turning machine &pumpping lemma

Turing machines use input alphabet {a,b} and tape alphabet {a,b,#}. first,need to Write, in table form, a Turing machine that accepts the input string aaaaa and crashes for every other input string. secondly,On a single line, write down a string over {a,b} that represents your Turing machine from first question in the Code Word Language (CWL) then, How many different strings in CWL represent this exact same Turing machine? • These strings must all represent identical Turing machines, not just Turing machines that are equivalent in the sense that they always give the same result. • You may assume that strings in CWL represent each Turing machine table row exactly once. another one is to explain how to construct, for each n ∈ N, a Turing machine Mn that accepts the input string a ^n and crashes for every other input string. Recall from lectures that the language CWL is regular. But CWL contains many strings that represent Turing machines that are either invalid or useless. Let GOOD-TM be the language of all strings in CWL that represent Turing machines that (i) are valid, and (ii) accept at least one string. For example, if you have done part (b) correctly, the string you constructed there should belong to GOOD-TM. (e) Give a string in GOOD-TM that has the property that, if at least one ‘a’ is inserted at the very start of the string, the resulting string is no longer in GOOD-TM. Use the Pumping Lemma for Regular Languages to show that GOOD-TM is not regular. FOR BONUS MARKS: determine, with proof, whether or not GOOD-TM is context-free.