so i have this language
$$ L = \{x^{i} v^{j} z^{j+2} w^{k} v^{i+k} | i,j,k \ge 0 \}$$
i made this PDA for it .
states $ = \{q_0 ... q_5 , final\} $
alphabet $= \{ x,v,z,w \}$
stack alphabet $= \{ A , B , \bot \}$
$\bot$ is the end of the stack symbol
transition function and start state and final state in the graph
i have two questions :
- is the PDA correct? the idea is simple :
in q0 push A for each x seen
in q1 push B for each v seen
in q2 pop B for each z seen
q3 is for the +2 of z
in q4 push A for each w seen
in q5 pop A for each v
if you get to the end of the stack symbol go to the final state
my main concern is : did i get the epsilon transitions right
- is it possible to give a DPDA for it ? (it seems that if we had $i,j,k \ge 1$ then omitting red epsilon transitions from the above PDA gives us a DPDA . cannot we just some how get along with the condition $\ge0$)