Context Free Language-
Before you go through this article, make sure that you have gone through the previous article on Context Free Language.
We have discussed-
- Context free language is generated using a context free grammar.
- Each context free language is accepted by a Pushdown automaton.
In this article, we will discuss a decision algorithm of CFL.
Algorithm To Decide Whether CFL Is Empty Or Not-
If we can not derive any string of terminals from the given grammar, then its language is called as an Empty Language. L(G) = ϕ |
For a given CFG, there exists an algorithm to decide whether its language is empty L(G) = ϕ or not.
Algorithm-
- Remove all the useless symbols from the grammar.
- A useless symbol is one that does not derive any string of terminals.
- If the start symbol is found to be useless, then language is empty otherwise not.
RememberThe language generated from a CFG is non-empty iff the start symbol is generating. |
Example-
Consider the following grammar-
S → XY
X → AX
X → AA
A → a
Y → BY
Y → BB
B → b
Now, let us check whether language generated by this grammar is empty or not.
The given grammar can be written as-
S → aabb
X → aX
X → aa
A → a
Y → bY
Y → bb
B → b
Clearly,
- The start symbol generates at least one string (many more are possible).
- Therefore, start symbol is useful.
- Thus, language generated by the given grammar is non-empty.
L(G) ≠ ϕ |
NOTE-
If L(G) = { ∈ } i.e.
- If the language generated by a grammar contains only a null string,
- then it is considered as non-empty.
Next Article- Algorithm To Decide Whether CFL Is Finite
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