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Floating-point arithmetic performance determines the overall performance of important applications, from graphics to AI. Meeting the IEEE-754 specification for floating-point requires that final results of addition, subtraction,…

Mathematical Software · Computer Science 2024-04-02 Lucas M. Dutton , Christopher Kumar Anand , Robert Enenkel , Silvia Melitta Müller

These notes outline a formal method for program verification of numerical computation. It forms the basis of the software package VPC in its initial phase of development. Much of the style of presentation is in the form of notes that…

Mathematical Software · Computer Science 2014-01-08 Garry Pantelis

In considering the reliability of numerical programs, it is normal to "limit our study to the semantics dealing with numerical precision" (Martel, 2005). On the other hand, there is a great deal of work on the reliability of programs that…

Symbolic Computation · Computer Science 2014-04-25 James H. Davenport , Russell Bradford , Matthew England , David Wilson

The paper proposes a control-theoretic framework for verification of numerical software systems, and puts forward software verification as an important application of control and systems theory. The idea is to transfer Lyapunov functions…

Systems and Control · Computer Science 2011-08-30 Mardavij Roozbehani , Alexandre Megretski , Eric Feron

Algorithms operating on real numbers are implemented as floating-point computations in practice, but floating-point operations introduce roundoff errors that can degrade the accuracy of the result. We propose $\Lambda_{num}$, a functional…

Programming Languages · Computer Science 2025-04-10 Ariel E. Kellison , Justin Hsu

Electronic exams (e-exams) have the potential to substantially reduce the effort required for conducting an exam through automation. Yet, care must be taken to sacrifice neither task complexity nor constructive alignment nor grading…

Computers and Society · Computer Science 2023-08-17 Ole Lübke , Konrad Fuger , Fin Hendrik Bahnsen , Katrin Billerbeck , Sibylle Schupp

Configurable software verification is a recent concept for expressing different program analysis and model checking approaches in one single formalism. This paper presents CPAchecker, a tool and framework that aims at easy integration of…

Programming Languages · Computer Science 2009-02-03 Dirk Beyer , M. Erkan Keremoglu

As we reach the limit of Moore's Law, researchers are exploring different paradigms to achieve unprecedented performance. Approximate Computing (AC), which relies on the ability of applications to tolerate some error in the results to…

Numerical Analysis · Mathematics 2023-04-14 Garima Singh , Baidyanath Kundu , Harshitha Menon , Alexander Penev , David J. Lange , Vassil Vassilev

CeTA was originally developed as a tool for certifying termination proofs which have to be provided as certificates in the CPF-format. Its soundness is proven as part of IsaFoR, the Isabelle Formalization of Rewriting. By now, CeTA can also…

Logic in Computer Science · Computer Science 2017-08-29 Julian Nagele , René Thiemann

Significant inaccuracy often occurs during the process of mathematical calculation due to the digit limitation of floating point, which may lead to catastrophic loss. Normally, people believe that adjustment of floating-point precision is…

Numerical Analysis · Computer Science 2015-12-07 Ran Wang , Xinrui He

Reliable numerical computations are central to scientific computing, but the floating-point arithmetic that enables large-scale models is error-prone. Numeric exceptions are a common occurrence and can propagate through code, leading to…

Programming Languages · Computer Science 2024-03-26 Taylor Allred , Xinyi Li , Ashton Wiersdorf , Ben Greenman , Ganesh Gopalakrishnan

How to apply automated verification technology such as model checking and static program analysis to millions of lines of embedded C/C++ code? How to package this technology in a way that it can be used by software developers and engineers,…

Software Engineering · Computer Science 2013-01-03 Ralf Huuck

In safety-critical applications that rely on the solution of an optimization problem, the certification of the optimization algorithm is of vital importance. Certification and suboptimality results are available for a wide range of…

Optimization and Control · Mathematics 2023-12-06 Pablo Krupa , Omar Inverso , Mirco Tribastone , Alberto Bemporad

The paper proposes a control-theoretic framework for verification of numerical software systems, and puts forward software verification as an important application of control and systems theory. The idea is to transfer Lyapunov functions…

Systems and Control · Computer Science 2011-08-02 Mardavij Roozbehani , Alexandre Megretski , Eric Feron

Formal verification provides mathematical guarantees that a software is correct. Design-level verification tools ensure software specifications are correct, but they do not expose defects in actual implementations. For this purpose,…

Software Engineering · Computer Science 2025-05-01 Paschal C. Amusuo , Parth V. Patil , Owen Cochell , Taylor Le Lievre , James C. Davis

Current static verification techniques support a wide range of programs. However, such techniques only support complete and detailed specifications, which places an undue burden on users. To solve this problem, prior work proposed gradual…

Reasoning about floating-point arithmetic is notoriously hard. While static and dynamic analysis techniques or program repair have made significant progress, more work is still needed to make them relevant to real-world code. On the…

Programming Languages · Computer Science 2026-03-11 Andrea Gilot , Tobias Wrigstad , Eva Darulova

Interactive proof assistants are computer programs carefully constructed to check a human-designed proof of a mathematical claim with high confidence in the implementation. However, this only validates truth of a formal claim, which may…

Programming Languages · Computer Science 2023-10-09 Colin S. Gordon , Sergey Matskevich

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…

Computation and Language · Computer Science 2020-05-27 Raphaël Cohen , Eric Féron , Pierre-Loïc Garoche

This paper proposes a new methodology for early validation of high-level requirements on cyber-physical systems with the aim of improving their quality and, thus, lowering chances of specification errors propagating into later stages of…