DFA Minimization Algorithm + Example

Here we consider the problem of minimizing the number of states in a deterministic finite automaton (DFA). The key here is to identify pairs of states that are "distinguishable", in the sense that reading any string from both of them eventually will lead to an accept state in one case, and a non-accept state in the other case. Then we build the definition of distinguishable states recursively. We conclude with two examples of DFAs: one where no states can be removed, and another where multiple states can be removed. Timeline: 0:00 - Intro 0:30 - Goals of the Video 1:04 - Distinguishing States Example 4:07 - Distinguishing Strings Example 7:17 - Distinguishing States Definition 9:40 - DFA Minimization Example 1 15:35 - DFA Minimization Example 2 20:18 - Conclusion Thanks to the following supporters of the channel for helping support this video. If you want to contribute, links are below. Dolev Abuhazira, Josh Hibschman, Micah Wood, Morgan Jones, Patrik Keinonen, Simone Glinz, Tao Su, Timothy Gorden, unit220, Valentine Eben Easy Theory Website: https://www.easytheory.org Become a member: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg/join Donation (appears on streams): https://streamlabs.com/easytheory1/tip Paypal: https://paypal.me/easytheory Patreon: https://www.patreon.com/easytheory Discord: https://discord.gg/SD4U3hs Merch: Language Hierarchy Apparel: https://teespring.com/language-hierarchy?pid=2&cid=2122 Pumping Lemma Apparel: https://teespring.com/pumping-lemma-for-regular-lang If you like this content, please consider subscribing to my channel: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg?sub_confirmation=1 ▶SEND ME THEORY QUESTIONS◀ [email protected] ▶ABOUT ME◀ I am a professor of Computer Science, and am passionate about CS theory. I have taught many courses at several different universities, including several sections of undergraduate and graduate theory-level classes.