Can you describe an algorithm that given two context-free grammars G1 and G2 outputs YES if and only if every string generated by G1 is also generated by G2. (I.e., output YES exactly when the set of strings generated by G1 is a subset of the set of strings generated by G2.)

2. What is the TG corresponding to the language of strings, over alphabet {a, b}, that are composed exactly of odd repetition of the substring ab, i.e. sample strings of this language are ab, ababab, ababab, etc.

Consider the language L of strings over the alphabet Σ = {a, b} which contain an equal number of a’s and b’s, and the set of b’s is consecutive in the string, e.g., ab, abba, aabb, abbbaa, aaabbbbbaa, etc. Note that ε ∈ L for completeness (0 number of a’s is equal to 0 number of b’s, which are also consecutive). Show that this language is context-free by giving a context-free grammar. Please make sure to test the answers onhttps://web.stanford.edu/class/archive/cs/cs103/cs103.1156/tools/cfg/

on A language L is called slithy if it contains at least two strings and has the following property: For every two strings x, y in L such that |x|< lyl, the string obtained by taking the first letter of y and inserting it at the start of x is also in L. For example, if L contains aaa and baaba, then it must also contain the string baaa. Prove by contradiction that every slithy language contains two strings of the same length.