Linked Questions

22
votes
1answer
5k views

How to show that L = L(G)?

Specifying formal languages by giving formal grammars is a frequent task: we need grammars not only to describe languages, but also to parse them, or even do proper science. In all cases, it is ...
7
votes
2answers
3k views

Inherent ambiguity of the language $L_2 = \{a^nb^mc^m \;|\; m,n \geq 1\}\cup \{a^nb^nc^m \;|\; m,n \geq 1\}$

I went through a question asking me to choose the inherently ambiguous language among a set of options. $$L_1 = \{a^nb^mc^md^n \;|\; m,n \geq 1\}\cup \{a^nb^nc^md^m \;|\; m,n \geq 1\}$$ $$and$$ $$L_2 ...
2
votes
2answers
5k views

How to show that given language is unambiguous

Given following grammar: $$ \begin{align} S \rightarrow &A1B \\ A \rightarrow & 0A \mid \varepsilon \\ B \rightarrow & 0B \mid 1B \mid \varepsilon \\ \end{align} $$ How can I show that ...
6
votes
4answers
723 views

What is the number of expressions containing n pairs of matching brackets with nesting limit?

I know the answer without nesting limit is the Catalan number. My question is, specifically, is there a recurrence relation that gives the number of expression containing $n$ pairs of matching ...
2
votes
1answer
1k views

Finding a unambiguous grammar

As an exercise we were supposed to find a grammar $G$ that generates language $L(G) = \{w \in \{a,b\}^* \mid |w|_a = |w|_b\}$. That was not so hard, I found a grammar which I think is correct: $S \...
2
votes
1answer
882 views

Unambiguity of Reverse Polish Notation

Lets say I have given following grammar which generates arithmetic expressions in reverse polish notation: $G=({E},{a,+,*},P,E)$ $P={ E \rightarrow EE+ | EE* | a }$ I know this grammar is ...
1
vote
1answer
387 views

How to check ambiguity of a specific grammar

Giving the following Grammar: S → ^ | SaSMSM | SMSaSM | SMSMSa M → b | c ^ means eopsilon. How can i check whether its ambgious or not? My intuition is that ...
0
votes
0answers
764 views

Show that any LL(k) grammar is unambiguous

I am confused on several areas of this. First, this is so obvious I am finding it hard to prove. Second, what are some definitions, axioms, or lemmas of an ll(k) grammar that I can use to build up a ...
0
votes
2answers
268 views

Grammar ambiguous or not?

So I've been struggling for the past hour with $G=(\{S\},\{a,b\},P,S)$ with productions $S\to aaSb | abSbS | \varepsilon$. I need to prove whether this grammar is ambiguous or not. Thus far I think it ...
0
votes
1answer
210 views

It has been asked to prove that a grammar is unambiguous which seem ambiguous to me

S->aAB A->bBb B->A|epsilon It seems that the string abbbb can be derived by using more than one ways. After using the starting production and the ...
1
vote
0answers
236 views

Given a context free grammar, prove if the grammar is ambiguous

Here is a context free grammar that I have been given for practice: Grammar $G = (V,\Sigma,R,S)$ where $V$ is $\{S,A,B,a,b,c\}$ and $\Sigma$ is $\{a,b,c\}$. $R$ has the following rules: $$\begin{...
-2
votes
1answer
119 views

Find an unambiguous grammar [closed]

S → aS | aSbS | (empty) where the alphabet is {a,b} in other words, the set of strings where any prefix has at least as many 'a's as 'b's.