Thermodynamic investigation of an insulator irradiated by a low-energy electron beam

The surface of an insulating material irradiated by a beam of low energy electrons charges positively if the yield of secondary electron is greater than unity. For such a dynamical equilibrium, the thermodynamic properties have been investigated by measuring the surface potential in response to a temperature oscillation of the material. It is shown that an oscillation amplitude of 0.4 K at 530 K induces an oscillation of the surface potential of about 0.5 volts. The frequency dependence indicates a monotonous decrease in the response with decreasing frequency, extrapolating to zero at zero frequency. We propose that this modification of the surface charge is driven by the temperature dependence of a gas of charged particles in equilibrium with the vacuum level

Quadratic Zonotopes:An extension of Zonotopes to Quadratic Arithmetics

Affine forms are a common way to represent convex sets of $\mathbb{R}$ using a base of error terms $\epsilon \in [-1, 1]^m$. Quadratic forms are an extension of affine forms enabling the use of quadratic error terms $\epsilon_i \epsilon_j$. In static analysis, the zonotope domain, a relational abstract domain based on affine forms has been used in a wide set of settings, e.g. set-based simulation for hybrid systems, or floating point analysis, providing relational abstraction of functions with a cost linear in the number of errors terms. In this paper, we propose a quadratic version of zonotopes. We also present a new algorithm based on semi-definite programming to project a quadratic zonotope, and therefore quadratic forms, to intervals. All presented material has been implemented and applied on representative examples.Comment: 17 pages, 5 figures, 1 tabl

A Sums-of-Squares Extension of Policy Iterations

In order to address the imprecision often introduced by widening operators in static analysis, policy iteration based on min-computations amounts to considering the characterization of reachable value set of a program as an iterative computation of policies, starting from a post-fixpoint. Computing each policy and the associated invariant relies on a sequence of numerical optimizations. While the early research efforts relied on linear programming (LP) to address linear properties of linear programs, the current state of the art is still limited to the analysis of linear programs with at most quadratic invariants, relying on semidefinite programming (SDP) solvers to compute policies, and LP solvers to refine invariants. We propose here to extend the class of programs considered through the use of Sums-of-Squares (SOS) based optimization. Our approach enables the precise analysis of switched systems with polynomial updates and guards. The analysis presented has been implemented in Matlab and applied on existing programs coming from the system control literature, improving both the range of analyzable systems and the precision of previously handled ones.Comment: 29 pages, 4 figure

Synthesizing Modular Invariants for Synchronous Code

In this paper, we explore different techniques to synthesize modular invariants for synchronous code encoded as Horn clauses. Modular invariants are a set of formulas that characterizes the validity of predicates. They are very useful for different aspects of analysis, synthesis, testing and program transformation. We describe two techniques to generate modular invariants for code written in the synchronous dataflow language Lustre. The first technique directly encodes the synchronous code in a modular fashion. While in the second technique, we synthesize modular invariants starting from a monolithic invariant. Both techniques, take advantage of analysis techniques based on property-directed reachability. We also describe a technique to minimize the synthesized invariants.Comment: In Proceedings HCVS 2014, arXiv:1412.082

Credible Autocoding of Convex Optimization Algorithms

The efficiency of modern optimization methods, coupled with increasing computational resources, has led to the possibility of real-time optimization algorithms acting in safety critical roles. There is a considerable body of mathematical proofs on on-line optimization programs which can be leveraged to assist in the development and verification of their implementation. In this paper, we demonstrate how theoretical proofs of real-time optimization algorithms can be used to describe functional properties at the level of the code, thereby making it accessible for the formal methods community. The running example used in this paper is a generic semi-definite programming (SDP) solver. Semi-definite programs can encode a wide variety of optimization problems and can be solved in polynomial time at a given accuracy. We describe a top-to-down approach that transforms a high-level analysis of the algorithm into useful code annotations. We formulate some general remarks about how such a task can be incorporated into a convex programming autocoder. We then take a first step towards the automatic verification of the optimization program by identifying key issues to be adressed in future work

Bridging the Gap Between Requirements and Simulink Model Analysis

Formal verification and simulation are powerful tools for the verification of requirements against complex systems. Requirements are developed in early stages of the software lifecycle and are typically expressed in natural language. There is a gap between such requirements and their software implementations.We present a framework that bridges this gap by supporting a tight integration and feedback loop between high-level requirements and their analysis against software artifacts. Our framework implements an analysis portal within the fret requirements elicitation tool, thus forming an end-to-end, open-source environment where requirements are written in an intuitive, structured natural language, and are verified automatically against Simulink models

Bridging the Gap Between Requirements and Model Analysis : Evaluation on Ten Cyber-Physical Challenge Problems

Formal verfication and simulation are powerful tools to validate requirements against complex systems. [Problem] Requirements are developed in early stages of the software lifecycle and are typically written in ambiguous natural language. There is a gap between such requirements and formal notations that can be used by verification tools, and lack of support for proper association of requirements with software artifacts for verification. [Principal idea] We propose to write requirements in an intuitive, structured natural language with formal semantics, and to support formalization and model/code verification as a smooth, well-integrated process. [Contribution] We have developed an end-to-end, open source requirements analysis framework that checks Simulink models against requirements written in structured natural language. Our framework is built in the Formal Requirements Elicitation Tool (fret); we use fret's requirements language named fretish, and formalization of fretish requirements in temporal logics. Our proposed framework contributes the following features: 1) automatic extraction of Simulink model information and association of fretish requirements with target model signals and components; 2) translation of temporal logic formulas into synchronous dataflow cocospec specifications as well as Simulink monitors, to be used by verification tools; we establish correctness of our translation through extensive automated testing; 3) interpretation of counterexamples produced by verification tools back at requirements level. These features support a tight integration and feedback loop between high level requirements and their analysis. We demonstrate our approach on a major case study: the Ten Lockheed Martin Cyber-Physical, aerospace-inspired challenge problems