Questions tagged [formal-grammars]
Questions about formal grammars, generative descriptions of formal languages.
1,078
questions
0
votes
1answer
36 views
Which of the following words is in the language of the grammar G?
This is taken from a practice quiz by my university.
I ruled out that aabbbaab is not part of the grammar:
S → aSb → aaSbb... This shows that I can't make this word because it would have to have ...
0
votes
0answers
15 views
Why can't I evaluate this L-Attributed SDD with a pre-order traversal?
My powerpoints for a compiler class says "an L-Attributed SDD can be evaluated with a pre-order (root, left, right) traversal", and to be L-Attributed the nodes need to have either ...
0
votes
2answers
27 views
How to evaluate a Kleene's Closure through CFG and attribute grammars
For a CFG with the production rules that can represent a regular expression. How can one calculate all the set of strings that regular expression would produce.
For T = {a, b,*,(,)}
and an arbitrary ...
0
votes
1answer
44 views
How can I make the following grammar unambiguous
Given the below ambiguous grammar how can I make it inambiguous and how can I prove the new modified unambiguous grammar is unambiguous? S -> S + S | S − S | S ∗ S | S / S | (S) | x | y
My attempt: ...
0
votes
1answer
22 views
Formal Grammar: derivation form posted on Wiki?
Wiki describes the binary relation $\underset{\mbox{G}}{\implies}$ as "G derives in one step". I have a question on the condition when there are multiple productions for a single non-...
1
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1answer
41 views
Is it possible to make a grammar LL($1$) which recognizes palindroms?
Is it possible to make an algebraic grammar LL($1$) which recognizes palindroms for an alphabet $\{a,b\}$?
-2
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0answers
39 views
Is this grammar context-free? What strings does it generate?
Is this grammar context-free? (Thanks! Someone pointed out it's context-sensitive because there's more than one Non-terminal on the left)
What strings does it generate? (...
0
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0answers
18 views
generating strings from this formal grammar [duplicate]
Hey guys I am having trouble generating strings from this language, I haven't seen a grammar that looks like this and can't figure how to generate strings from this grammar, is this Context Sensitive ...
1
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0answers
49 views
A Formal Grammar: defining English counting numbers?
I would like to define a grammar that produces and recognizes the counting numbers of the English language. I created the production rules below based on the assumption this is context-free, but I am ...
0
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1answer
15 views
Compilers: How to see “the number of grammars where there exists a string that has at least two different left-most derivations”?
Could someone tell why "G1 and G3 are ambiguous" and how to see whether a string has at least two different left-most derivations in general?
2
votes
1answer
43 views
Proof that $L = \{a, b\}^* - \{(a^n b^n)^m \mid n, m \ge 1\}$ is a CFL
I want to prove that $L = \{a, b\}^* - \{(a^n b^n)^m \mid n, m \ge 1\}$ is a Context Free Language.
so far, I tried to find a Context Free Grammar for $L$ or to use properties of Context Free ...
0
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0answers
20 views
I am trying to design an LL(1) Parser that accepts T = {a, b *, +, ?, E, U, (, ) }
I am trying to design an LL(1) Parser that accepts regular notation where 'E' represents epsilon, and 'U' represents "or" like ' | '.
So far I made one that accepts T = { a, b, *, +, (, ), E}...
0
votes
1answer
34 views
Removing left recursion with terminals only
I have a grammar:
$G → id > id$
$| id < id$
$| G and id$
Does anybody know how I can do left recursive elimination on this one, when it doesn't have any extra non terminals?
1
vote
0answers
17 views
Compile XPath Abbreviated Query to Unabbreviated version
The Xpath 3.1 presented by W3C includes the full grammar of the language with both abbreviated and unabbreviated syntax.
I am interested in references (if any) for any formal work done to compile/...
3
votes
2answers
64 views
Context free grammar for $L = \{w \text{ | }w \in \{a,b\}^*, |w|_a=|w|_b-1\}$
I'm trying to find a grammar for $L = \{w \text{ | }w \in \{a,b\}^*, |w|_a=|w|_b-1\}$, which is proving to be tricky.
I know that $L_2 = \{w \text{ | }w \in \{a,b\}^*, |w|_a=|w|_b\}$ has the following ...
0
votes
1answer
36 views
Computing FOLLOW sets of left recursive grammar
Left recursive ambiguous expression Grammar:
$E \rightarrow E+E \mid E*E \mid (E) \mid \mathbf i\mathbf d$
I tried computing FIRST and FOLLOW sets of both left recursive grammar and after ...
