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The following results are known.
* NFA to DFA: <math>2^n</math> states. This is the [[subset construction]] by [[Michael O. Rabin|Rabin]] and [[Dana Scott|Scott]],<ref name="RabinScott1959">{{cite journal|last1=Rabin|first1=M. O.|last2=Scott|first2=D.|title=Finite Automata and Their Decision Problems|journal=IBM Journal of Research and Development|volume=3|issue=2|year=1959|pages=114–125|issn=0018-8646|doi=10.1147/rd.32.0114}}</ref> proved optimal by [[Oleg Lupanov|Lupanov]].<ref>{{cite journal
| last = Lupanov
| first = Oleg B.
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