What's the meaning of Oblivious Turing Machine

Question

I really don't understand the the difference between OTM and Standard TM. Could any explain it for me? Thanks

Answer 1

A regular Turing Machine's transition function is a function $$\delta : Q \times \Gamma^k \rightarrow Q \times \Gamma^k \times \{\rightarrow, \leftarrow, \text{stay}\}^k$$ which means that it looks on its current state $q \in Q$, looks on a symbol $\in \Gamma$ on each of $k$ tapes, and based on that decides how to change its state, what symbol to write on each of the tapes, and where to go on each of the tapes.

In contrast, an Oblivious Turing Machine's transition function is a function $$\delta : Q \times \Gamma^k \rightarrow Q \times \Gamma^k$$ so it has no choice over where to go but still has a choice to change its state and write a new symbol on each of the tapes.

That means the same how an Oblivious Turing Machine defined in Computational Complexity: A Modern Approach, p. 49

Define a TM $M$ to be oblivious if its head movement does not depend on the input but only on the input length. That is, $M$ is oblivious if for every input $x \in \{0, 1\}^*$ and $i \in N$, the location of each of M’s heads at the $i$th step of execution on input $x$ is only a function of $|x|$ and $i$.

P.S. Another answer which claims "if it will accept input string $aabab$, it will also accept $babaa$, and indeed any other string of length $5$" is wrong.