https://lucamarx.com/blog/A blog about automata theoryhttp://www.rssboard.org/rss-specificationpython-feedgenenWed, 03 Jan 2024 14:28:50 +0000https://lucamarx.com/blog/2022/0207-automata_introduction/ Why are automata so interesting? Automata are so simple that they fit in many places and situations. https://lucamarx.com/blog/2022/0207-automata_introduction/https://lucamarx.com/blog/2022/0211-regular_expressions_brzozowski/ Regular expressions are an algebraic notation to describe regular languages. They can be converted into minimal deterministic finite automata with the elegant Brzozowski algorithm. https://lucamarx.com/blog/2022/0211-regular_expressions_brzozowski/https://lucamarx.com/blog/2022/0316-weighted_automata/ Automata can be generalized by adding weights to transitions. This way they can compute more complicated functions than just predicates. https://lucamarx.com/blog/2022/0316-weighted_automata/https://lucamarx.com/blog/2022/0323-spectral_learning/ How can we build a weighted automaton that does what we want it to do? Does there exist a high level language to <span class="underline">program</span> automata? What if we could just <span class="underline">learn</span> them? https://lucamarx.com/blog/2022/0323-spectral_learning/https://lucamarx.com/blog/2022/0331-automata_real_functions/ If we encode real numbers as strings then we can use spectral learning to model real functions as weighted automata. https://lucamarx.com/blog/2022/0331-automata_real_functions/https://lucamarx.com/blog/2022/0512-automata_and_matrix_product_states/ Looking closely at weighted automata we see that they resemble models used in quantum many body physics. https://lucamarx.com/blog/2022/0512-automata_and_matrix_product_states/https://lucamarx.com/blog/2022/0516-the_dmrg_algorithm/ The density matrix renormalization group algorithm is the workhorse for simulating one dimensional quantum systems on a lattice. The interesting thing is that it can be used also for machine learning tasks. https://lucamarx.com/blog/2022/0516-the_dmrg_algorithm/https://lucamarx.com/blog/2022/0523-dmrg_for_classification/ Having seen how DMRG works we apply it to some classification tasks. https://lucamarx.com/blog/2022/0523-dmrg_for_classification/https://lucamarx.com/blog/2023/0403-chatgpt_mcluhan_and_the_end_of_the_world/ Why is ChatGPT so unsettling? Are we as humans in danger of being <i>marginalized</i> by AI? We definitely need Marshall McLuhan's help. https://lucamarx.com/blog/2023/0403-chatgpt_mcluhan_and_the_end_of_the_world/