Related papers: Computer-Assisted Verification of Four Interval Ar…

Verification of microkernels, device drivers, and crypto routines requires analyses at the binary level. In order to automate these analyses, in the last years several binary analysis platforms have been introduced. These platforms share a…

Arb is a C library for arbitrary-precision interval arithmetic using the midpoint-radius representation, also known as ball arithmetic. It supports real and complex numbers, polynomials, power series, matrices, and evaluation of many…

Some recent processors are not equipped with an integer division unit. Compilers then implement division by a call to a special function supplied by the processor designers, which implements division by a loop producing one bit of quotient…

Formal verification of floating-point arithmetic remains challenging due to non-linear arithmetic behavior and the tight coupling between control and datapath logic. Existing approaches often rely on high-level C models for equivalence…

The need to solve non-linear arithmetic constraints presents a major obstacle to the automatic verification of smart contracts. In this case study we focus on the two overapproximation techniques used by the industry verification tool…

Elementary function calls are a common feature in numerical programs. While their implementions in library functions are highly optimized, their computation is nonetheless very expensive compared to plain arithmetic. Full accuracy is,…

Interactive proof assistants make it possible for ordinary mathematicians to write definitions and theorems in a formal proof language, like a programming language, so that a computer can parse them and check them against the rules of a…

Termination is an important property of programs; notably required for programs formulated in proof assistants. It is a very active subject of research in the Turing-complete formalism of term rewriting systems, where many methods and tools…

In earlier work, we developed an approach for automatic complexity analysis of integer programs, based on an alternating modular inference of upper runtime and size bounds for program parts. In this paper, we show how recent techniques to…

An invaluable feature of computer algebra systems is their ability to plot the graph of functions. Unfortunately, when one is trying to design a library of mathematical functions, this feature often falls short, producing incorrect and…

Auto-active verifiers provide a level of automation intermediate between fully automatic and interactive: users supply code with annotations as input while benefiting from a high level of automation in the back-end. This paper presents…

In recent years, machine learning (ML) and neural networks (NNs) have gained widespread use and attention across various domains, particularly in transportation for achieving autonomy, including the emergence of flying taxis for urban air…

We consider feasibility of linear integer programs in the context of verification systems such as SMT solvers or theorem provers. Although satisfiability of linear integer programs is decidable, many state-of-the-art solvers neglect…

Optimizing compilers have become a cornerstone for high-performance program generation in research and industry. Optimizations, including those implemented manually by a user and those target-specific and non-target-specific, are used to…

In basic computational physics classes, students often raise the question of how to compute a number that exceeds the numerical limit of the machine. While technique of avoiding overflow/underflow has practical application in the electrical…

This paper presents TIRA, a Matlab library gathering several methods for the computation of interval over-approximations of the reachable sets for both continuous- and discrete-time nonlinear systems. Unlike other existing tools, the main…

Minimal-interval semantics associates with each query over a document a set of intervals, called witnesses, that are incomparable with respect to inclusion (i.e., they form an antichain): witnesses define the minimal regions of the document…

The correct computation of orbits of discrete dynamical systems on the interval is considered. Therefore, an arbitrary-precision floating-point approach based on automatic error analysis is chosen and a general algorithm is presented. The…

This paper presents a specification-guided safety verification method for feedforward neural networks with general activation functions. As such feedforward networks are memoryless, they can be abstractly represented as mathematical…

Runtime verification is an effective automated method for specification-based offline testing and analysis as well as online monitoring of complex systems. The specification language is often a variant of regular expressions or a popular…