Regenerating a context free grammar

Question

I need to generate unambiguous grammar to access the language L= { a^i b^j c^k | i, j, k ≥ 0 , i = j or i = k }

What I already have is:

S : X | Y
X : TC
T : aTb | ԑ
C : cC | ԑ
Y : aYc | F
F : bF | ԑ

but this grammar is ambiguous, it can recognize the strings with equal number of a,b,c in two different ways. Is there any better suggestion to make it unambiguous?

Correct me if I'm wrong but this line `X : aXb | T` will result in strings of type `aaaacccbbbb` rather than `aaaabbbbccc`. Is that intentional? According to your language description it is not allowed. — PiotrWolkowski, Jun 02 '14 at 08:19
Yes You are right. I fixed the line, but the grammar is still an ambiguous grammar. — Lucy, Jun 02 '14 at 08:26

PiotrWolkowski · Accepted Answer · 2014-06-02T09:35:44.840

1

S : X | Y | Z
X : aXb | ԑ
Y : aYc | F
Z : Zc | X | ԑ
F : Fb | ԑ

The above has less rules and produces correct strings but I admit it's still ambiguous.

The grammar of the language L in the question can be divided into two sub-grammars producing following strings: a^i b^i c^j and a^i b^j c^j and intersection of these two will result in this kind of expressions: a^i b^i c^i. It can be proved that if intersection of two grammars produces this kind of expressions then the grammar is inherently ambiguous: http://en.wikipedia.org/wiki/Ambiguous_grammar#Inherently_ambiguous_languages

edited Jun 02 '14 at 09:35

answered Jun 02 '14 at 08:30

PiotrWolkowski

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`Z` isn't referenced by any other production here? – Damien_The_Unbeliever Jun 02 '14 at 08:32
Thanks for the answer, but I think the grammar can still derive aabbcc (an equal number of a,b,c) from Y and from Z as well. means its still ambiguous. – Lucy Jun 02 '14 at 08:43
I'll try to fix it. I popped it in first to fix the problem with incorrect strings but you already corrected it in your edit. – PiotrWolkowski Jun 02 '14 at 08:47
I think the language is inherently ambiguous, means it doesn't have un ambiguous grammar, am I right? – Lucy Jun 02 '14 at 09:15

score 0 · Answer 2 · edited May 23 '17 at 11:49

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I think this topics will help you Converting ambiguous grammar to unambiguous and Removing Ambiguity From Grammars

edited May 23 '17 at 11:49

Community

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answered Jun 02 '14 at 08:33

Karo

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Regenerating a context free grammar

2 Answers2