analysis are: (i) dynamical system interpretation and modeling of computer programs, (ii) Lyapunov invariants as behavior certificates for computer programs, and (iii) a computational procedure for finding the Lyapunov invariants. (i) The view in this dissertation is that software defines a rule for iterative modification of the operating memory at discrete instances of time. Hence, it can be modeled as a discrete-time dynamical system with the program variables as the state variables, and the operating memory as the state space. Three specific modeling languages are introduced which can represent a broad range of computer programs of interest to the control community. These are: Mixed Integer-Linear Models, Graph Models, and Linear Models with Conditional Switching. (ii) Inspired by the concept of Lyapunov functions in stability analysis of nonlinear dynamical systems, Lyapunov invariants are introduced and proposed for analysis of behavioral properties, and verification of various safety and performance specifications for computer programs. In the same spirit as standard Lyapunov functions, a Lyapunov invariant is an appropriately defined function of the state which satisfies a difference inequality along the trajectories. It is shown that variations of Lyapunov invariants satisfying certain technical conditions can be formulated for verification of several common specifications.(cont.) These include but are not limited to: absence of overflow, absence of division-by-zero, termination in finite time, and certain user-specified program assertions. (iii) A computational procedure based on convex relaxation techniques and numerical optimization is proposed for finding the Lyapunov invariants that prove the specifications. The framework is complemented by the introduction of a notion of optimality for the graph models. This notion can be used for constructing efficient graph models that improve the analysis in a systematic way. It is observed that the application of the framework to (graph models of) programs that are semantically identical but syntactically different does not produce identical results. This suggests that the success or failure of the method is contingent on the choice of the graph model. Based on this observation, the concepts of graph reduction, irreducible graphs, and minimal and maximal realizations of graph models are introduced. Several new theorems that compare the performance of the original graph model of a computer program and its reduced offsprings are presented. In reference to the software implementation problem for safety-critical systems, the main contribution of the dissertation is the introduction of an algorithm, based on optimization of quadratic Lyapunov functions and semidefinite programming, for computing optimal state space implementations for digital filters. The particular implementation that is considered is a finite word-length implementation on a fixed-point processor with quantization before or after multiplication. The objective is to minimize the effects of finite word-length constraints on performance deviation while respecting the overflow limits. The problem is first formulated as a special case of controller synthesis where the controller has a specific structure, which is known to be a hard non-convex problem in general.(cont.) It is then shown that this special case can be convexified exactly and the optimal implementation can be computed by solving a semidefinite optimization problem. It is observed that the optimal state space implementation of a digital filter on a machine with finite memory, does not necessarily define the same transfer function as that of an ideal implementation.by Mardavij Roozbehani.Ph.D

Bit-precise Verification of Numerical Properties in Fixed-point Programs

Numerical software is prone to inaccuracies due to the finite representation of numbers. These inaccuracies propagate, possibly non-linearly, throughout the statements of a program, making it hard to predict the accumulated errors. Moreover, in programs that contain control structures, numerical errors can affect the control flow. As a result of these inaccuracies, reachability, and thus safety, may be altered with respect to the intended infinite-precision computation. This thesis considers programs that use fixed-point arithmetic to compute over non-integer quantities in finite precision. We first define a semantics of fixed-point operations in terms of operations over bit-vectors. The proposed semantics generalizes current attempts to a standardization of fixedpoint arithmetic. We then consider the problem of bit-precise numerical accuracy certification of fixed-point programs with control structures and arithmetic over variables of arbitrary, mixed precision and possibly non-deterministic value. By applying a set of parametrized transformation rules based on computable expressions for the errors incurred by single program statements, we reduce the problem of assessing whether a fixed-point program can exceed a given error bound to a reachability problem in a bit-vector program. We present an experimental evaluation of the certification technique, implemented in a prototype analyzer in a bounded model checking-based verification workflow. Our experiments on a set of fixed-point arithmetic routines commonly used in the industry show that the proposed technique can successfully certify numerical errors and can do so bitprecisely, making it the only such verification technique

