__Identify the language category:__

__You should know:__

Before we see the solution of all given languages please follow previous chapters and examples: ** How to identify language**,

__Solutions:__

**Answer:**

This given same language is already discussed in __Example 3__** **

This language has two infinite comparisons ‘**a**’ & ‘**b**’ and ‘**b**’ & ‘**c**’.

So, more than one infinite comparison is always **Context-Sensitive Language** (**CSL**).

**For more details visit to see** ** Example 3**.

**Answer:**

It is clear that given language has three infinite comparisons at a time i.e. ‘**a**’ & ‘**b**’ and ‘**b**’ & ‘**c**’ and ‘**c**’ &‘**d**’.

And we know very well that more than one infinite comparison only possible with **Linear Bounded Automata** and language is **Context-Sensitive language**.

** **

To clear the basic concept of language identification **please follow the previous chapter:** ** How to identify language**.

**Answer:**

And

So, as we know any language with **non-linear power **is only possible by **Linear Bounded Automata** and language is **Context-Sensitive language**.

**For more details see chapter:**** **** Language Identification: Important points**.

** **

**Answer:**

This given language has two comparisons i.e. number of ‘**a**’ with the number of ‘**b**’ and number of ‘**c**’ with the number of ‘**d**’ but this two comparison is not at a time.

First, we compare the number of ‘**a**’ with the number of ‘**b**’ after finished it then we will check the number of ‘**c**’ with the number of ‘**d**’.

In this case, it is very easy to check both comparisons because push and pop are cleared i.e. by a single use of stack we can solve this problem.

Push all ‘**a**’s and pop every time when ‘**b**’ will come so, the stack will be empty after deleting all ‘**a**’s by ‘**b**’s because of the **number of ‘****a****’ = number of ‘****b****’**.

Now, after completed first operation stack is empty, we will start the second one.

Push all ‘**c**’s and pop every time when ‘**d**’ will come so, stack will be empty after deleting all ‘**c**’s by ‘**d**’s because of the **number of ‘****c****’ = number of ‘****d****’**.

As an **example**,

We can write the string as: aaa bbb ccc ddd

Because push and pop are cleared so, this language is **Deterministic Context-Free Language (DCFL).**

**Answer:**

This language is the same as previous **Example 4**** **

Just only difference is an alteration of power **m** and **n**.

So, it has two infinite comparisons but not at a time and push, pop is cleared.

**For details concept please follow the previous example:** **Example 4**.