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We review state-of-the-art formal methods applied to the emerging field of the verification of machine learning systems. Formal methods can provide rigorous correctness guarantees on hardware and software systems. Thanks to the availability…

Programming Languages · Computer Science 2021-04-22 Caterina Urban , Antoine Miné

Declarative machine learning (ML) aims at the high-level specification of ML tasks or algorithms, and automatic generation of optimized execution plans from these specifications. The fundamental goal is to simplify the usage and/or…

Databases · Computer Science 2016-05-20 Matthias Boehm , Alexandre V. Evfimievski , Niketan Pansare , Berthold Reinwald

Answer Set Programming (ASP) is an important logic programming paradigm within the field of Knowledge Representation and Reasoning. As a concise, human-readable, declarative language, ASP is an excellent tool for developing trustworthy…

Logic in Computer Science · Computer Science 2025-02-14 Zachary Hansen

The rise of multi-paradigm languages challenges traditional classification methods, leading to practical software engineering issues like interoperability defects. This systematic literature review (SLR) maps the formal foundations of…

Programming Languages · Computer Science 2025-08-04 Mikel Vandeloise

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

Decisions suggested by improperly designed software systems might be prone to discriminate against people based on protected characteristics, such as gender and ethnicity. Previous studies attribute such undesired behavior to flaws in…

Software Engineering · Computer Science 2025-09-26 Qusai Ramadan , Jukka Ruohonen , Abhishek Tiwari , Adam Alami , Zeyd Boukhers

Online Analytical Processing (OLAP) comprises tools and algorithms that allow querying multidimensional databases. It is based on the multidimensional model, where data can be seen as a cube, where each cell contains one or more measures…

Databases · Computer Science 2016-09-19 Bart Kuijpers , Alejandro Vaisman

In this paper, we provide a comprehensive, hands-on tutorial on how to apply deductive verification to programs written in OCaml. In particular, we show how one can use the GOSPEL specification language and the Cameleer tool to conduct…

Logic in Computer Science · Computer Science 2024-07-23 Mário Pereira

Large language models (LLMs) demonstrate considerable potential in various natural language tasks but face significant challenges in mathematical reasoning, particularly in executing precise, multi-step logic. However, current evaluation…

Computation and Language · Computer Science 2025-05-22 Tiasa Singha Roy , Aditeya Baral , Ayush Rajesh Jhaveri , Yusuf Baig

In this paper, we outline an approach to verifying parallel programs. A new mathematical model of parallel programs is introduced. The introduced model is illustrated by the verification of the matrix multiplication MPI program.

Logic in Computer Science · Computer Science 2021-10-19 Andrew M. Mironov

The Message Passing Interface specification (MPI) defines a portable message-passing API used to program parallel computers. MPI programs manifest a number of challenges on what concerns correctness: sent and expected values in…

Programming Languages · Computer Science 2015-08-21 César Santos , Francisco Martins , Vasco Thudichum Vasconcelos

This paper presents an operational semantics for UML activity diagrams. The purpose of this semantics is three-fold: to give a robust basis for verifying model correctness; to help validate model transformations; and to provide a…

Logic in Computer Science · Computer Science 2016-04-11 Zamira Daw , Rance Cleaveland

Application of formal models provides many benefits for the software and system development, however, the learning curve of formal languages could be a critical factor for an industrial project. Thus, a natural language specification that…

Software Engineering · Computer Science 2016-12-07 Phan Vo Thu Nhat , Maria Spichkova

This book explores an alternative to the current dominant paradigm where a discrete computer model is constructed as an attempt to approximate some continuum theory. We focus on a class of discrete computer models that are based on simple…

Logic in Computer Science · Computer Science 2017-04-14 Garry Pantelis

The possibility of interaction between Maple and numeric compiled languages in performing extensive numeric calculations is exemplified by the Ndynamics package, a tool for studying the (chaotic) behavior of dynamical systems. Programming…

Numerical Analysis · Mathematics 2025-10-20 E. V. Correa Silva , L. G. S. Duarte , L. A. C. P. da Mota , J. E. F. Skea

We propose a methodology for verifying security properties of network protocols at design level. It can be separated in two main parts: context and requirements analysis and informal verification; and formal representation and procedural…

Cryptography and Security · Computer Science 2013-10-29 Jesus Diaz , David Arroyo , Francisco B. Rodriguez

Formal semantics provides rigorous, mathematically precise definitions of programming languages, with which we can argue about program behaviour and program equivalence by formal means; in particular, we can describe and verify our…

Programming Languages · Computer Science 2020-11-23 Péter Bereczky , Dániel Horpácsi , Simon Thompson

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…

Logic in Computer Science · Computer Science 2022-07-21 Daniel Castanho , Mário Pereira

We present the first formalization and metatheory of language soundness for a user-schedulable language, the widely used array processing language Halide. User-schedulable languages strike a balance between abstraction and control in…

Programming Languages · Computer Science 2022-10-31 Alex Reinking , Gilbert Louis Bernstein , Jonathan Ragan-Kelley

OpenJML is a tool for checking code and specifications of Java programs. We describe our experience building the tool on the foundation of JML, OpenJDK and Eclipse, as well as on many advances in specification-based software verification.…

Software Engineering · Computer Science 2014-04-29 David R. Cok
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