1
vote
1answer
36 views
Is there a formal language of Combinatory Logic's expressions?
The Combinatory Logic uses expressions of the form (x y) called "applications" (here, we have an "application of x to y"). Thus, the language of CL is a set of "parenthetic ...
1
vote
1answer
75 views
Derivation from grammar
Given the grammar $G=(\{S, L_x, R_x, W_x\}, \{a,b\}, P, S)$ derive the words $abaaba$ and $aabbaabb$.
$$
P=\left\{
\begin{align}S\phantom{{}_x R_y} &\to \epsilon \mid L_x R_x,\\
L_x \...
1
vote
1answer
36 views
Finding a grammar for $L=\{a^nb^mc^rd^s| n+m<r+s\}$
I am trying to find a grammar for $L=\{a^nb^mc^rd^s| n+m<r+s\}$, which has the hint of it having "some similarity" to $L=\{a^ib^j|i<j\}$
This last one is quite easy to get ($S\to aSb | ...
2
votes
4answers
73 views
If $L$ is regular then $L^{|2|}=\{w_1w_2 \mid w_1,w_2\in L, |w_1|=|w_2|\}$ is context-free
I have found a problem about proving whether $L^{|2|}=\{w_1w_2 \mid w_1,w_2\in L, |w_1|=|w_2|\}$ is context-free or not, knowing that $L$ is regular
So far I know that:
There are examples where $L$ ...
1
vote
2answers
61 views
Finding a grammar for $L = \{ 0^x1^y0^z1^w | x+w=y+z\}$
I have found an exercise where it tasks to provide a grammar and a pushdown automata for
$L = \{ 0^x1^y0^z1^w | x+w=y+z\}$
While finding a pushdown automata for it is quite easy (four states and two ...
1
vote
2answers
185 views
Trying to remove ϵ rules from a formal grammar resulted in L(G) ≠ L(G')
I am trying to remove ϵ rules from the following grammar (after applying the remove redundant symbols algorithm): $G = (\{S,A,B,C\},\{0,1\},P,S)$, where the productions are
\begin{align}
&S \to AB ...
3
votes
1answer
45 views
Is there a method to generate the complement of a context-free grammar?
Given the languages $L_0 = {w \in \{0,1\}^*}$ such that $w$ is a palindrome and $L_1 = {w \in \{0,1\}^*}$ such that $w$ is not a palindrome, meaning $L_1$ is the complement of $L_0$, we want to find ...
0
votes
1answer
25 views
Is the complement of the language generated by $S \to aSbS|\epsilon$ context-free?
How is it possible to prove whether the language $\{a, b\}^{∗} \setminus \{S → ε, S → aSbS\}$ is context free?
4
votes
1answer
229 views
Context-free grammar for all words not of the form w#w
I was asked to define a CFG for the complement of $\{w\#w \mid w \in \{0,1\}^*\}$ and I'm struggling to define it. I think it is quite similar to defining a CFG for the complement of $\{ww \mid w \in \...
1
vote
1answer
30 views
Trying to find two CFGs for the following languages
I'm trying to get CFGs for these two languages which still remain unsolved in my practice problems sheet:
$L = \{ a^kb^ra^m | m=k+r\}$
$L = \{ a^nb^m | 1\leq n\leq 2m\}$
With the first one, I thought ...
0
votes
1answer
27 views
How can Chomsky hierarchy be applied to languages with alternated letters?
I have the following grammar, which I know it is regular because it can be represented by a finite state automata:
\begin{array}{l}
\mathrm{S} \rightarrow \mathrm{X} \mid \mathrm{Y} \\
\mathrm{X} \...
0
votes
0answers
22 views
Building Context sensitive grammars?
I just discovered Context-sensitive grammars.
The problem is most of the examples are weird non-interesting toy languages !
Second the descriptions are math oriented, rather than programmer oriented.
...
0
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0answers
26 views
Parsing a context free grammar, Backus Naur question
Does anyone know how BNF rules expecting the empty string ($\epsilon$ or the "") behave during creation of a parse tree using grammar from a string of ...
1
vote
1answer
595 views
What does it mean for a grammar to be LR(0)?
I am unsure what it means for a grammar to be $X$. More specifically, what it means for a grammar to be LR(0).
For part of an assignment I had to form the DFA for a grammar, which I had no issues with....
2
votes
1answer
68 views
How can I show that this language is context sensitive?
I have this language $L=\{a^nb^nc^n,n\geq0\}$, I know this language is not context free, but I don't know how to show that it is context sensitive, do I have to use a PDA?
