Related papers: Stochastic Formal Methods: An application to accur…
Quantifying errors and losses due to the use of Floating-Point (FP) calculations in industrial scientific computing codes is an important part of the Verification, Validation and Uncertainty Quantification (VVUQ) process. Stochastic…
Numerical software are widely used in safety-critical systems such as aircrafts, satellites, car engines and so on, facilitating dynamics control of such systems in real time, it is therefore absolutely necessary to verify their…
Test instability in a floating-point program occurs when the control flow of the program diverges from its ideal execution assuming real arithmetic. This phenomenon is caused by the presence of round-off errors that affect the evaluation of…
Programs with floating-point computations are often derived from mathematical models or designed with the semantics of the real numbers in mind. However, for a given input, the computed path with floating-point numbers may differ from the…
Round-off errors arising from the difference between real numbers and their floating-point representation cause the control flow of conditional floating-point statements to deviate from the ideal flow of the real-number computation. This…
We provide a framework to bound the probability that accumulated errors were never above a given threshold on hybrid systems. Such systems are used for example to model an aircraft or a nuclear power plant on one side and its software on…
Verification of programs using floating-point arithmetic is challenging on several accounts. One of the difficulties of reasoning about such programs is due to the peculiarities of floating-point arithmetic: rounding errors, infinities,…
Computer programs may go wrong due to exceptional behaviors, out-of-bound array accesses, or simply coding errors. Thus, they cannot be blindly trusted. Scientific computing programs make no exception in that respect, and even bring…
Roundoff errors cannot be avoided when implementing numerical programs with finite precision. The ability to reason about rounding is especially important if one wants to explore a range of potential representations, for instance for FPGAs…
Formal Methods are mathematically-based techniques for software design and engineering, which enable the unambiguous description of and reasoning about a system's behaviour. Autonomous systems use software to make decisions without human…
High confidence in floating-point programs requires proving numerical properties of final and intermediate values. One may need to guarantee that a value stays within some range, or that the error relative to some ideal value is well…
Autonomous systems -- such as self-driving cars, autonomous drones, and automated trains -- must come with strong safety guarantees. Over the past decade, techniques based on formal methods have enjoyed some success in providing strong…
Cyber-physical systems (CPS) such as autonomous cars, aircraft, and robots are often also safety-critical; thus it is imperative that they operate as intended with a high degree of certainty. Formal verification has been employed to verify…
Finite-precision floating point arithmetic unavoidably introduces rounding errors which are traditionally bounded using a worst-case analysis. However, worst-case analysis might be overly conservative because worst-case errors can be…
Advanced embedded algorithms are growing in complexity and they are an essential contributor to the growth of autonomy in many areas. However, the promise held by these algorithms cannot be kept without proper attention to the considerably…
This paper addresses the problem of risk-aware fixed-time stabilization of a class of uncertain, output-feedback nonlinear systems modeled via stochastic differential equations. First, novel classes of certificate functions, namely…
This paper studies the problem of enforcing safety of a stochastic dynamical system over a finite-time horizon. We use stochastic control barrier functions as a means to quantify the probability that a system exits a given safe region of…
Current critical systems commonly use a lot of floating-point computations, and thus the testing or static analysis of programs containing floating-point operators has become a priority. However, correctly defining the semantics of common…
The study addresses the problem of precision in floating-point (FP) computations. A method for estimating the errors which affect intermediate and final results is proposed and a summary of many software simulations is discussed. The basic…
The failure of hardware or software in a critical system can lead to loss of lives. The design errors can be main source of the failures that can be introduced during system development process. Formal techniques are an alternative approach…