Let $M$ be a Turing Machine Transducer that computes a function $f$:$NN$ where $N=$ set of

positive integers written in unary notation.

$M$

a$.$ Give an instantaneous description trace of $M$ when the input is $w=111.$ What is the

output?

b$.$ What is the output when the input is $w=11?$ You do not have to give an instantaneous

description trace.

c$.$ Give a simple description of $f(n).$ Justify your answer.

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