We introduce a new automaton on a word p, sequence of letters taken in an alphabet , that we call factor oracle. This automaton is acyclic, recognizes at least the factors of p, has m + 1 states and a linear number of transitions. We give an on-line construction algorithm of the factor oracle. The tight links between this structure and the suux automaton allows us to introduce a second structur...

A fundamental task in data science is the discovery, description, and identification of any symmetries present data. We developed a deep learning methodology for simultaneous discovery multiple non-trivial continuous across an entire labeled dataset. The symmetry transformations corresponding generators are modeled with fully connected neural networks trained specially constructed loss function...