Transition to final state if the stack is not empty after reading all $\text{'}$b$\text{'}$s: $\backslash$delta $($q$\_(1),\backslash$epsi lon,A$)=($q$\_($f$),\backslash$epsi lon$)\backslash$delta $($q$\_(1),\backslash$epsi lon,Z$\_(0))=($q$\_($f$),$Z$\_(0))$ Reject if more $\text{'}$b$\text{'}$s are read than $\text{'}$a$\text{'}$s: If at any point a $\text{'}$b$\text{'}$ is read and the stack is empty $($other than Z$\_(0)),$ the input is rejected. Explanation of the DPDA Initial state q$\_(0)$ : The machine starts in state q$\_(0)$ and pushes an $\text{'}$A$\text{'}$ onto the stack for every $\text{'}$a$\text{'}$ read. State q$\_(1)$ : When a $\text{'}$b$\text{'}$ is read, it pops an $\text{'}$A$\text{'}$ from the stack and transitions to state q$\_(1).$ If more $\text{'}$b$\text{'}$s are read, it continues popping $\text{'}$A$\text{'}$s from the stack. Accepting state q$\_($f$)$ : After reading all input, if the stack still contains $\text{'}$A$\text{'}$s$,$ it transitions to q$\_($f$)$ and accepts.