**Identification of language:**

__Solutions:__

**You should know:**

Before seeing the solution please follow the previous chapter to clear the concept ** How to identify language**,

**Answer: **

In this language

has one infinite condition i.e. number of **b**** =** twice the number of **a**.

Now we will check push and pop will be cleared or not.

**1.** Push ‘**a****’** twice into the stack when we will get single ‘**a****’** at input tape because the number of b is twice the number a. To equalize the number of b and number of **a** at stack to make the operation easy we push ‘**2****a****’**when we will ‘**a****’** at the input.

**2.** Pop ‘**a**’ from the top of the stack whenever we will get ‘**b**’ at input tape. After completion of operation stack and input tape will be empty.

**Example:**

Let take a string **aabbbb**

Now push and pop is cleared.

So, this given language has one infinite comparison and push, pop is cleared, then it is **Deterministic Context-Free Language (DCFL)****.**

**You should know:**

Before seeing the solution please follow the previous chapter to clear the concept ** How to identify language**,

**Answer: **

This given language

But this comparison is finite because the range of **k** and **n** is finite i.e. **n, k ≤ 0**.

As you know that any language which has one or more comparison with finite range, is Regular Language.

All finite languages are Regular Language.

**You should know:**

Before seeing the solution please follow the previous chapter to clear the concept** **** How to identify language**,

**Answer:**

This given language

has more than one infinite comparison but not at a time, because

So, **it creates multiple copies of the stack for all comparisons**.

Now, this given language has more than one comparison but not at a time and it needs multiple copies of the stack.

So, it is a **Non-Deterministic Context-Free Language (NCFL)**

** **

**You should know:**

Before seeing the solution please follow the previous chapter to clear the concept ** How to identify language**,

**Answer:**

This language is similar to the above example **Example 1**

This given language

also has one infinite condition** n ≤ 5k**** **i.e. number of **a ≤ 5** times number of b.

So, that it has one infinite condition, and if we see properly push, pop is also cleared.

**This language is Deterministic Context-Free Language but not Regular.**

**You should know:**

Before seeing the solution please follow the previous chapter to clear the concept ** How to identify language**,

**Answer:**

We already discuss this type of language in the previous example like __Example 1__

In that case given language is similar to the previous example

We know **‘****∩****’ (Intersection) **and **AND**** **are the same**.**

So, this given language

has two infinite conditions but in between two conditions **Intersection (****‘∩’****)** operator is present. As we know the property of **Intersection (****‘∩’****) **is** **the same as **AND**** **i.e. if both conditions are true then the total condition will true.

So, this given language has two infinite conditions at a time because of **(****‘∩’****)**.

Any language with multiple conditions and if it is separated by **‘****∩****’ (Intersection) **or **AND**** **then this language is **Context Sensitive Language (CSL)**.

But in that case, we can think about this problem another way that if we notice the given language

Now we know from previous example ** Example 3** and

because it has two infinite comparisons at a time.