Question

Build a TM that produces the lexicographically next binary string on input w (which is a binary string). The first few binary strings in the order are 0,1,00,01,10,11,000,001 The procedure for generating the next string is - If the input contain only 1 s and k of them, then next string is contains k+10 s. - Otherwise, find the first 0 from the right end. Change it to 1 , and change the remainder of string (all theway to the right end) to 0s. The python code for these two steps is below in the function next \# first few strings in the sequence s = 'o'; for i in range(30): print (s) s =next(s) If the TM gets an input of 10 , the output will be the next string in this ordering, 11 in this case. It might be helpful to bring the head back to the start of the output.

Answer 1

A Turing Machine (TM) can be built to produce the lexicographically next binary string based on the given input.

Step-by-step explanation:

A Turing Machine (TM) can be built to produce the lexicographically next binary string based on the given input. Here's how:

1. If the input contains only '1's and 'k' of them, the next string will contain 'k+1' '0's.
2. Otherwise, find the first '0' from the right end, change it to '1', and change the remaining characters to '0's.

Using the provided Python code s = '0'; for i in range(30): print(s); s = next(s), you can generate the next string in the lexicographic order. If the input is '10', the output will be '11'.