DFA Minimization

Here we show how to minimize a DFA. The idea is to consider all "groups" of states that can be "equivalent" to each other in terms of accepting a string (e.g., a state that is non-final and a final state cannot be equivalent, because one accepts a string and the other doesn't). Then, we further refine the groups until it is not possible to refine them any more (which must happen at some point because at worst, every state is in its own group). Then, the "minimized" DFA is just one state for each group, and transitions between the groups as defined in the given DFA (since each state within a group is equivalent to each other one).

#easytheory #nfa #dfa #gate #gateconcept #theoryofcomputing #turingmachine #nfatoregex #cfg #pda #undecidable #ricestheorem

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▶ADDITIONAL QUESTIONS◀
1. Would this process work for NFAs?
2. Can you give an explicit runtime on the algorithm?

▶SEND ME THEORY QUESTIONS◀
ryan.e.dougherty@icloud.com

▶ABOUT ME◀
I am a professor of Computer Science, and am passionate about CS theory. I have taught over 12 courses at two different universities, including several sections of undergraduate and graduate theory-level classes.