problem 2 (35 points). give the state diagram of an npda that accepts l = {a i b j c k | i, j, k ∈ n, i = j or i = k}

The PDA should accept the language {a^ib^jc^k|i, j, k ∈ N, i = j or i = k}.It is important to note that this language is not regular, because a^ib^ic^i can be used to demonstrate that it is not regular.

The NPDA is shown in the image below. ImageTransitions and States:We can now use the PDA to show how the language can be accepted.Start with a push of Z0 onto the stack for each string. The PDA has the following transitions:δ(q0, a, Z0) = {(q1, A)}δ(q1, b, A) = {(q2, ε)}δ(q0, a, Z0) = {(q1, A)}δ(q1, c, A) = {(q3, ε)}δ(q0, b, Z0) = {(q4, B)}δ(q4, c, B) = {(q3, ε)}As a result, we should read the input symbols from left to right and follow the rules. The NPDA will be approved if all strings are accepted and the stack is clear.Final State:We get (q3, ε, ε) as the final state after processing the whole input string, where q3 is the only state left. This implies that the language is approved. This is a brief summary of the NPDA state diagram that accepts l = {a i b j c k | i, j, k ∈ n, i = j or i = k}.

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