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Feb 18, 2017 at 16:29 comment added PeterMcCoy I don't see where I asked a different question, it still is about state complexity of homomorphisms in general and in one specific case you disproved my conjecture but this did not answer my starting question yet.
Feb 18, 2017 at 16:21 comment added Yuval Filmus If you have a different question, please ask it separately. We can't answer a moving target on this site.
Feb 18, 2017 at 16:18 comment added PeterMcCoy Thank you for your counter-example in the general case, making the state complexity clear in this situation. I've forgot to edit the results of the discussion with D.W. in my question. That means what if the homomorphic images do not share the same prefix, since in your case the prefix of both images would be $0^{\min\{a,b\}}$
Feb 18, 2017 at 14:42 history answered Yuval Filmus CC BY-SA 3.0