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 B. X → RT / TR C. P → qP / sQ D. M → MN / MP Choose the correct answer from the options given below:
A → a
B → b
C → d
T → t
R → XT / r
Q → r / s
N → nm / n
P → p
B only
A context-free grammar is in Chomsky Normal Form (CNF) when every production has one of only two shapes: a variable deriving exactly two variables (A → BC) or a variable deriving exactly one terminal (A → a). (S → ε is allowed only for the start symbol when ε is in the language.) Each grammar is checked production by production.
Step 1 — Grammar A: S → ABC has three variables on the right side, which CNF does not allow. Grammar A is not in CNF even though S → AB, A → a, B → b and C → d are fine.
Step 2 — Grammar B: X → RT and X → TR are two-variable bodies; T → t is a single terminal; R → XT is a two-variable body and R → r is a single terminal. Every production fits, so Grammar B is in CNF.
Step 3 — Grammar C: P → qP and P → sQ mix a terminal with a variable (Greibach-style), which is not allowed in CNF. Grammar C is not in CNF.
Step 4 — Grammar D: M → MN, M → MP, N → n and P → p are fine, but N → nm has two terminals on the right side, so Grammar D is not in CNF.
Therefore only Grammar B qualifies; any choice including A, C or D (such as the pairs with A or D, or C alone) contains a grammar that breaks the CNF shape rules.
B only option is correct.
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. \(S \to a\,B\,S\,B\)
\(B \to b\)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
For the above specified passage, which of the following represent the grammar for the language accepted the machine?
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.
