Related papers: Verified reductions for optimization
Optimization is used extensively in engineering, industry, and finance, and various methods are used to transform problems to the point where they are amenable to solution by numerical methods. We describe progress towards developing a…
Formal verification techniques are widely used for detecting design flaws in software systems. Formal verification can be done by transforming an already implemented source code to a formal model and attempting to prove certain properties…
Empirical software engineering is concerned with the design and analysis of empirical studies that include software products, processes, and resources. Optimization is a form of data analytics in support of human decision-making.…
In various provers and deductive verification tools, logical transformations are used extensively in order to reduce a proof task into a number of simpler tasks. Logical transformations are often part of the trusted base of such tools. In…
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…
Program reductions are used widely to simplify reasoning about the correctness of concurrent and distributed programs. In this paper, we propose a general approach to proof simplification of concurrent programs based on exploring generic…
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…
Building mathematical optimization models is critical in operations research (OR), while it requires substantial human expertise. Recent advancements have utilized large language models (LLMs) to automate this modeling process. However,…
Logical specifications are widely used to represent software systems and their desired properties. Under system degradation or environmental changes, commonly seen in complex real-world robotic systems, these properties may no longer hold…
Optimizing compilers have become a cornerstone for high-performance program generation in research and industry. Optimizations, including those implemented manually by a user and those target-specific and non-target-specific, are used to…
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…
The diverse world of machine learning applications has given rise to a plethora of algorithms and optimization methods, finely tuned to the specific regression or classification task at hand. We reduce the complexity of algorithm design for…
The efficiency of modern optimization methods, coupled with increasing computational resources, has led to the possibility of real-time optimization algorithms acting in safety critical roles. There is a considerable body of mathematical…
Verifying software correctness has always been an important and complicated task. Recently, formal proofs of critical properties of algorithms and even implementations are becoming practical. Currently, the most powerful automated proof…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
Traditional approaches for validating molecular simulations rely on making software open source and transparent, incorporating unit testing, and generally employing human oversight. We propose an approach that eliminates software errors…
Education in the practical applications of logic and proving such as the formal specification and verification of computer programs is substantially hampered by the fact that most time and effort that is invested in proving is actually…
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…
Automated software verification is a very active field of research which has made enormous progress both in theoretical and practical aspects. Recently, an important amount of research effort has been put into applying these techniques on…
We introduce a numerical framework to verify the finite step convergence of first-order methods for parametric convex quadratic optimization. We formulate the verification problem as a mathematical optimization problem where we maximize a…