Trace the execution of the language-recognition algorithm described in the previoussection for each of the following strings, and show the contents of the stack at each step.
a. a$a
b. ab$ab
c. ab$a
d. ab$ba
(Stack contents are listed from top to bottom.)
a.
aStack: a
inLanguage: true
stackTop: a
aStack:
The while loop exits because we are at the end of the string.
inLanguage is true and aStack is empty, so a$a is in the language.
?
b.
aStack: a
aStack: b a
inLanguage: true
stackTop: b
aStack: a
ch: $
ch: a
stackTop != ch, so inLanguageis set to false.
The while loop exits because inLanguage is false.
inLanguage is false, so ab$ab is not in the language.
c.
aStack: a
aStack: b a
inLanguage: true
stackTop: b
aStack: a
ch: $
ch: a
stackTop != ch, so inLanguage is set to false.
The while loop exits because inLanguage is false.
inLanguage is false, so ab$a is not in the language.
d.
aStack: a
aStack: b a
inLanguage: true
stackTop: b
aStack: a
ch: $
ch: b
stackTop == ch
stackTop: a
aStack:
ch: a
stackTop == ch
The while loop exits because we are at the end of the string.
inLanguage is true and aStack is empty, so ab$ba is in the language.
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