The questions are also attached in the uploaded file

………………………………………………………………………………………………………………………………………………..

• ALEX is the set of valid algebraic expressions recursively defined by:
• (1 pt) Let x and y be two words (both different than the empty string) and xy is their concatenation. Show that if x, y and xy are all in PALINDROME, then there is a word z such that x= zⁿ and y=z^m for some integers n and m.
• (1 pt) Let S={ab, bb} and T={ab, bb, bbb}. Show that S*≠T* but that S*⊂T*.
• (1 pt) Write the regular expression for the language of all strings, over alphabet {a, b}, that end in a double letter, i.e. ending in aa or bb but not ab or ba
• (1 pt) Draw Deterministic Finite Automata to accept the following sets of strings, over the alphabet {0,1}, that contain exactly four 0s (not necessarily consecutive zeros)

Rule 1: All polynomials are in ALEX

Rule 2: If f(x) and g(x) are in ALEX, then so are:

• (f(x))
• -(f(x))
• f(x) + g(x)
• f(x) – g(x)
• f(x)g(x)
• f(x)/g(x)
• f(x)^g(x)
• f(g(x))

Assuming that the rules seen in class recursively defining polynomials can be used here to prove x+2 and 3x are polynomials, show that (x + 2)^3x is in ALEX.

Extra Credit: (1 pt) Write the regular expression for the language of all strings, over alphabet {0, 1}, the set of all strings in which every pair of adjacent zeros appears before any pair of adjacent ones. Justify.

Do you need a similar assignment done for you from scratch? We have qualified writers to help you. We assure you an A+ quality paper that is free from plagiarism. Order now for an Amazing Discount!
Use Discount Code "Newclient" for a 15% Discount!

NB: We do not resell papers. Upon ordering, we do an original paper exclusively for you.