##### Reference no: EM13699454

You need to prepare the finite automata and draw the machine diagram.

Part A- Give state diagram of DFA recognizing the following languages, alphabet S = {0, 1}:

1. {w | w contain the substring 01001}

2. {w | w contain at least two 1s and one 0}

Part B- Give state diagram of NFA recognizing the following languages, alphabet S = {0, 1}:

1. {w | w contain the substring 01001}

2. {w | w contain at least two 1s and one 0}

3. Construct DFA that accepts the set of strings on S = {0, 1} that consisting all the strings with precisely one 0

4. Construct DFA that accepts the set of strings on S = {0, 1} that consisting all the strings with at least one 0

5. Use induction proof, and prove that: a binary tree of height n has at most 2nleaves. Note: a binary tree is a tree in which no parent can have more than two children.

6. How cardinality of infinite sets is measured? Provide couple of closure properties of countable sets.

I cannot seem to get this to work for some reason could somebody provide me a code to compare and test? You have to satisfy the requirements specific in the instruction.