Let A={+,x,a,b}. Show that (a*V ba)+ b is regular over A.

5. Find a closed form representation for the function defined recursively by f(0) = 5 and f(n+1)=2f(n)+4". Prove that your representation is correct using an inductive argument.

2.

I am trying to work with some generic search algorithms in a coding homework, and I am having trouble understanding some of it. Here are my questions:   1. For this linear search algorithm below I am trying to send an array of x and y cordinate points into it and search to see if a specific x, y point is in the array, but I don't know how to send the points into the linear search function. By the way, I am using a struct point type for the array of points and the point I am looking for. (The below code is an exact example from our teacher during a lecture.)   void* linearSearchG(void* key, void* arr, int size, int elemSize, int(*compare)(void* a, void* b)) {   for (int i = 0; i < size; i++) {   void* elementAddress = (char*)arr + i * elemSize; if (compare(elementAddress, key) == 0) return elementAddress; } return NULL; }     2. I forgot what this line of code specifically does: void* elementAddress = (char*)arr + i * elemSize;   I need to code this myself, so if you could explain…

How do I show that the following is regular?

Given the following recursively defined set S: Basis: 0 € S and 7 € S Recursive rule: if x ES and y = S, then: • x+yЄS x-yes Prove that every element in S is divisible by 7.

Let ∑ = {a, b, #} and L = { w | w cannot be written as t#s#t with s, t ∈ {a, b}*}.  Show that L is not regular.

The correct statements are: A set is countable iff it is either finite or countably infinite. The set of natural numbers is countable. The power set of the set of natural numbers is countable. For any Σ Ø, Σ* is countably infinite.