Let *k0* be an integer. A *k*-**tape offline Turing machine**
has k+1 doubly infinite tapes numbered from *0* to *k*.
Tape *0* is also called the **input tape**. Each tape has has
a **head**. At any moment, head *i* (*i=0,...,k*) scans a tape
cell in tape *i*. All tape cells contains the blank symbol
initially, except for the input word stored in tape *0*.
Initially, head *0* scans the first symbol of the input word, and
the state is *q _{0}* (start state).
There after, the machine makes transitions that
corresponds to executing some instruction from
a finite set called the

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