Related papers: Recognising the small Ree groups in their natural …

In constructive recognition of a representation of a Classical group $G$, much attention has been paid to the natural representation as well as to generic (Black Box) algorithms that treat all representations uniformly. There are…

Let Omega be a quasisimple classical group in its natural representation over a finite vector space V, and let Delta be its normaliser in the general linear group. We construct the projection from Delta to Delta/Omega and provide fast,…

We employ techniques of machine-learning, exemplified by support vector machines and neural classifiers, to initiate the study of whether AI can "learn" algebraic structures. Using finite groups and finite rings as a concrete playground, we…

We introduce an approach based on moving frames for polygon recognition and symmetry detection. We present detailed algorithms for recognition of polygons modulo the special Euclidean, Euclidean, equi-affine, skewed-affine and similarity…

Let $G$ be a finite group given as input by its multiplication table. For a subset $S$ of $G$ and an element $g\in G$ the Cayley Group Membership Problem (denoted CGM) is to check if $g$ belongs to the subgroup generated by $S$. While this…

The integration of large language models (LLMs) into peer review raises a concern beyond authorship and detection: the potential cascading automation of the entire editorial process. As reviews become partially or fully machine-generated,…

Endowing machines with abstract reasoning ability has been a long-term research topic in artificial intelligence. Raven's Progressive Matrix (RPM) is widely used to probe abstract visual reasoning in machine intelligence, where models will…

We propose an algorithm that test membership for regular expressions and show that the algorithm is correct. This algorithm is written in the style of a sequent proof system. The advantage of this algorithm over traditional ones is that the…

It has been found that many networks display community structure -- groups of vertices within which connections are dense but between which they are sparser -- and highly sensitive computer algorithms have in recent years been developed for…

We develop a practical algorithm to decide whether a finitely generated subgroup of a solvable algebraic group $G$ is arithmetic. This incorporates a procedure to compute a generating set of an arithmetic subgroup of $G$. We also provide a…

In the context of Higman embeddings of recursive groups into finitely presented groups we suggest an algorithm which uses Higman operations to explicitly constructs the specific recursively enumerable sets of integer sequences arising…

Many methods for the verification of complex computer systems require the existence of a tractable mathematical abstraction of the system, often in the form of an automaton. In reality, however, such a model is hard to come up with, in…

Retrieval-Augmented Generation (RAG) enables Large Language Models (LLMs) to generate grounded responses by leveraging external knowledge databases without altering model parameters. Although the absence of weight tuning prevents leakage…

Regular expression inference (REI) is a supervised machine learning and program synthesis problem that takes a cost metric for regular expressions, and positive and negative examples of strings as input. It outputs a regular expression that…

A standard method for finding a rational number from its values modulo a collection of primes is to determine its value modulo the product of the primes via Chinese remaindering, and then use Farey sequences for rational reconstruction.…

In this paper an algorithm is given to determine all possible structurally different linearly conjugate realizations of a given kinetic polynomial system. The solution is based on the iterative search for constrained dense realizations…

We consider whether given a simple, finite description of a group in the form of an algorithm, it is possible to algorithmically determine if the corresponding group has some specified property or not. When there is such an algorithm, we…

We develop a penalized likelihood estimation framework to estimate the structure of Gaussian Bayesian networks from observational data. In contrast to recent methods which accelerate the learning problem by restricting the search space, our…

This paper describes an efficient algorithm REx for generating symbolic rules from artificial neural network (ANN). Classification rules are sought in many areas from automatic knowledge acquisition to data mining and ANN rule extraction.…

For each family of finite classical groups, and their associated simple quotients, we provide an explicit presentation on a specific generating set of size at most 8. Since there exist efficient algorithms to construct this generating set…