Pushdown Automaton: CFL and the pumping lemma
Pushdown Automaton: CFL and the pumping lemma
Pushdown Automaton: CFL and the pumping lemma
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Proof – condition 3<br />
S<br />
S<br />
R<br />
R<br />
R<br />
x<br />
u v R y z<br />
u<br />
z<br />
v<br />
Replacing <strong>the</strong> smaller by<br />
<strong>the</strong> larger repeatedly<br />
generates <strong>the</strong> string<br />
uv i xy i z at each i>0.<br />
x<br />
y<br />
Replacing <strong>the</strong> larger by<br />
<strong>the</strong> smaller generates<br />
<strong>the</strong> string uxz or uv i xy i z<br />
where i=0.<br />
Therefore, for all i0, w i =uv i xy i z is also in L<br />
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