Define a deterministic 1-band Turing machine with input and working alphabet = { _,0,1,2,3,4,5,6,7,8,9} (where "_" is to represent the blank symbol), which recognizes a character string (_0815_) enclosed in blanks. Assume that the read/write head of the Turing machine is positioned at the beginning directly on the last symbol before the blank (i.e. for the character string _0815_ on the5). The Turing machine should replace all digits except the leftmost one by blanks ("_"). If the string _0815_ was recognized, the first digit should be replaced by 1 , otherwise by 0. As syntax for the rules of the Turing machine please use the following definitions from the course:

- Each line should represent a tuple of the following form: " ".

- You can use any word or number for , e.g. "10", "a", "state1".

- Use "_" for the space (blank).

- is "l", "r" or "*" for "move left", "move right" or "no movement".

- "*" can be used in or as a placeholder for any symbol.

- More than one rule matches the input, the first one is used.

- "*" can be used in or for "no change".

- The final states of the machine are marked by the word "halt" in the name, e.g. "hold", "hold-accept".