Luca Marxhttps://lucamarx.com/blog/A blog about automata theoryhttp://www.rssboard.org/rss-specificationpython-feedgenenThu, 04 Jul 2024 09:34:34 +0000An Introduction to Automatahttps://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/Regular Expressions & Brzozowski Algorithmhttps://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/Weighted Automatahttps://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/Spectral Learninghttps://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/Automata & Real Functionshttps://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/Automata & Matrix Product Stateshttps://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/The DMRG Algorithmhttps://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/DMRG for Classificationhttps://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/ChatGPT, Marshall McLuhan & the end of the worldhttps://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/