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1. Write a regular expression that captures the set of strings composed of a, b, and c, where any string uses at most two of the three letters (for example, abbab is a valid string, or bccbb, or ccacaa, but not abccba; strings that contain only one of the three letters are also fine). 2. G ive a non-deterministic finite automaton that captures the regular expression from 3. Using the construction described in class, give a deterministic version of the automa- 4. Repeat the previous three steps for strings composed of a, b, c, and d, where above. Show the automaton in graphical form ton. You only need to show the transition table. any string uses at most three of the four letters

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