feat: add Cslib/Computability/Languages/RegularLanguage.lean and associated changes #141
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@chenson2018: Looks like some linters have failed. How do I run them locally on my machine? |
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Thanks for the info. The linter failures should be fixed now. |
chenson2018
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eric-wieser
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Looks good to me now, minus the merge conflicts. |
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Rebase on top of the current |
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This patch proves the closure properties of regular languages under boolean operations. We first prove that
Language.IsRegular, which is defined in mathlib, can also be characterized using cslib's DFA and NFA. We then prove those closure properties usingCslib.DFA. The key idea is a product construction forDA, which allows us to prove that regular languages are closed under both union and intersection (calledaddandinfin Language). The definition ofDFA.mtris moved toDA.mtr, so that it can be applied toDAin general. Some miscellaneous properties aboutLanguageare also proved.The closure properties under concatenation and Kleene star will be proved later. They require some nontrivial work.
This PR depends on #135.