Draw the transition diagrams for push-down automata for the following languages. Give direct constructions, not conversions from CFGS, and give a brief description in English of your strategy for each problem. (a) {a'b'c* : 2i = \j – k|} (b) {w e {a, b}* : na(w) = 2n,(w)}

1. Convert the following regular grammar into a Finite Automata S➜X XXXIXY Y➜yylyz 2-22 12 2. Convert the previous problem to a regular expression. 3. Write a grammar that generates an even number of X's.

Can you please help me with parts E beause I am really really struggling.

Question 2 c) Give a regular expression for the following regular languages, assuming the alphabet is Σ := {0, 1}. I. The set of all strings, when viewed as binary representation of integers, that are divisible by 2. II. The set of all strings containing 00. III. Give a closed-form regular expression for the set of all string not containing consecutive 00.

Draw the transition diagrams for push-down automata for the following languages. Give direct constructions, not conversions from CFGS, and give a brief description in English of your strategy for each problem. (a) {a*b'c* : 2i = k or i = j+1} (b) {w e {a, b}* : na(w) = ns(w) and for every prefix v of w, we have na(v) > no(v)}