JFiZO - Zadanie 09.021

  1. L_1 \cup L_2
    • niech L_1 = L_{re1}
    • niech L_2 = L_{re2}
    • więc L_1 \cup L_2 = L_{re1 + re2}
  2. L_1 \cap L_2
    • niech L_1 = L(M_1)
    • niech L_2 = L(M_2)
    • niech L_1 \cap L_2 = L(M)
    • niech M_1 = (Q_1, \Sigma, \delta_1, q_1, F_1)
    • niech M_2 = (Q_2, \Sigma, \delta_2, q_2, F_2)
    • niech M = (Q, \Sigma, \delta, q_0, F)
      • niech Q = Q_1 x Q_2
      • niech \delta ( (q_1, q_2), a) = (\delta_1(q_1, a), \delta_2(q_2, a)), \delta(q_0, \epsilon) = (q_1, q_2)
      • niech F = (F_1, F_2)
  3. A^* - L
    • Automaty to DFA
    • niech A^* - L = L(M)
    • niech L = L( (Q, \Sigma, \delta, q_0, F))
    • wtedy M = (Q, \Sigma, \delta, q_0, Q - F)