Pda For A-ib-jc-k Where J I K ~upd~ • Proven

Let's do clearly:

[ \beginaligned &(q_0, a, Z) \to (q_0, XZ) \ &(q_0, a, X) \to (q_0, XX) \ &(q_0, \epsilon, Z) \to (q_f, Z) \ &(q_0, \epsilon, X) \to (q_1, X) \ &(q_1, b, X) \to (q_1, \epsilon) \ &(q_1, \epsilon, Z) \to (q_2, Z) \ &(q_2, b, Z) \to (q_2, YZ) \ &(q_2, b, Y) \to (q_2, YY) \ &(q_2, \epsilon, Y) \to (q_3, Y) \ &(q_2, \epsilon, Z) \to (q_3, Z) \ &(q_3, c, Y) \to (q_3, \epsilon) \ &(q_3, \epsilon, Z) \to (q_f, Z) \endaligned ] pda for a-ib-jc-k where j i k

[ \beginaligned &\delta(q_0, a, Z_0) = (q_0, XZ_0) \ &\delta(q_0, a, X) = (q_0, XX) \ &\delta(q_0, \varepsilon, X) = (q_1, X) \ &\delta(q_0, \varepsilon, Z_0) = (q_1, Z_0) \ \ &\delta(q_1, c, Z_0) = (q_1, XZ_0) \ &\delta(q_1, c, X) = (q_1, XX) \ &\delta(q_1, \varepsilon, X) = (q_2, X) \ &\delta(q_1, \varepsilon, Z_0) = (q_2, Z_0) \ \ &\delta(q_2, b, X) = (q_2, \varepsilon) \ &\delta(q_2, \varepsilon, Z_0) = (q_3, Z_0) \endaligned ] Let's do clearly: [ \beginaligned &(q_0, a, Z)