<p>To precisely de&#64257;ne the language A, we &#64257;rst de&#64257;ne the con

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<p>To precisely de&#64257;ne the language A, we &#64257;rst de&#64257;ne the context-free grammar G =(V, &#931;, R, S), where V = {S, T, X, Y },</p>
<p>&#931; = { a, b, c, . . . , z, +, &#8722;, &#8727;, /, (, ), $ },</p>
<p>(1)the starting variable is S, and the rules are</p>
<p>S &#8594; $T $</p>
<p>T &#8594; T +T | T -T | T *T | T /T | (T ) | X</p>
<p>X &#8594; Y | Y Y</p>
<p>Y &#8594; a | b | c | &#183; &#183; &#183; | z</p>
<p>&#160;</p>
<p>Note that you cannot use the algorithm in Lemma 2.21 to convert the CFG G into a PDAfor A since the resulting PDA will not satisfy the last four properties above. However,those properties ensure that the PDA M is essentially deterministic, so once you &#64257;gureout M, it will be easy to implement as a program. (Implementing a nondeterministicmachine is more di&#64259;cult since the program needs to check every branch in the tree ofcomputation.)</p>
<p>&#160;</p>

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