\text { Problem } 1 \text { (20): Let } L=\left\{\mathbf{w} \mid \mathbf{w} \in\{\mathbf{a}, \boldsymbol{b}\}^{*} \text { and } \mathbf{w} \text { has twice as many } \boldsymbol{d} \text {

's than } \boldsymbol{b} \text { 's }\right\} \text { . } (a) Design a CFG to generate L (b) Convert the CFG to Chomsky Normal Form (CNF) (c) Design a PDA to accept L