# Questions tagged [formal-grammars]

Questions about formal grammars, generative descriptions of formal languages.

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### How to eliminate ambiguity of the follwing CFG?

Consider the following CFG: $S\to AED | F \\ A \to Aa | a\\ B \to Bb | b\\ C \to Cc | c\\ D \to Dd | d\\ E \to bEc | bc\\ F \to aFd | BC$ The CFG produces $a^*bbb...ccc...d^*$ (equal number of b,...
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### Proof that the grammar is LL(2)

I am given the following grammar: $S \rightarrow AabAba \\ A \rightarrow a | \epsilon$ and I have to prove it is LL(2). I know what LL(k) means - one can choose a production based on k characters ...
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### Why can't exhaustive search parsing stop after |w| + 1 derivations?

If my grammar does not have productions of the form $A\rightarrow\lambda$ and $A\rightarrow B$ for some variables $A$ and $B$ then I know that each step in the derivation must involve an increase in ...
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### How to prove prove $L(G) = \{~w\in\{a,b\}^*~|~\#_aw= \#_bw\}$ for my CFG $G$?

For language $L = \{ x \in \{a,b\}^* \mid \#_a x = \#_b x \}$, I came up with the following CFG: $$S \rightarrow aSbS \mid bSaS \mid \varepsilon.$$ It can be easily shown that it is correct (quick ...
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### Context-Free Grammar from this language

I'm having difficulties with an exercise in a theoretical CS class. The problem is: let $L_{2}$ be a language defined as follows: after every "a" come atleast two "b" or after every "b" comes atleast ...
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### How to transform lambda function to multi-argument lambda function and how to rewrite or approximate terms?

I am trying to do the formal semantics (Montague grammar, abstract categorial grammar) of natural language and encode the sentence John is boss. The type system has ...
156 views

### Using a context free grammar to generate sample utterances for Amazon Alexa/Google Assistant?

I would like to get some opinions about using a context free grammar to generate sample utterances for Amazon Alexa/Google Assistant skills. When developing these skills one has to provide a large ...
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### What is handle in bottom up LR parsing?

I was taking course on compilers by Alex Aiken. You can find the slide discussing handles on this page. On the page of the slide, the instructor defines handle as follows: Assume a rightmost ...
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### Define a grammar to emmulate chess rules

Is it possible to define a 《chess language》: language={alphabet = {(chess pieces, squares of chess board)}, grammar={rules of movement of pieces over the board}}? I looked online but I cannot find a ...
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### Formal grammar with variables for consistent substitutions

In a rewriting system, suppose the production rule S→xAyAz (or <S>:=x<A>y<A>z, in BNF), where S and A are ...
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### Intuition on what an attribute grammar can achieve

I have seen attribute grammars for a small handful of tasks: Parsing simple arithmetical expressions Type checking Checking that a variable is initialized anbncn (seems to be a favorite toy example).....
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### Why I can't parse factorial? [closed]

Given that I have a simplified Bison BNF grammar: ...
### Context-free grammar for $L=\{0^n1^{2n} \mid n \geq 0\}$ [closed]
How can I express this language $L = \{0^n 1^{2n} \mid n ≥ 0\}$ as a context-free grammar? I am new to this field and I am not sure what should I do. Please help me.