Let us begin with Turing Machine for a is less than b, a^{m}b^{n} where a=b or m=n.
Logic:
If machine reads anyone a from the input tape, then machine write X and if machine reads any b then machine write y;
a = X
b = Y
in the end, the machine must read Y, write Y, and move right as illustrated in the diagram(start to state 4).
After that, there are multiple b’s to enforce that b’s are larger in number and a’s are smaller in number.
Video Lecture with full of Animations
Accepted strings:
Such kind of strings should be accepted by Turing Machine.
e.g, abB, aabbbb, aaabbbbb,…..etc.
Rejected strings:
Such kind of strings should be rejected by Turing Machine.
e.g, ab, aab, aaabb,…..etc.
Read More Examples of Turing Machine
 Turing Machine to copy a string: with animations
 Turing Machine of numbers divisible by 3: with animations
 Turing machine for anbncn: with animations

Turing machine of two equal binary strings: with animations

Turing Machine to Accepts palindromes: with animations

Turing machine for a’s followed by b’s then c’s where the number of a’s multiplied by the number of b’s and equals to the number of c’s: with animations

Turing machine to Add two binary numbers: with animations
 Turing machine to Multiply two unary numbers: with animations
 Turing machine to Multiply two binary numbers: with animations
 Turing Machine for the complement of a string
 Turing Machine for the language of a^{n}b^{n} where a=b.
 Turing Machine for a is less than b, a^{m}b^{n} where a=b or m=n.

Turing machine for the language of all those string in which a is less than b