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I have a PTM with following transition:

$\delta(Z_0, \square , 0) = \delta(Z_0, \square , L, R)$,

$\delta(Z_0, \square , 1) = \delta(Z_0, \square , R, R)$

Suppose that this PTM executes n steps. What is the probability that the head has moved k steps to the right on the work tape (in total, i.e., k is the difference between moves to the right and moves to the left) ?

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1 Answer 1

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It seems to me as first thought, it is the summation of all moves i to R, j to L where
( i+j = n) AND (i - j = k) which leads to
i =(n+k) /2

Assuming the prob of each step of the walk is indep. from the current position (I can't read the probs u r writing, the 2nd parameter is appearing as a square). So, it would be something like

Pij= (PR ^ i) * (PL ^ j)

Ps

(I'm talking probability, I do not have a fresh memory of Probabilistic Turing m/cs at the moment)

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