解释图灵机的计算

Question

I am having some trouble interpreting what this Turing machine actually does (ie, I am uncertain how to explain it in plain English).

I believe I have created the state diagram correctly using the transition table I was given (although not 100% on this either).

From what I can see this TM will halt in an accepting state (q2) whenever the input is of the form

(a || b || B)*Ba*c(a || b || c || B)* ,

that is any amount of a 's, b 's, and blanks (but no c 's), followed by at least one blank, any amount of a 's, and exactly one c . Anything can come after since we go left upon finding first c .

I suppose my question is

a) Is my work up to this point correct? and

b) Is there a more meaningful explanation of this Turing machine (ie a richer description than I wrote of the input that halts in (q2) ).

Answer 1

Some observations:

1. q0 reads left to right, doesn't change the tape, and stops when it hits c.
2. q1 reads left to right, swaps a and b, halts when it sees a B and turns around when it hits an a.
3. The only way to for the TM to halt is if
   • There is ac somewhere on the tape to the right of the initial tape position
   • In q1, the last pass from right to left sees only b and leaves only a between the first c and the rightmost B to the left of c.
4. q1 changes everything between the first c and the rightmost b to the left of that c to ab eventually

Given initial tape configuration >BxBycz, the machine will always halt in configuration >BxB(a^|y|)cz. It accepts any string that contains c.

Your state diagram disagrees with the table in that the table has the transition function defined so that f(q1, a) = (q0, b, L) and f(q1, b) = (q1, a, L), but your diagram shows f(q1, a) = (q1, a, L) and f(q1, b) = (q0, b, L).