Question

Show a pushdown machine that will accept each of the following language

{anbmcmdn}m, n > 0

Answer 1

Explanation:

I flow 4 Scenario While Drawing the pushdown machine They are

3 for {anbmcmdn}m, n > 0

Final Scenario is for {anbmcmdn}m, n >= 0

• Scenario-1: m = 0 – In this Scenario, the input language will be of the form {ancn}. In this Scenario, keep on push a’s into the stack until we encounter with c. On receiving c check if the top of the stack is a, then pop it (a) from the stack. Pop a’s until all the c's of the input string are processed. If we reach to the end of the input string and stack becomes empty, then reach to final state i.e. accept the input string else move to the dead state.
• Scenario-2: n = 0 – In this Scenario, the input string will be of the form {bmcm }.In this Scenario, keep on push b’s into the stack until we encounter with c. On receiving c check if the top of the stack is b, then pop it (b) from the stack. Keep on pop b’s until all the c’s of the input string are processed. If we reach to the end of the input string and stack becomes empty, then reach to final state i.e. accept the input string else move to the dead state.
• Scenario-3: m, n>0 – In this Scenario the input string will be of the form {anbmcmdn }. In this Scenario, keep on push a’s and b's into the stack until we encounter with c. On receiving c check if the top of the stack is b, then pop it (b) from the stack. Keep on pop b’s until all the c’s of the input string are processed. Then on receiving d check if the top of the stack is a, then pop it (a) from the stack. Pop a’s until all the d’s of the input string are processed. If we reach to the end of input string and stack becomes empty, then reach to final state i.e. accept the input string else move to dead state.

This case for {anbmcmdn}m, n >= 0 if you not requred eleminate it.

• Scenario-4: m = 0, n = 0 – In this case the input string will be empty. Therefore directly jump to the final state.