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QUESTION: 1

Which of the following is called Bar-Hillel lemma?

Solution:

In automata theory, the pumping lemma for context free languages, also kmown as the Bar-Hillel lemma, represents a property of all context free languages.

QUESTION: 2

Which of the expressions correctly is an requirement of the pumping lemma for the context free languages?

Solution:

Let L be a CFL. Then there is an integer n so that for any u that belong to language L satisfying |t| >=n, there are strings u, v, w, x, y and z satisfying

t=uvwxy

|vx|>0

|vwx|<=n For any m>=0, uv^{n}wx^{n}y ∈ L

QUESTION: 3

Let L be a CFL. Then there is an integer n so that for any u that belong to language L satisfying

|t|>=n, there are strings u, v, w, x, y and z satisfying

t=uvwxy.

Let p be the number of variables in CNF form of the context free grammar. The value of n in terms of p :

Solution:

This inequation has been derived from derivation tree for t which must have height at least p+2(It has more than 2^{p} leaf nodes, and therefore its height is >p+1).

QUESTION: 4

Which of the following gives a positive result to the pumping lemma restrictions and requirements?

Solution:

A positive result to the pumping lemma shows that the language is a CFL and ist contradiction or negative result shows that the given language is not a Context Free language.

QUESTION: 5

Using pumping lemma, which of the following cannot be proved as ‘not a CFL’?

Solution:

There are few rules in C that are context dependent. For example, declaration of a variable before it can be used.

QUESTION: 6

State true or false:Statement: We cannot use Ogden’s lemma when pumping lemma fails.

Solution:

Although the pumping lemma provides some information about v and x that are pumped, it says little about the location of these substrings in the string t. It can be used whenever the pumping lemma fails. Example: {a^{p}b^{q}c^{r}d^{s}|p=0 or q=r=s}, etc.

QUESTION: 7

Which of the following cannot be filled in the blank below?

Statement: There are CFLs L1 nad L2 so that ___________is not a CFL.

Solution:

A set of context free language is closed under the following operations:

a) Union

b) Concatenation

c) Kleene

QUESTION: 8

The pumping lemma is often used to prove that a language is:

Solution:

The pumping lemma is often used to prove that a given language L is non-context-free, by showing that arbitrarily long strings s are in L that cannot be “pumped” without producing strings outside L.

QUESTION: 9

What is the pumping length of string of length x?

Solution:

There exists a property of all strings in the language that are of length p, where p is the constant-called the pumping length .For a finite language L, p is equal to the maximum string length in L plus 1.

QUESTION: 10

Which of the following does not obey pumping lemma for context free languages ?

Solution:

: Finite languages (which are regular hence context free ) obey pumping lemma where as unrestricted languages like recursive languages do not obey pumping lemma for context free languages.

### Pumping Lemma for Context-Free Languages

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