Related papers: Program Verification of Numerical Computation

This note concerns a search for publications in which the pragmatic concept of a test as conducted in the practice of software testing is formalized, a theory about software testing based on such a formalization is presented or it is…

This report describes the state of the art in verifiable computation. The problem being solved is the following: The Verifiable Computation Problem (Verifiable Computing Problem) Suppose we have two computing agents. The first agent is the…

Cooperation between verification methods is crucial to tackle the challenging problem of software verification. The paper focuses on the verification of C programs using pointers and it formalizes a cooperation between static analyzers…

Reliably determining system trajectories is essential in many analysis and control design approaches. To this end, an initial value problem has to be usually solved via numerical algorithms which rely on a certain software realization.…

Confidential computing is a key technology for isolating high-assurance applications from the large amounts of untrusted code typical in modern systems. Existing confidential computing systems cannot be certified for use in critical…

Formal verification is at the heart of model validation and correctness. With model checking, invaluable realizations have been accomplished in software engineering and particularly in software development. By means of this approach,…

Nowadays, formal methods are used in various areas for the verification of programs or for code generation from models in order to increase the quality of software and to reduce costs. However, there are still fields in which formal methods…

VeriFast is a prototype tool based on separation logic for modular verification of C and Java programs. We are in the process of adding support for C++. In this report, we describe the features of C++ for which we added support so far, as…

Quantum computers are expected to offer substantial speedups over their classical counterparts and to solve problems that are intractable for classical computers. Beyond such practical significance, the concept of quantum computation opens…

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,…

Formal methods provide systematic and rigorous techniques for software development. We strongly believe that they must be taught in computer science curricula. In this paper we present the pedagogic rationale and the concrete implementation…

This paper is an example-based demonstration of our initial results on the formal specification of programs written in the computer algebra language MiniMaple (a substantial subset of Maple with slight extensions). The main goal of this…

These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…

This lecture addresses some general ideas behind numerical computations ranging from representation of numbers in computers to stability and accuracy of standard algorithms for some simple mathematical problems.

The subject of this work is quantum predicative programming -- the study of developing of programs intended for execution on a quantum computer. We look at programming in the context of formal methods of program development, or programming…

We formally prove correct a C program that implements a numerical scheme for the resolution of the one-dimensional acoustic wave equation. Such an implementation introduces errors at several levels: the numerical scheme introduces method…

While concepts and tools from Theoretical Computer Science are regularly applied to, and significantly support, software development for discrete problems, Numerical Engineering largely employs recipes and methods whose correctness and…

Formal methods for verification of programs are extended to testing of programs. Their combination is intended to lead to benefits in reliable program development, testing, and evolution. Our geometric theory of testing is intended to serve…

Ensuring the correct functionality of systems software, given its safety-critical and low-level nature, is a primary focus in formal verification research and applications. Despite advances in verification tooling, conventional programmers…

Formal verification of complex algorithms is challenging. Verifying their implementations goes beyond the state of the art of current automatic verification tools and usually involves intricate mathematical theorems. Certifying algorithms…