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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

A program verifier is a tool that can be used to verify that a "contract" for a program holds - i.e. given a precondition the program guarantees that a given postcondition holds - by only working at the level of the annotated program. An…

Software Engineering · Computer Science 2014-06-12 Gudmund Grov

Formal verification plays a crucial role in making smart contracts safer, being able to find bugs or to guarantee their absence, as well as checking whether the business logic is correctly implemented. For Solidity, even though there…

Cryptography and Security · Computer Science 2025-11-18 Massimo Bartoletti , Silvia Crafa , Enrico Lipparini

We present a safety verification framework for design-time and run-time assurance of learning-based components in aviation systems. Our proposed framework integrates two novel methodologies. From the design-time assurance perspective, we…

Systems and Control · Electrical Eng. & Systems 2022-05-17 Ali Baheri , Hao Ren , Benjamin Johnson , Pouria Razzaghi , Peng Wei

Since software performance requirements are documented in natural language, quantifying them into mathematical forms is essential for software engineering. Yet, the vagueness in performance requirements and uncertainty of human cognition…

Software Engineering · Computer Science 2026-04-28 Shihai Wang , Tao Chen

We present an approach to program reasoning which inserts between a program and its verification conditions an additional layer, the denotation of the program expressed in a declarative form. The program is first translated into its…

Logic in Computer Science · Computer Science 2012-02-23 Wolfgang Schreiner

We propose a conceptual integration of deductive program verification into existing user interfaces for software debugging. This integration is well-represented in the "Debug Adapter Protocol", a widely-used and generic technology to…

Logic in Computer Science · Computer Science 2021-08-09 Gidon Ernst , Johannes Blau , Toby Murray

We propose a framework for synthesizing inductive invariants for incomplete verification engines, which soundly reduce logical problems in undecidable theories to decidable theories. Our framework is based on the counter-example guided…

Programming Languages · Computer Science 2018-01-15 Daniel Neider , Pranav Garg , P. Madhusudan , Shambwaditya Saha , Daejun Park

This article examines two approaches to verification, one based on using a logic for expressing properties of a system, and one based on showing the system equivalent to a simpler system that obviously has whatever property is of interest.…

Logic in Computer Science · Computer Science 2007-05-23 Riccardo Pucella

The increasing use of deep neural networks for safety-critical applications, such as autonomous driving and flight control, raises concerns about their safety and reliability. Formal verification can address these concerns by guaranteeing…

Artificial Intelligence · Computer Science 2018-02-06 Lindsey Kuper , Guy Katz , Justin Gottschlich , Kyle Julian , Clark Barrett , Mykel Kochenderfer

Verification of complex, safety-critical systems is a significant challenge. Manual testing and simulations are often used, but are only capable of exploring a subset of the system's reachable states. Formal methods are mathematically-based…

Software Engineering · Computer Science 2021-10-19 Matt Luckcuck , Marie Farrell , Oisín Sheridan , Rosemary Monahan

Software correctness is ensured mathematically through formal verification, which involves the resources of generating formal requirement specifications and having an implementation that must be verified. Tools such as model-checkers and…

Software Engineering · Computer Science 2025-08-29 Arshad Beg , Diarmuid O'Donoghue , Rosemary Monahan

Writing documentation about software internals is rarely considered a rewarding activity. It is highly time-consuming and the resulting documentation is fragile when the software is continuously evolving in a multi-developer setting.…

Software Engineering · Computer Science 2013-11-13 Tobias Kuhn , Alexandre Bergel

Control systems are sets of interconnected hardware and software components which regulate the behaviour of processes. The software of modern control systems rises for some years by requirements regarding the flexibility and functionality.…

Software Engineering · Computer Science 2009-04-24 Rolf Andreas Rasenack , Karsten Wolke , Kostyantyn Yermashov , Karl Hayo Siemsen

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

This paper aims to develop a verification method for procedural programs via a transformation into Logically Constrained Term Rewriting Systems (LCTRSs). To this end, we extend transformation methods based on integer TRSs to handle…

Logic in Computer Science · Computer Science 2025-09-01 Carsten Fuhs , Cynthia Kop , Naoki Nishida

The safety of automated driving systems must be justified by convincing arguments and supported by compelling evidence to persuade certification agencies, regulatory entities, and the general public to allow the systems on public roads.…

Software Engineering · Computer Science 2024-10-28 Jonas Krook , Yuvaraj Selvaraj , Wolfgang Ahrendt , Martin Fabian

In top-down multi-level design methodologies, design descriptions at higher levels of abstraction are incrementally refined to the final realizations. Simulation based techniques have traditionally been used to verify that such model…

Logic in Computer Science · Computer Science 2013-08-02 Salim Ismail Al-Akhras , Sofiène Tahar , Gabriela Nicolescu , Michel Langevin , Pierre Paulin

Noisy data, non-convex objectives, model misspecification, and numerical instability can all cause undesired behaviors in machine learning systems. As a result, detecting actual implementation errors can be extremely difficult. We…

Software Engineering · Computer Science 2017-06-28 Daniel Selsam , Percy Liang , David L. Dill

We introduce a new methodology based on refinement for testing the functional correctness of hardware and low-level software. Our methodology overcomes several major drawbacks of the de facto testing methodologies used in industry: (1) it…

Logic in Computer Science · Computer Science 2017-03-17 Mitesh Jain , Panagiotis Manolios