Linked Questions

6 votes
2 answers
9k views

Defining a context-free grammar for $\{w \in \{0, 1\}^* : \#_0(w) = \#_1(w)\}$ [duplicate]

I have a language where each string in the language has even amount of $0$'s as $1$'s (e.g., $0101$, $1010$, $1100$, $0011$, $10$ are all in the language). I was hoping to define a context-free ...
Andrew Reynolds's user avatar
0 votes
2 answers
3k views

Proving that a CFG generates a language [duplicate]

Is a suitable way to prove that any given CFG generates (or not) any given language to draw its total language tree? What if the tree is infinite? What would then be a better way to prove that a ...
ethane's user avatar
  • 264
-1 votes
1 answer
2k views

Proving correctness of a CFG by induction on length of strings generated [duplicate]

Consider the following grammar with starting symbol of $S$. $$S \rightarrow 0S11\;|\;S1\;|\;0$$ Let $L = \{0^i1^j:\; \ge 1\; and\; j \ge2i-2\}$ . Give a formal proof of the following claim : For all ...
Altaïr's user avatar
  • 49
0 votes
1 answer
886 views

How do I use induction to show that the language of a grammar is contained in a given set? [duplicate]

Given that I have the grammar $\qquad\displaystyle G_1 = (\{a, b, c, d\}, \{S, X, Y \}, S, \{S → XY, X → aXb, X → ab, Y → cYd, Y → cd\})$, how am I supposed to prove that $\qquad\displaystyle S(G1) ...
user3148942's user avatar
4 votes
2 answers
181 views

Gyorgy E. ReveszExercise 1.1: Show the grammar $G$ generates the language $L$ [duplicate]

The exercise says "Show that the grammar $G = \langle\{S\}, \{a, b\}, S, \{S \to \lambda, S \to aSb\}\rangle$ generates the language $L = \{a^i b^i \mid i = 0, 1, 2, \ldots\}$." Now, I'm new to ...
لويس العرب's user avatar
1 vote
0 answers
527 views

Proof of completeness for CFG having twice as many zeroes as ones [duplicate]

One possible CFG containing twice as many zeros as ones can be, S -> 0S0S1S | 0S1S0S | 1S0S0S | ϵ (This CFG is redundant but it will do the job. So I am not interested in the redundancy. Other ...
arman's user avatar
  • 136
2 votes
1 answer
175 views

How do I get and/or verify a formal Grammar for a given formal Language? [duplicate]

I was given the Language $L=\left \{ a^nb^na^nb^n |n\epsilon \mathbb{N} \right \}$ and I'm supposed to find a Grammar that generates that Language. After some trying and fiddling I found one that I ...
user2247969's user avatar
0 votes
0 answers
102 views

A context free grammar for the language of even-length non-palindromes [duplicate]

I am trying to find a context free grammar for the language $L = \{xy \mid |x|=|y| \text{ and } x≠y^R\}$ where $y^R$ is the reverse of string y and $x, y\in \{a,b\}^*$ . Here is a possible ...
mgus's user avatar
  • 171
0 votes
0 answers
68 views

Context free grammar of $ L=\{a^nb^m, n\neq 2m\} $ [duplicate]

I have to find the context-free grammar of this language: $ L=\{a^nb^m, n\neq 2m\} $ So I did: $ S \to a \mid aYb \mid \epsilon$ $Y \to aSb \mid X \mid \epsilon$ $X \to bX \mid \epsilon $ is it ...
Mah's user avatar
  • 1
0 votes
0 answers
67 views

How i can use Mathematical induction to prove CFG production? [duplicate]

If I have production $G_n$ $S \rightarrow A_i b_i \quad$ for $1 \le i \le n$ $A_i \rightarrow a_j A_i \mid a_j\quad$ for $1 \le i$ and $i \ne j$ Prove $G_n$ is sub-productions from $2n^2 - n$ ...
M.B's user avatar
  • 1
-1 votes
1 answer
63 views

Tools or techniques for studying the language a CFG produces? [duplicate]

When developing a CFG, I find that one can be confused about whether the grammar is correct, i.e. whether it recognizes only the required strings and not other strings. But this can be hard to see? ...
mavavilj's user avatar
  • 579
0 votes
0 answers
37 views

Context Free Grammar for a language [duplicate]

I have a language L = {a^n b^m c^k | n = m or m != k} When I was working the problem out this is what I got: S -> S1|S2 S1 -> AC A -> aAb|$\lambda$ C -> Cc |$\lambda$ S2 -> BD B -> aB|$\lambda$ D ->...
Andrew Mingst's user avatar
0 votes
0 answers
31 views

Grammar that generates a language with more "a" than "b" [duplicate]

I need to find a grammar that generates the language composed by all words that have more $a$ than $b$ given an alphabet $\{a,b\}$ I tried the following production rules: ...
user1868607's user avatar
  • 2,194
34 votes
4 answers
32k views

How to prove that a grammar is unambiguous?

My problem is how can I prove that a grammar is unambiguous? I have the following grammar: $$S → statement ∣ \mbox{if } expression \mbox{ then } S ∣ \mbox{if } expression \mbox{ then } S \mbox{ else } ...
user1594's user avatar
  • 541
28 votes
2 answers
47k views

How to prove that a language is context-free?

There are many techniques to prove that a language is not context-free, but how do I prove that a language is context-free? What techniques are there to prove this? Obviously, one way is to exhibit ...
D.W.'s user avatar
  • 160k

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