Show that if L is regular, so is L U {a}, for all a ∈ Σ by constructing an FSM.

Show that L = {w|w = a2n} is not regular, where Σ = {a}.
Prove that, if L is a regular language over the alphabet Σ=(0,1), then L': { ax | x E L } is also regular for any a E Σ
Question 2. Define σ: R2-R by σ(u,t)-(u+cosu, sinu, u), and let S be the image of σ. (1) Show that S is a ruled surface. (2) Give a quadratic equation for S, and show S is a quadric. (3) Show that S is an elliptic cylinder, so that a cross section of S perpendicular to the rulings is an ellipse. What are the lengths of its axes?
Question 2. Define σ: R2-R by σ(u,t)-(u+cosu, sinu, u), and let S be...
I know that there are non-regular languages, so that L? is regular, but all examples I can find are context-sensitive but not context free. In case there are none how do you prove it?
A Discrete mathematics question shows on the image, could you
please show the detailed procedures, thank you!
Given the following deterministic FSM M over the alphabet Σ- (0,13: 1 S1 S2 1 1 S3 (a) Give an English language description of L(M), the language recognised by M. (b) Add an error state (labelled X) to the diagram, and draw all transitions to it (c) Describe how to derive an FSM that accepts the complement of L(M) over the set ....
If L is a regular language, prove that the language {uv : u ∈L, v ∈LR} is also regular
Let Σ {0, 1, 2} Use the Pumping Lemma to show that the language L defined below is not regular L-(w: w Σ*, w is a palindrome} Note that a palindrome is a word, number, or other sequence of characters which reads the same backward as forward, such as mom or eye.
Which of the following is a method for showing that a language L is not regular? a) Constructing a finite state automaton recognizing L b) Showing that the opponent can always win the regular expression game for L. c) Showing that the relation L has infinitely many equivalence classes. d) Constructing a push-down automaton recognizing L
************Theory of Computing ***************** 1. Generate a regular expression of “all words over the alphabet Σ = {a b} that either begin with a and end with b OR begin with b and end in a.” Thus, the first few shortest words in this language are “ab” “ba” “aab” “baa” “abb” “bba” “aaab” etc. So, if a word begins with a it must in end b, and if it begins with b it must end in a. 2. Consider the...
6. Determine whether or not the following languages on Σ-(a) are regular (a) L = {an : n > 2, is a prime number) (b) L fa"n : n is not a prime number. (c) L-(an . Ti--k3 for some k 20} Tt . L={an : n = 2k for some k > 0} (e) L an: n is the product of two prime numbers). (f) L = {an : n is either prime or the product of two or...