# Build PDA for a language with unknown input alphabet

$$L_1 ,L_2$$ are regular language. We form a new language $$L_{12}$$ as follows: $$L_{12}=\left \{ w_1\cdot w_2|w_1\in L_1\wedge w_2\in L_2\wedge|w_1|=|w_2| \right \}$$

In this exersice I am not given any alphabet and I’m required to build PDA for $$L_{12}$$, but by definition $$M=\left \{Q,\sum,\Gamma ,\delta ,q_0,-|,F\right\}$$ and I don’t have any alphabet to work with.By intuition if the alphabet is similiar can effect the solution than if it wasn’t similiar.