Re: Top down parsing

In the book "Principles of compiler design, Aho Ullman" the
following exercise caught my attention. The grammar given is

S -> aSa | aa

It is quoted that a "top down parse with backtracking" can establish
the inputs with 2,4 or 8 a's but not 6 a's .... How is this possible ?

The trick lies in the statement that the production S->aSa is tried
first, a recursive descent parser will only work in this case for an
even no. of inputs (try constructing the parse tree and look at the
discrepancy found for strings of length n where n/2 is odd.)

.

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