Draw a DFA that accepts all binary strings of length 4 modulo 7.

Design a DFA with 2 states that accepts the language of all binary numbers that are divisible by 3. Demonstrate it with a two-state DFA and a proof that the accepted language is precisely binary strings representing numbers divisible by 3. Otherwise, prove that such a two-state DFA is impossible.
For ∑ = {a, b}, construct a dfa that accepts the set consisting of all strings with exactly one a
Give a DFA over {a,b} that accepts all strings containing a total of exactly 4 'a's (and any number of 'b's). For each state in your automaton, give a brief description of the strings associated with that state.
For ∑ = {a, b}, construct a dfa that accepts the set consisting of all strings with at least one b and exactly two a’s
Consider the ternary number system. Draw a state diagram for a DFA that accepts ternary strings that are not divisible by nine. What is the corresponding regular expression?
Design a DFA that accepts the set of all strings with 3 consecutive zeros at anywhere?
Draw a state diagram for a DFA that accepts any binary string (e.g.,0101000) that ends with three or more consecutive zeroes.
2. a. Draw a NFA that accepts all strings over Σ = {?, ?} that either end in ?? or contain the substring ??. b. Then convert the NFA in the previous exercise to a DFA
Draw a DFA which accepts the following language over the alphabet of {0,1}: the set of all strings such that there are two consecutive 0s or the number of 1s is not divisible by 5. Your DFA must handle all intput strings in {0,1}*. (Hint: look at solution of previous question)
Draw a DFA which accepts the following language over the alphabet of {0,1}: the set of all strings such that there are no consecutive 0s, and the number of 1s is divisible by 5. Your DFA must handle all intput strings in {0,1}*. Here is a way to approach the problem: First focus only building the DFA which accepts the language: As you build your DFA, label your states with an explanation of what the state actually represents in terms...