https://lucamarx.com/blog/ en A blog about automata theory luca@lucamarx.com (Luca Marx) http://www.rssboard.org/rss-specification bash-feedgen Wed, 01 Jul 2026 09:33:54 GMT https://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 program automata? What if we could just learn 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 marginalized by AI? We definitely need Marshall McLuhan's help. https://lucamarx.com/blog/2023/0403-chatgpt_mcluhan_and_the_end_of_the_world/ https://lucamarx.com/blog/2025/0609-the_tale_of_the_strange_coffee_machine/ Where I want to convince you that coffee vending machine are more interesting than they look. https://lucamarx.com/blog/2025/0609-the_tale_of_the_strange_coffee_machine/ https://lucamarx.com/blog/2025/1002-weighted_automata_and_parallelism/ Weighted automata have a peculiar kind of parallelism. In this post we will see how to exploit it to evaluate a function over many arguments at once, this will lead to a "poor-man's" version of Deutsch-Jozsa algorithm. https://lucamarx.com/blog/2025/1002-weighted_automata_and_parallelism/ https://lucamarx.com/blog/2025/1105-automatic_deutsch_jozsa_algorithm/ Last time we saw a parody of the Deutsch-Jozsa algorithm that used automata to evaluate a function over all of its arguments at once. Today I want to show you how it can be made more serious and how it compares to the true quantum algorithm. https://lucamarx.com/blog/2025/1105-automatic_deutsch_jozsa_algorithm/ https://lucamarx.com/blog/2025/1113-automatic_grover_algorithm/ Last time we devised a recipe to turn quantum algorithms into automata based ones and used it on the Deutsch-Jozsa algorithm. But why stop there? Let's automatize Grover's algorithm too. https://lucamarx.com/blog/2025/1113-automatic_grover_algorithm/ https://lucamarx.com/blog/2026/0525-power_series_and_quantum_states/ In the last few posts we saw a mysterious analogy between formal power series and quantum states, it's time to dig into it. https://lucamarx.com/blog/2026/0525-power_series_and_quantum_states/