I want to draw a Turing machine that checks if a string belongs to the language of the following grammar, The machine should simulate the behaviors of a parser, i.e., it starts with the start symbol and rewrites it to produce the given string and not just accept the same language as the CFG. Also, it is needed to provide an explanation that how that Turing machine works
For example: for the string “bb” the following things need to appear in the tape even if you wipe them or rewrite them afterward: X bY bbY bbepsilon bb.
there should be some configuration that shows each of the intermediate rewritings and the end string. and any finite string that can be given as input should either be able to parse it and accept or not be able to parse it and reject.
The Context-free grammar: the alphabet is : {a,b}
X->bY|a
Y->aX|bY|epsilon
Important note: I can draw a Turing machine that accepts the same language as the above CFG, The problem is that I need a Turing machine that simulates the parser behavior not just accepting the grammar as explained above.
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