Write out a detailed program for the computation in considering the language $\{a^nb^n\}$. We described a laborious method by which this language can be accepted by a Turing machine with one tape. Using a two-tape machine makes the job much easier. Assume that an initial string $a^nb^m$ is written on tape $1$ at the beginning of the computation. We then read all the $a’s$, we match the $b’s$ on tape $1$ against the copied $a’s$ on tape $2$. This way, we can determine whether there are an equal number of $a’s$ and $b’s$ without repeated back-and-forth movement of the read-write head.
