Problem 1. From a language description to a PDA Show state diagrams of PDAs for the following languages: a. The set of strings over the alphabet {a, b} with twice as many a's as b's. Hint: in class, we showed a PDA when the number of a's is the same as the number ofb's, based on the idea of a tally. Can we use something similar in this case? b. tx are strings over the alphabet (a, b;wis a substring ofx Try to make your PDAs as simple and elegant as possible (do not convert from CFG to PDA). Name your states and provide a short description of what each state represents. Problem 1. From a language description to a PDA Show state diagrams of PDAs for the following languages: a. The set of strings over the alphabet {a, b} with twice as many a's as b's. Hint: in class, we showed a PDA when the number of a's is the same as the number ofb's, based on the idea of a tally. Can we use something similar in this case? b. tx are strings over the alphabet (a, b;wis a substring ofx Try to make your PDAs as simple and elegant as possible (do not convert from CFG to PDA). Name your states and provide a short description of what each state represents