Create DFAs for the following language specifications.
1. All strings on Σ = {A, B, C} that contain each letter (A, B, and
C) at least once.

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Create DFAs for the following language specifications. 1. All strings on Σ = {A, B, C}...
Create Regular Expression for the following language: Σ = { 0, 1 } All strings that optionally start with 1111 and must end with 0000.
Create a DFA for the language L = {w ∈ {0, 1}∗ : w is a set of strings with 011 as a substring AND is not divisible by 3 }. First, create two separate DFAs for is a set of strings with 011 as a substring and not divisible by 3. Then, create the intersection between those DFAs by using the product construction. Show all your work. Hint: Use the least amount of states as possible.
Find a regular expression for the following language over the alphabet Σ = {a,b}. L = {strings that begin and end with a and contain bb}.
John Doe claims that the language L, of all strings over the alphabet Σ = { a, b } that contain an even number of occurrences of the letter ‘a’, is not a regular language. He offers the following “pumping lemma proof”. Explain what is wrong with the “proof” given below. “Pumping Lemma Proof” We assume that L is regular. Then, according to the pumping lemma, every long string in L (of length m or more) must be “pumpable”. We...
For each of the following, create an NFA that recognizes exactly the language described. (1) The set of binary strings with at most three 0s or at least four 1s. (2) The set of binary strings that contain the substring 000 and whose third to last digit is 1.
Give regular expressions for the following languages: (a) The language of all strings over {a,b} except the empty string. (b) The language of all strings over {a,b} that contain both bab and bba as substrings. (c)L k = {w ∈ {a,b} * | w contains a substring having 3 more b’s than a’s}. (d) The language of all strings over {a,b} that have a b in every odd position (first symbol is considered position 1; empty string should be accepted)...
Construct an DFA automaton that recognizes the following language of strings over the alphabet {a,b}: the set of all strings over alphabet {a,b} that contain aa, but do not contain aba.
1. Find expressions for each of the following. (Leave your answer as a mathematical expression rather than a number.) (a) The number of strings of 8 lower case letters (a-z) that do not contain any letter more than once. (b) The number of binary strings of length 10 that contain at most two Os. (c) The number of subsets of 11,2,,10 with three elements that contain at least one even number and at least one odd number. [Give brief justifications.]...
(a) Suppose we create strings from the alphabet {a, b}, for example, “baba”, “abab”, or “aaab”. How many strings of length 10 are there that have at least one of each letter in the alphabet? (b) Suppose we change to the alphabet {a, b, c}. Now how many strings of length 10 are there that have at least one of each letter in the alphabet?
(a) Suppose we create strings from the alphabet {a, b}, for example “baba”, “abab”, or “aaab”. How many strings of length 10 are there that have at least one of each letter in the alphabet? (b) Suppose we change to the alphabet {a, b, c}. Now how many strings of length 10 are there that have at least one of each letter in the alphabet?