2.3 context free grammars and languages

Context Free
Grammars and
Languages
-Sampath Kumar S,
AP/CSE, SECE

Definition of CFG
A context-free grammar (CFG) consisting of a finite
set of grammar rules is a quadruple G= (N, T, P,
S) where
 N is a set of Non-Terminal symbols.
 T is a set of Terminals where N ∩ T = NULL.
 P is a set of Production rules, P: N → (N ∪ T)*
 S is the Start symbol.
11/21/2017
Sampath Kumar S, AP/CSE, SECE
2

Example
 The grammar
G= ({A}, {a, b, c}, P, A), P : A → aA, A → abc.
 The grammar
G=({S}, {a, b}, P, S), P: S → aSa, S → bSb, S → ε
 The grammar
G=({S, F}, {0, 1}, P, S), P: S → 00S | 11F, F → 00F | ε
11/21/20173

Problems to discuss:
52. What is language of CFG G=({A,B}, {a,b}, P, A)
where P: A → Ba, B → b.
53. Construct the CFG for Regular Expression (0+1)*.
54. Construct the CFG for defining a palindrome over
{a, b}.
55. Construct the CFG for the set of strings with equal
number of a’s and b’s.
56. Construct the CFG for the language L(G)={anb2n
where n>1}.
11/21/20174

Problems to discuss:
57. Construct the CFG for the language containing
all string of different 1st and last symbol over Σ =
{0,1}.
58. Give CFG for R.E (a+b)*cc(a+b)*.
59. What is language of CFG G=({S,C}, {a,b},P,S)
where P: S → aCa, C → aCa|b.
60. What is language of CFG G=({S}, {0,1},P,S)
where P: S → 0S1 | ε.
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Answers:
52. L(G) = {ab}
53. P = { S → 0S | 1S |ε }
54. P = { S → aSb | bSa | a | b |ε }
55. P = { S → SaSbS | SbSaS |ε }
56. P = { S → aSbb |abb }
57. P = { S → 0A1 | 1A0 , A → 0A | 1A |ε }
58. P = { S → AccA, A → aA | bA |ε }
59. L(G) = {anban where n>1}
60. L(G) = {0n1n where n>1}
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11/21/2017
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நன்றி
11/21/2017
10

2.3 context free grammars and languages

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