NPTEL IIT Guwahati

Since the string w gets modified during simulation (in step 2), the grammar G has to remember it, so that it can reproduced once M enters a final state. So, G is constructed such that it generates two copies of a representation of some string w

and then simulates the behaviour of the TM M on one copy, preserving the other. If M accepts, by entering a final state, then G transforms the second copy to a terminal string; otherwise G doesnot transform the second copy to a terminal string.

Let = , for some k >=1

Construction of G is given below.

N =
The production in P are
1. Sq₀T
2. T [a_i, a_i]T for all i =1, 2 , ... , k
3. T R
4. R [, B ] R
5. R


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	Since the string w gets modified during simulation (in step 2), the grammar G has to remember it, so that it can reproduced once M enters a final state. So, G is constructed such that it generates two copies of a representation of some string w and then simulates the behaviour of the TM M on one copy, preserving the other. If M accepts, by entering a final state, then G transforms the second copy to a terminal string; otherwise G doesnot transform the second copy to a terminal string. Let = , for some k >=1 Construction of G is given below. N = The production in P are Sq₀T T [a_i, a_i]T for all i =1, 2 , ... , k T R R [, B ] R R

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