I'm trying to construct a deterministic multi-tape turing machine for the following language in order to show that $L$ is in $DTIME(n)$:$$L = \{ www \mid w \in \{a,b\}^+ \}$$I'm not sure how to get started. Any hints would be appreciated.
Deterministic Multi-tape Turing Machine construction
turing machines;complexity classes
You could copy the input to 3 tapes, then move the heads on tapes 2 and 3 until they point to the same substring and on tape 3, the end of substring matches the end of string.The exact steps could be..   1. copy input 2. erase first symbol on tape two and first two symbols on tape three 3. go forward on all tapes until... 4. if one of the symbols is different than on other tapes, go back to the start of each tape and return to step 2 5. if tape three reaches end of input, you are done  