Comments on: How do you determine if a dfa is minimal
http://ask.metafilter.com/89328/How-do-you-determine-if-a-dfa-is-minimal/
Comments on Ask MetaFilter post How do you determine if a dfa is minimalSun, 20 Apr 2008 13:11:41 -0800Sun, 20 Apr 2008 13:11:41 -0800en-ushttp://blogs.law.harvard.edu/tech/rss60Question: How do you determine if a dfa is minimal
http://ask.metafilter.com/89328/How-do-you-determine-if-a-dfa-is-minimal
Is there an elegant algorithm to determine if a dfa is minimal? Obviously you can minimize a dfa and then check to see if the result is isomorphic to the original. Is there another way?post:ask.metafilter.com,2008:site.89328Sun, 20 Apr 2008 12:19:10 -0800rdrdfafiniteautomatadeterministicminimalalgorithmBy: b1tr0t
http://ask.metafilter.com/89328/How-do-you-determine-if-a-dfa-is-minimal#1312779
Did you try <a href="http://www.google.com/search?q=minimal+dfa">google</a>?comment:ask.metafilter.com,2008:site.89328-1312779Sun, 20 Apr 2008 13:11:41 -0800b1tr0tBy: rdr
http://ask.metafilter.com/89328/How-do-you-determine-if-a-dfa-is-minimal#1312800
That's not what I asked. I'm not asking how to build a minimal dfa. I'm asking if there's a way to test if a dfa is minimal.comment:ask.metafilter.com,2008:site.89328-1312800Sun, 20 Apr 2008 13:30:43 -0800rdrBy: zixyer
http://ask.metafilter.com/89328/How-do-you-determine-if-a-dfa-is-minimal#1312830
It seems like all you have to check for is unreachable states and equivalent states. If there aren't any of either, the DFA is minimal.<br>
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You can check for equivalent states by looking at the transition function. If delta(<em>q</em>, <em>a</em>) = delta(<em>r</em>, <em>a</em>) for all <em>a</em> in the alphabet and two states <em>q</em> and <em>r</em>, the states are equivalent.<br>
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Unreachable states are ones that have no path from the initial state.comment:ask.metafilter.com,2008:site.89328-1312830Sun, 20 Apr 2008 14:14:59 -0800zixyerBy: rdr
http://ask.metafilter.com/89328/How-do-you-determine-if-a-dfa-is-minimal#1312852
Thanks. Once I read your answer I can see how your answer is implied by how subset construction terminates.comment:ask.metafilter.com,2008:site.89328-1312852Sun, 20 Apr 2008 14:42:59 -0800rdr