Prerequisites: 

1)  Theory of Computation (CS F351) course.

2) Solve the following problem:

Consider a restricted model of a Deterministic Turing Machine (we call it DTM(1, 1)) which works in two phases. In the first phase, DTM(1, 1) continuously moves to the right, possibly scanning the cells, overwriting the cells, and changing states according to its transition function like a normal DTM, until it reaches the end of its input. Now phase 2 starts in which DTM(1, 1) continuously moves to the left, possibly scanning the cells, overwriting the cells, and changing states according to its transition function like a normal DTM, until it reaches the start of its input. Prove or disprove: 

The set of languages accepted by DTM(1, 1) is exactly the set of Regular languages.

References:

[1] J. E. Pin, Open Problems About Regular Languages, 35 Years Later, The Role of Theory