Question

Show that if G is a CFG in Chomsky normal form, then for any string w is a member of L(G) of length n >=1, exactly 2n-1 steps are required for any derivation of w.

Answer #1

Theory of Computation Problem 3:
Let G be an arbitrary CFG (Context-free Grammer), and
let DG be the string-pushing
PDA(pushdown automata) for it. Let w be
some string of length n in L(G).
Suppose you know that the leftmost derivation of
w in G consists of m
substitutions. How many transitions would be in the corresponding
computation of DG for input string
w? Justify your answer
carefully!
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