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marks ] Suppose = { 0 , 1 } , Q = { q 1 , q 2 , q 3 } , q 0

marks] Suppose ={0,1},Q={q1,q2,q3},q0=q1 and FO? with
FQ. How many possible unique finite automata are there? Use counting
techniques and do not try to list them, as there are just too many.
[6 marks] Design 2 different specific finite automata that could potentially
satisfy restrictions in the previous question. Give them first as state dia-
grams. Then give their formal descriptions. If working with others, make
your automata different from theirs.
[3 marks] Give examples of 3 strings of length at least 8 accepted from
each of your automata from the previous question, and so give 6 total strings.
[2 mark] What are the longest substring(s) that have repeated instances
in your 3 strings in the previous question for your last machine?
[3 marks] Design a finite automata in the form of a state diagram that
recognizes the language contains at least three 1s.
[8 marks](Problem 1.31, p.88) For any language A, let AR={wR|winA}.
Show that if A is regular, so is AR.(Hint: consider Exercise 1.11, pg 85)
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