Final answer:
A Turing machine cannot write the blank symbol on its tape.
Step-by-step explanation:
A Turing machine is a hypothetical device that processes symbols on an infinite tape according to a set of rules. The tape is divided into cells, and each cell can contain a symbol. The machine can read and write symbols on the tape as it moves along it. However, the blank symbol, usually denoted as a blank or an empty cell, cannot be written by a Turing machine. The tape is initially blank except for the input data, and the machine can only change existing symbols or write new symbols other than the blank symbol.
The question is whether a Turing machine can ever write the blank symbol on its tape. The formal definition of a Turing machine includes a set of symbols that it can write, which may or may not include the blank symbol. The blank symbol is typically used to represent an empty space on the tape that has not been written on.
Whether a Turing machine can write the blank symbol depends on the specific rules defined for the machine. However, in a general Turing machine, it is indeed possible for the machine to write a blank symbol to signify a position on the tape that doesn't hold any meaningful data.