Turing Machines
I'm reading a book on Languages & Automata and I'm not understanding Turing Machines. I've taught myself about DFA's NFA's and Pushdown Automata without any problems. Can someone please explain what this is doing?
B = {w#w|w ∈ {0, 1}*}
The following figure contains several snapshots of Ml 's tape while it is computing in stages 2 and 3 when started on input 011000#011000.
Thanks alot!
Turing machine is a hypothetical machine with a tape where symbols are stored. It can have multiple heads that can read symbols from the tape or write symbols to the tape.
Now your grammar says B = {w#w|w ∈ {0, 1}*}, that is any string of the form "w#w", where w is any combination of 0's and 1's or none at all. So let's say w = 011000 for this particular example. The resulting string will be 011000#011000 and your turing machine will be verifying if it follows this grammar.
Your turing machine has one head in this case. It starts at the beginning of string. Reads the first character which is 0. Mark it "x": meaning I've read this. Then goes immediately after the # and checks if what it just read is matching. In this case it's 0 as well so it marks it as matching "x". It then goes back to previous position and does the same for next character. It keeps doing this until it reaches #. When it reads hash or #, it checks for the end of the string and if it is the end of string, it accepts this string saying yes this follows the given grammar.