Related papers: Formalizing Size-Optimal Sorting Networks: Extract…

In recent work, we formalized the theory of optimal-size sorting networks with the goal of extracting a verified checker for the large-scale computer-generated proof that 25 comparisons are optimal when sorting 9 inputs, which required more…

This paper presents the benefits of formal modelling and verification techniques for self-stabilising distributed algorithms. An algorithm is studied, that takes a set of processes connected by a tree topology and converts it to a ring…

This paper settles the optimality of sorting networks given in The Art of Computer Programming vol. 3 more than 40 years ago. The book lists efficient sorting networks with n <= 16 inputs. In this paper we give general combinatorial…

In this paper a new method for checking the subsumption relation for the optimal-size sorting network problem is described. The new approach is based on creating a bipartite graph and modelling the subsumption test as the problem of…

This paper describes a computer-assisted non-existence proof of nine-input sorting networks consisting of 24 comparators, hence showing that the 25-comparator sorting network found by Floyd in 1964 is optimal. As a corollary, we obtain that…

This paper presents a short and simple proof of the Four-Color Theorem that can be utterly checkable by human mathematicians, without computer assistance. The new key idea that has allowed it and the global structure of the proof are…

We present a novel propositional proof tracing format that eliminates complex processing, thus enabling efficient (formal) proof checking. The benefits of this format are demonstrated by implementing a proof checker in C, which outperforms…

Formal verification of neural networks is an active topic of research, and recent advances have significantly increased the size of the networks that verification tools can handle. However, most methods are designed for verification of an…

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…

Machine learning models are increasingly deployed for critical decision-making tasks, making it important to verify that they do not contain gender or racial biases picked up from training data. Typical approaches to achieve fairness…

Acceptable but due to extensive usage of a computer rather unpleasant proof of the famous four color map problem of Francis Guthrie were settled eventually by W. Appel and K. Haken in 1976. Using the same method but shortening the proof…

In the last decade, a large body of work has emerged on robustness of neural networks, i.e., checking if the decision remains unchanged when the input is slightly perturbed. However, most of these approaches ignore the confidence of a…

We describe a formal correctness proof of RANKING, an online algorithm for online bipartite matching. An outcome of our formalisation is that it shows that there is a gap in all combinatorial proofs of the algorithm. Filling that gap…

In [J. Combin. Theory Ser. B 70 (1997), 2-44] we gave a simplified proof of the Four-Color Theorem. The proof is computer-assisted in the sense that for two lemmas in the article we did not give proofs, and instead asserted that we have…

This notes explains how standard algorithms that construct sorting networks have been formalised and proved correct in the Coq proof assistant using the SSReflect extension.

We give a near-linear time 4-coloring algorithm for planar graphs, improving on the previous quadratic time algorithm by Robertson et al. from 1996. Such an algorithm cannot be achieved by the known proofs of the Four Color Theorem (4CT).…

A formal proof has not been found for the four color theorem since 1852 when Francis Guthrie first conjectured the four color theorem. Why? A bad idea, we think, directed people to a rough road. Using a similar method to that for the formal…

We develop the first (to the best of our knowledge) provably correct neural networks for a precise computational task, with the proof of correctness generated by an automated verification algorithm without any human input. Prior work on…

Formalizing mathematical proofs using computerized verification languages like Lean 4 has the potential to significantly impact the field of mathematics, it offers prominent capabilities for advancing mathematical reasoning. However,…

Local certification is a distributed mechanism enabling the nodes of a network to check the correctness of the current configuration, thanks to small pieces of information called certificates. For many classic global properties, like…