Question

Read the informal definition of the finite state transducer given in Exercise 1.24. Give the state diagram of an FST with the following behaviour. Its input and output alphabets are $\left\{0,1\right\}$ . Its output string is identical to the input string on the even positions but inverted on the odd positions. For example, on input 0000111 it should output 1010010 .

Short answer

In even positions output string is same as input string

In odd positions, output string is inverted

Step-by-step solution

Introduction 

Given alphabets for FST are $\left\{0,1\right\}$. It has the following behavior

Its output string is identical to the input string on the even positions.

Its output string is inverted on the odd positions.

So that the state diagram of that FST is

Explanation 

So, by this state diagram,

In even positions output string is same as input string

i.e. for input $0\to$output is also 0

for input $1\to$output is also 1

In odd positions, output string is inverted

i.e. for input $0\to$output is 1

for input $1\to$output is 0.