The context free grammar for the language \(L = \{a^{n}b^{m}c^{k} \mid k = |n - m|, n \geq 0, m \geq 0, k \geq 0\}\) is
\(S \rightarrow S_{1} \mid S_{3}, S_{1} \rightarrow aS_{1}c \mid S_{2} \mid \lambda, S_{2} \rightarrow aS_{2}b \mid \lambda, S_{3} \rightarrow aS_{3}b \mid S_{4} \mid \lambda, S_{4} \rightarrow bS_{4}c \mid \lambda\)
Split the language into two cases depending on whether \(n \geq m\) or \(m \geq n\).
If \(n \geq m\), the string is \(a^{n-m}(a^{m}b^{m})c^{n-m}\), generated by \(S_{1} \rightarrow aS_{1}c \mid S_{2}\) with \(S_{2} \rightarrow aS_{2}b \mid \lambda\).
If \(m \geq n\), the string is \((a^{n}b^{n})b^{m-n}c^{m-n}\), generated by \(S_{3} \rightarrow aS_{3}b \mid S_{4}\) with \(S_{4} \rightarrow bS_{4}c \mid \lambda\).
The two cases are alternatives, so the start rule must be \(S \rightarrow S_{1} \mid S_{3}\); concatenating \(S_{1}S_{3}\) would allow extra symbols, and the other grammars use wrong rules for \(S_{1}\).
Hence, \(S \rightarrow S_{1} \mid S_{3}, S_{1} \rightarrow aS_{1}c \mid S_{2} \mid \lambda, S_{2} \rightarrow aS_{2}b \mid \lambda, S_{3} \rightarrow aS_{3}b \mid S_{4} \mid \lambda, S_{4} \rightarrow bS_{4}c \mid \lambda\).
Similar Questions
The following Context-Free Grammar (CFG) :
S → aB | bA
A → a | as | bAA
B → b | bs | aBB
will generate
The context free grammar given by
\(S \to XYX\)
\(X \to aX \mid bX \mid \lambda\)
\(Y \to bbb\)
generates the language which is defined by regular expression :
A context free grammar for \(L = \{ w \mid n_{0}(w) \gt n_{1}(w) \}\) is given by :
If all the production rules have single non - terminal symbol on the left side, the grammar defined is :
Match the following :
List - I List - II a. Chomsky Normal form i. \(S \to b\,S\,S \mid a\,S \mid c\) b. Greibach Normal form ii. \(S \to a\,S\,b \mid ab\) c. S-grammar iii. \(S \to AS \mid a\)
\(A \to SA \mid b\)d. LL grammar iv. \(S \to a\,B\,S\,B\)
\(B \to b\)For the above specified passage, which of the following represent the grammar for the language accepted the machine?
Which of the folowing CFG(s) is/are in chomsky Normal form (All capital letters are variables & lower case are terminals)
A. S → ABC / AB
A → a
B → b
C → dB. X → RT / TR
T → t
R → XT / rC. P → qP / sQ
Q → r / sD. M → MN / MP
N → nm / n
P → pChoose the correct answer from the options given below:
Let G = (V, T, S, P) be a context-free grammar such that every one of its productions is of the form A → v, with |v| = K > 1. The derivation tree for any W ∈ L(G) has a height h such that
Important Questions from Context Free Grammars
- Which of the following Grammars is/are only Context Free?
A S $\rightarrow$ Ab
aS$\rightarrow$ aA
A$\rightarrow$ aB S $\rightarrow$ Ab
A $\rightarrow$ Sa
A $\rightarrow$ aC S $\rightarrow$ AS
S $\rightarrow$ aA
A$\rightarrow$ aD S $\rightarrow$ Ab
S $\rightarrow$ aA
A$\rightarrow$ aE S $\rightarrow$ Sb
A $\rightarrow$ Aa
A $\rightarrow$ $\varepsilon$
Choose the correct answer from the options given below: Which of the following grammars is (are)ambiguous ?
(1) S → SS | aSb | bSa |e(2) S → aSbS | bSaS |e
(3) S → aAB
A → bBb
B → A Ι eConsider the grammar,
G = S → abScB | e,
B→ bB | b.
What is the language generated by the given grammar ?
Consider the given grammar
S → Abc | adA → eS | Cr| ξ
C → f/p/ξ
Compute FIRST (A)Select the sentence which is meaningful and grammatically correct.
