Related papers: Auto-active Verification of Floating-point Program…

Even competent programmers make mistakes. Automatic verification can detect errors, but leaves the frustrating task of finding the erroneous line of code to the user. This paper presents an automatic approach for identifying potential error…

Formal verification tools are often developed by experts for experts; as a result, their usability by programmers with little formal methods experience may be severely limited. In this paper, we discuss this general phenomenon with…

Scientific computing programs often undergo aggressive compiler optimization to achieve high performance and efficient resource utilization. While performance is critical, we also need to ensure that these optimizations are correct. In this…

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…

Writing accurate numerical software is hard because of many sources of unavoidable uncertainties, including finite numerical precision of implementations. We present a programming model where the user writes a program in a real-valued…

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…

Floating-point accumulation networks (FPANs) are key building blocks used in many floating-point algorithms, including compensated summation and double-double arithmetic. FPANs are notoriously difficult to analyze, and algorithms using…

A critical step towards certifying safety-critical systems is to check their conformance to hard real-time requirements. A promising way to achieve this is by building the systems from pre-verified components and verifying their correctness…

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…

Formal proof checkers such as Coq are capable of validating proofs of correction of algorithms for finite field arithmetics but they require extensive training from potential users. The delayed solution of a triangular system over a finite…

This paper presents a novel approach to automatically verify properties of pure data-parallel programs with non-linear indexing -- expressed as pre- and post-conditions on functions. Programs consist of nests of second-order array…

This paper provides a bound on the number of numeric operations (fixed or floating point) that can safely be performed before accuracy is lost. This work has important implications for control systems with safety-critical software, as these…

In deductive verification and software model checking, dealing with certain specification language constructs can be problematic when the back-end solver is not sufficiently powerful or lacks the required theories. One way to deal with this…

Bounded verification has proved useful to detect bugs and to increase confidence in the correctness of a program. In contrast to unbounded verification, reasoning about calls via (bounded) inlining and about loops via (bounded) unrolling…

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…

Auto-active program verification rests on the ability to effectively the translation from annotated programs into verification conditions that are then discharged by automated theorem provers in the background. Characteristic such tools,…

Probabilistic model checking computes probabilities and expected values related to designated behaviours of interest in Markov models. As a formal verification approach, it is applied to critical systems; thus we trust that probabilistic…

Numerical accuracy of floating point computation is a well studied topic which has not made its way to the end-user in scientific computing. Yet, it has become a critical issue with the recent requirements for code modernization to harness…

Functional programming offers the perfect ground for building correct-by-construction software. Languages of such paradigm normally feature state-of-the-art type systems, good abstraction mechanisms, and well-defined execution models. We…

We present a method for verifying partial correctness properties of imperative programs that manipulate integers and arrays by using techniques based on the transformation of constraint logic programs (CLP). We use CLP as a metalanguage for…