## formal languages – How to say if this grammar is LL(1)?

I need some help with understanding if a grammar is $$LL(1)$$ or not.

begin{align} S rightarrow AB\ A rightarrow a mid varepsilon \ B rightarrow bCd\ C rightarrow c mid varepsilon end{align}

I have computed the first and follow sets and I’ve tried to use $$LL(1)$$ definition, but I don’t know how to answer it.

## Is this an LL(1) grammar? How to solve First – Follow conflict?

im trying to check if this grammar is LL(1).

S -> L = R
L -> * L | id
R -> L | R + R | num

As you can see there is a Left recursion on R production. So i remove that and what i get is:

S -> L = R
L -> * L | id
R -> L R’ | num R’
R’ -> + R R’ | ε

Now the problem that i have is that First and Follow set of R’ rule have a common non-terminal (“+”) and also FIRST(R) and FOLLOW(R’) has a common non-terminal.
So i wonder how to create the parsing table if there’s this conflict. My question is: is there a way to solve this problem or simply this isn’t an LL(1) grammar?

Thanks.

## Parser – grammar still not clear after removing left recursion LL (1)

I have the following grammar, there is no epsilon derivation problem. I can only see the left recursion:

``````S -> a b S
S -> S a b
S -> c d
S -> a d
``````

In production number 2 there is another recursion that I removed and received:

``````S -> a b S F
S -> c d F
S -> a d F
F -> a b F | EPSILON
``````

But is it still not clear?

## Define nullable symbols and the first sentence of a grammar

I am practicing for an upcoming exam and am stumbled upon by a review problem. The problem gives the following grammar:

$$S rightarrow AB$$
$$A rightarrow epsilon | a | (T)$$
$$T rightarrow T, S | S$$
$$B rightarrow b$$

As far as I can tell, the only nullable symbol is $$A$$. It is the only non-terminal whose production contains the zero symbol $$epsilon$$. I do not think so $$S$$, that includes $$A$$ is a nullable symbol in its production, since the same production also contains $$B$$which is not a nullable symbol, and both $$A$$ and $$B$$ should be nullable for zero $$S$$ also be nullable. Is $$A$$ really the only nullable symbol in this grammar, or am I misinformed?

As far as the first sentence is concerned, I honestly only have problems following my professor's notes to create the first sentence. Could someone help here or point me to a good resource for it?

Thank you all.

## Language of context sensitive grammar – Computer Science Stack Exchange

I have the following context sensitive grammar:

begin {align *} & S to xSy mid a mid b \ & Xa to aa \ & Xb to bb \ & Y to a end {align *}

I know what it does because it always ends $$a$$ and is preceded by 3 $$a$$s or 3 $$b$$s. I'm just not sure how to write that in sentence notation and would appreciate any help. Would it be something like that?
$$L = {a ^ n, b ^ m mid n ge 1, 0

## Automata – context-free grammar for words of odd length

I have to write a CFG that has length strings, is divided by a b in the middle, and which are a before the b It's a language about {a, b}

I wrote the following grammar:

`````` S-> AbC
A -> BaBaBA | epsilon
B -> bB | epsilon
C -> aC | bC | a | b
``````

This grammar should ensure the even number of a and be divided by b. How do I make sure the length is odd?
Does this grammar ensure that b is in the middle?
Any help is appreciated!

## What is the best way to improve your English grammar skills?

All valuable contributions. Thanks a lot.

I don't think I can do good grammar when I watch or read films and so on. It will improve word flow, but for grammar it seems like I should go the dry way.

When I write in my mother tongue, the words flow like a river, smoothly, but when I write in English, I get blocks. Heavy. Sometimes I write in my mother tongue and then convert to English, but it seems to be an intellectual exercise. Needs a lot of coffee.

Learning grammar in English is like learning a programming language. Hard work for a perfectionist writer. But I should make it. I like to give my readers only decent pieces.

## regular languages ​​- Let 𝐺 = (𝑉, Σ, 𝑆, 𝑃) be a CFG. How is it possible to derive a grammar that generates 𝐿 (𝐺) +?

To let $$𝐺 = (𝑉, Σ, 𝑆, 𝑃)$$ be a CFG. How is it possible to derive a grammar that generates $$𝐿 (𝐺) ^ +$$?

1. $$𝐴 → 𝑆𝐵$$ e $$𝐵 → 𝑆𝐵 | 𝜀$$ for new variables $$𝐴$$ e $$𝐵$$.
2. $$𝐴 → 𝑆𝐴 | 𝜀$$ for a new variable $$𝐴$$.
3. $$𝐴 → 𝐵𝐵$$ e $$𝐵 → 𝑆 | 𝜀$$ per new variable $$𝐴$$ e $$𝐵$$.

My ideas are either Answer 1 or Answer 2, but I can't understand which one is the right answer.