暗号ハードウェアの形式的設計に関する研究

Tohoku University青木孝文課

Computer Aided Verification

This open access two-volume set LNCS 13371 and 13372 constitutes the refereed proceedings of the 34rd International Conference on Computer Aided Verification, CAV 2022, which was held in Haifa, Israel, in August 2022. The 40 full papers presented together with 9 tool papers and 2 case studies were carefully reviewed and selected from 209 submissions. The papers were organized in the following topical sections: Part I: Invited papers; formal methods for probabilistic programs; formal methods for neural networks; software Verification and model checking; hyperproperties and security; formal methods for hardware, cyber-physical, and hybrid systems. Part II: Probabilistic techniques; automata and logic; deductive verification and decision procedures; machine learning; synthesis and concurrency. This is an open access book

Non-Convex Optimization and Applications to Bilinear Programming and Super-Resolution Imaging

Bilinear programs and Phase Retrieval are two instances of nonconvex problems that arise in engineering and physical applications, and both occur with their fundamental difficulties. In this thesis, we consider various methods and algorithms for tackling these challenging problems and discuss their effectiveness. Bilinear programs (BLPs) are ubiquitous in engineering applications, economics, and operations research, and have a natural encoding to quadratic programs. They appear in the study of Lyapunov functions used to deduce the stability of solutions to differential equations describing dynamical systems. For multivariate dynamical systems, the problem formulation for computing an appropriate Lyapunov function is a BLP. In electric power systems engineering, one of the most practically important and well-researched subfields of constrained nonlinear optimization is Optimal Power Flow wherein one attempts to optimize an electric power system subject to physical constraints imposed by electrical laws and engineering limits, which can be naturally formulated as a quadratic program. In a recent publication, we studied the relationship between data flow constraints for numerical domains such as polyhedra and bilinear constraints. The problem of recovering an image from its Fourier modulus, or intensity, measurements emerges in many physical and engineering applications. The problem is known as Fourier phase retrieval wherein one attempts to recover the phase information of a signal in order to accurately reconstruct it from estimated intensity measurements by applying the inverse Fourier transform. The problem of recovering phase information from a set of measurements can be formulated as a quadratic program. This problem is well-studied but still presents many challenges. The resolution of an optical device is defined as the smallest distance between two objects such that the two objects can still be recognized as separate entities. Due to the physics of diffraction, and the way that light bends around an obstacle, the resolving power of an optical system is limited. This limit, known as the diffraction limit, was first introduced by Ernst Abbe in 1873. Obtaining the complete phase information would enable one to perfectly reconstruct an image; however, the problem is severely ill-posed and the leads to a specialized type of quadratic program, known as super-resolution imaging, wherein one attempts to learn phase information beyond the limits of diffraction and the limitations imposed by the imaging device

Non-Convex Optimization and Applications to Bilinear Programming and Super-Resolution Imaging

Bilinear programs and Phase Retrieval are two instances of nonconvex problems that arise in engineering and physical applications, and both occur with their fundamental difficulties. In this thesis, we consider various methods and algorithms for tackling these challenging problems and discuss their effectiveness. Bilinear programs (BLPs) are ubiquitous in engineering applications, economics, and operations research, and have a natural encoding to quadratic programs. They appear in the study of Lyapunov functions used to deduce the stability of solutions to differential equations describing dynamical systems. For multivariate dynamical systems, the problem formulation for computing an appropriate Lyapunov function is a BLP. In electric power systems engineering, one of the most practically important and well-researched subfields of constrained nonlinear optimization is Optimal Power Flow wherein one attempts to optimize an electric power system subject to physical constraints imposed by electrical laws and engineering limits, which can be naturally formulated as a quadratic program. We study the relationship between data flow constraints for numerical domains such as polyhedra and bilinear constraints. The problem of recovering an image from its Fourier modulus, or intensity, measurements emerges in many physical and engineering applications. The problem is known as Fourier phase retrieval wherein one attempts to recover the phase information of a signal in order to accurately reconstruct it from estimated intensity measurements by applying the inverse Fourier transform. The problem of recovering phase information from a set of measurements can be formulated as a quadratic program. This problem is well-studied but still presents many challenges. The resolution of an optical device is defined as the smallest distance between two objects such that the two objects can still be recognized as separate entities. Due to the physics of diffraction, and the way that light bends around an obstacle, the resolving power of an optical system is limited. This limit, known as the diffraction limit, was first introduced by Ernst Abbe in 1873. Obtaining the complete phase information would enable one to perfectly reconstruct an image; however, the problem is severely ill-posed and the leads to a specialized type of quadratic program, known as super-resolution imaging, wherein one attempts to learn phase information beyond the limits of diffraction and the limitations imposed by the imaging device.</p