Question $3$: $(\frac{1\mathrm{.}5}{5})$ : ACGT is an acronym for the four types of bases found in a DNA molecule: adenine $($A$),$ cytosine $($C$),$ guanine $($G$),$ and thymine $($T$).$ A DNA molecule consists of two strands wound around each other, with each strand held together by bonds between the bases.

Let's assume that we can use only the alphabet $=\{0,1\}$ for the input component of our TM$.$ Design a proper encoding for a Turing Machine that will receive as input a collection of the letters representing the bases of a DNA molecule. The TM will scan the tape and will validate the input. If the object entered agrees with the valid alphabet and encoding, the TM will start to process.

Note: you don't have to write the instruction for the Turing Machine! You just have to design the right encoding for the input of the problem at hand, so it can be fed to our TM; all parts of the definition of a TM should be considered. A possible formal definition of a Turing Machine is the following $7-$tuple:

$(Q,,,,q_0,q_{\text{a}\text{c}\text{c}\text{e}\text{p}\text{t}},q_{\text{r}\text{e}\text{j}\text{e}\text{c}\text{t}})$

where $Q,,$ are all finite sets and:

$Q$ is the set of states,

$$ is the input alphabet not containing the blank symbol $,$

$$ is the tape alphabet, where $in$ and $sube,$

$$:$QQ\{L,R\}$ is the transition function,

$q_0$inQ is the start state,

$q_{\text{a}\text{c}\text{o}\text{p}\text{p}\text{t}}$inQ is the accept state, and

$q_{\text{r}\text{e}\text{j}\text{e}\text{c}\text{t}}$inQ is the reject state, where $q_{\text{r}\text{e}\text{j}\text{e}\text{d}}{q}_{\text{a}\text{c}\text{c}\text{e}\text{p}\text{t}}$

In summary:

Provide the encoding for the input.

Give an example for the encoding you have created, by showing how the input tape would look like.

Write clearly any assumption you might make.