Answer: Finite automata

Question: What is the next array for aardvark? For tartans?

Answer:

  i  pattern[i]  next[i]
  0     a          -1
  1     a          -1
  2     r           1
  3     d           0
  4     v           0
  5     a          -1
  6     r           1
  7     k           0

  i  pattern[i]  next[i]
  0     t          -1
  1     a           0
  2     r           0
  3     t          -1
  4     a           0
  5     n           2
  6     s           0