[Math] Blanks in the Tape of a Turing Machine

automataformal-languagesturing-machines

I used to have a lot of trouble with Turing Machines, primarily because I thought that in-between input symbols on the tape, one could have an arbitrary number of blanks, so every input would need to be delimited with start- and end-symbols, so the TM doesn't go reading an infinite number of blanks in search for more input symbols.

Is this true or not? Is it assumed that there are no blanks in-between input symbols on the tape?

Edit: moreover, when our TM reads in some input string, can we assume that there are no blanks in-between the symbols of our input string? Are there any conventions here?

Best Answer

In Turing Machines, there are two types of alphabet: input alphabet and tape alphabet. Input alphabet includes symbols for input, blank symbol does not belong to input alphabet. Tape alphabet includes input alphabet and blank symbol. In addition, it may be additional symbols(i.e for marking start and end of inputs). So, initially, there is no blank in-between input symbols on the tape. After a several steps, TM manipulates the input and may put blanks between input symbols according to its algorithm.