Given a modified type of turning machine where the next step is determined as followed:

$ \delta = Q\times \Gamma^* \implies Q\times \Gamma \times \{L,R\}$

where the next step of the machine is determined by the current state and whatever written on the tape up to the current point.

For example: if the tape content is $ a\_ab\_$ $ a$ , and the head is on the left $ , then the next step is determined by the state and the word $ a\_ab\_$ $ .

- How can I prove that unrecognized languages can be recognized with these types of machines?
- Do those machines contradict the Churchâ€“Turing thesis?

Informative answer would be really appreciated as I’m finding it hard to understand this subject specifically. Thanks in advance