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Argosy University/ Phoniex University/
Nov-2005 - Oct-2011
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Phoniex University
Oct-2001 - Nov-2016
Convert the CFG G4 given in Exercise 2.1 to an equivalent PDA, using the procedure given in Theorem 2.20
Exercise 2.1
Recall the CFG G4 that we gave in Example 2.4. For convenience, let’s rename its variables with single letters as follows.
E → E + T | T
T → T x F | F
F → (E) | a
Give parse trees and derivations for each string
a. a
b. a+a
c. a+a+a
d. ((a))
EXAMPLE 2.4
Consider grammar G4 = (V, Σ, R,(EXPR)

The two strings a+axa and (a+a)xa can be generated with grammar G4. The parse trees are shown in the following figure.

Theorem 2.20
A language is context free if and only if some pushdown automaton recognizes it.
Â
Hel-----------lo -----------Sir-----------/Ma-----------dam-----------Tha-----------nk -----------You----------- fo-----------r u-----------sin-----------g o-----------ur -----------web-----------sit-----------e a-----------nd -----------acq-----------uis-----------iti-----------on -----------of -----------my -----------pos-----------ted----------- so-----------lut-----------ion-----------.Pl-----------eas-----------e p-----------ing----------- me----------- on-----------cha-----------t I----------- am----------- on-----------lin-----------e o-----------r i-----------nbo-----------x m-----------e a----------- me-----------ssa-----------ge -----------I w-----------ill----------- be-----------