We start with a discussion on computational problems and algorithms. We define a generic form of decision problems, and then introduce deterministic finite automaton (DFA) as a basic decider. After having a few examples on the DFAs with discussions on their limitations, we introduce their probabilistic and quantum variants. We present a representative algorithm for each of these variants, followed by a discussion on the quantum advantages in finite automata settings. We shortly review the recent implementations of QFA algorithms on real quantum hardware.

The topic of the talk concerns an innovative approach in the preparation of data used for training of convolutional neural networks for segmentation of color images. The problem of selecting training data and acquiring enough of them, necessary to obtain a model with the highest possible predictive accuracy, is an important issue in the topic of neural networks. Incorrect approach to it can cause that even the best prepared network architecture will not be able to generate a model that will work with satisfactory accuracy.

Gilbert proposed an iterative algorithm for bounding the distance between a given point and a convex set. We apply the Gilbert's algorithm with a few modifications and simplifications to get an upper bound on the Hilbert-Schmidt distance between a given state and the set of separable states. While Hilbert-Schmidt distance does not form a proper entanglement measure, it can nevertheless be used as a very robust indicator of the amount of entanglement.