1. A <=r B, so we have a TM moving only right that can compute function f such that xe(A) iff f(x)eB.

2. B is regular, so we have DFA accepting it.

Now, you first compute the f(x) on TM and then check it on DFA. What is wrong?

]]>( every computable thing can be computed by a TM , but most of things can't be computed through DFA ) ]]>

suppose A = 0*. Our function f just counts the number (denote n) of 0(let's say with states) and concatenate it with n 1's. So B is {0

Let D

on input w:

compute f(w)

run f(w) on M

thanks… ]]>

But for the second question, I think we can say that B is Atm, and f builds a TM that runs a turing machine that decides A on x and returns the same.

All the conditions of the question hold in this case. ]]>

if A <=r B and B is regular then A is .

if A <=r B and A is regular then B is'nt .

Why ?

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