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Skip to content Toggle navigation Sign up Product Actions Automate any workflow Packages Host and manage packages Security Find and fix vulnerabilities Codespaces Instant dev environments Copilot Write better code with AI Code review Manage code changes Issues Plan and track work Discussions Collaborate outside of code Explore All features Documentation GitHub Skills Blog Solutions For Enterprise Teams Startups Education By Solution CI/CD & Automation DevOps DevSecOps Resources Customer Stories White papers, Ebooks, Webinars Partners Open Source GitHub Sponsors Fund open source developers The ReadME Project GitHub community articles Repositories Topics Trending Collections Pricing Sea...

Skip to content Toggle navigation Sign up Product Actions Automate any workflow Packages Host and manage packages Security Find and fix vulnerabilities Codespaces Instant dev environments Copilot Write better code with AI Code review Manage code changes Issues Plan and track work Discussions Collaborate outside of code Explore All features Documentation GitHub Skills Blog Solutions For Enterprise Teams Startups Education By Solution CI/CD & Automation DevOps DevSecOps Resources Customer Stories White papers, Ebooks, Webinars Partners Open Source GitHub Sponsors Fund open source developers The ReadME Project GitHub community articles Repositories Topics Trending Collections Pricing Sea...

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Skip to content Pravesh Koirala Language, Computers, and Philosophy .site-branding #masthead .entry-header Read my manifesto on Code as an alternative to Mathematics . Code for this article can be found on this Colab Notebook should you choose to follow along. Kalman filters are ingenius. If you have never heard of them, then a very intuitive (and arguably reductive) way to think about them is to consider them as a funnel where you pour information from multiple noisy sources to condense them into a single more accurate statistic. Do not worry if all this sounds vague. In moments, we’ll be stripping that statement into a more accessible example in hopes of furthering our intuition. It is best said early that there is no better tool to study and reason about Kalman Filters than Mathematics. But it is equally true that the underlying Mathematics of Kalman Filters is ...

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Given an alphabet Σ , recall that a regular language R is a certain subset of the free monoid M generated by Σ , which can be obtained by taking singleton subsets of Σ , and perform, in a finite number of steps, any of the three basic operations : taking union, string concatenation, and the Kleene star . The construction of a set like R is still possible without M being finitely generated free. Let M be a monoid, and 𝒮 M the set of all singleton subsets of M . Consider the closure ℛ M of S under the operations of union, product , and the formation of a submonoid of M . In other words, ℛ M is the smallest subset of M such that • ∅ ∈ ℛ M , • A , B ∈ ℛ M imply A ∪ B ∈ ℛ M , • A , B ∈ ℛ M imply A ⁢ B ∈ ℛ M , where A ⁢ B = { a ⁢ b ∣ a ∈ A , b ∈ B } , • A ∈ ℛ M implies A * ∈ ℛ M , where A * is the submonoid generated by A . Definition . A rational set ...