Classroom Management with Technology

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Formal languages and automata theory
Li Fan
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Pumping Lemma

• Let L be a regular set. Then there is a constant
  n such that if z is any word in L, and zgtn, we
  may write zuvw in such a way that uvltn,
  vgt1, and for all igt0, u(vi)w is in L.
  Furthermore, n is no greater than the number of
  states of the smallest FA accepting L.

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Exercise

• The set L0(i2) i is an integer, igt1,
  which consists of all strings of 0s whose length
  is a perfect square, is not regular.
• Prove that L (an)(bk) n gt k and ngt0 is
  not regular.

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Which of the following languages are regular sets?

• 0(2n) ngt1
• (0m)(1n)(0(mn)) mgt1 and ngt1
• 0n n is a prime
• The set of all strings that do not have three
  consecutive 0s

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• The set of all strings with an equal number of
  0s and 1s
• x x in (01), and xxR xR is x written
  backward for example, (011)R110.
• xwxR x,w in (01).

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Thank you