0
votes
1answer
36 views
Formal proof of language accepted by a specific CFG
Let $G=(V,\Sigma,R,S)$ be the grammar given by the following rules:
\begin{align}
&S \to aS \mid B \\
&B \to abBc \mid \epsilon
\end{align}
Please provide a formal proof for the following ...
1
vote
1answer
54 views
How do you create a sentential form in a given grammar?
I am given the following grammar:
$$S ::= aBS| abT |a$$ $$T::= d | dT$$$$B ::= da | ϵ | S$$
I need to decide whether $aBaabda$ can be produced in the given grammar.
I am unsure how the grammar can ...
0
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0answers
14 views
Having trouble understanding how to prove a language context free? [duplicate]
I've been studying the theory of automata. I came across this problem in the book and unable to understand how to solve this. I've solved some examples using the Pumping lemma but this one uses ...
1
vote
1answer
44 views
How can we generate a grammar for $\{a^n b^n c^n d^n; n > 0\}$ if it is NOT context free?
This page on Wiki states that $\{a^nb^nc^nd^n \ | \ n > 0\}$ can not be generated by a CFG. This does not make sense to me as $\{$S $\to$ ABCD, A $\to$ aA | a, B $\to$ bB | b, C $\to$ cC | c, D $\...
0
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0answers
19 views
CFG for the language x^n y^m, where n ≥ 1, m ≥ 1, and n ≠ m [duplicate]
Can anyone help me construct a CFG for this? It really has me stuck for some reason.
0
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1answer
22 views
Are these production rules for a formal grammar?
I have a question on if production rules of a formal grammar are being specified correctly. Wikipedia defines the syntax of grammars as the following finite set of production rules, where it states ...
-1
votes
1answer
41 views
Transform grammar to Chomsky Normal Form
Question:
S → abSab | baSba | TT
T → aTa| bTb | ε
My answer:
Eliminate ε rules:
S-> abSab | baSba | TT | T
T-> aTa | bTb | aa | bb
Correct answer:
S → abSab | baSba | TT | abab | baba | T
T → ...
0
votes
2answers
36 views
How to tell if a grammar is LALR(1) formally?
There is an “informal” definition of $\operatorname{LR}(k)$ (can be recognised by a parser that looks at $k$ symbols ahead) and a “formal” one (as a property of the set of rightmost derivations ...
0
votes
2answers
117 views
How do Context Sensitive Grammar systems work?
The Quest: Use context sensitive grammar (CSG) to produce an equal N number of repeating a, b, and c using the alphabet {a, b, c}. For example, if N = 5 use CSG and a, b, and c to produce a result ...
1
vote
1answer
111 views
Linear Grammar in less than cubic time
I have a linear grammar $G$ and a string $s$. $G$ is is not limited to right or left linear only but rather has a mix of rules of both types.
Is there an algorithm to determine whether $s \in L(G)$ ...
2
votes
1answer
40 views
Is “A -> aAA” convertible to regular grammar?
I have a simple grammar as below and wonder if it is convertible to regular grammar?
If yes, what is the conversion sequence? If no, how can we prove it?
...
1
vote
1answer
55 views
How to find the language of a CFG from Production rules
I'm having problems in finding language of the CFG from given production rules. For example if the production rules are
\begin{align}
&S \to AS \mid \epsilon \\
&A \to aa \mid ab \mid ba \mid ...
6
votes
1answer
365 views
What are the closure properties of LL(k) languages?
Suppose I have two LL languages $L_1, L_2$, both describable by LL($k$) grammars for the same $k$, and regular language $R$. Which of the following are also LL languages, and can they be described by ...
0
votes
1answer
40 views
left/right derivations of grammars and parse trees
I'm having a hard time understanding how left/right derivations work. I have a very simple example that I've attempted but I don't really know how to check if it's correct.
$S-> NP$ $V$ $NP$
$NP -&...
0
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0answers
59 views
Converting a regular expression to a grammar and regular grammar
I am working on a pretty small lab for my university course and I'm having trouble converting a given regex into a set of regular definitions, then into a grammar and finally a regular grammar. I have ...
0
votes
0answers
15 views
What's the context-free grammar for { w | 2*(number of a's in w) != 3*(number of b's in w) +2 }? [duplicate]
So I have this language:
$$
A= \{ w \in \{a,b\}^* \mid 2*\#_a(w) \ne 3*\#b(w) + 2\}
$$
I know it's context free, I know how to make a PDA for it, I just can't, for the life of me, figure out how to ...
0
votes
0answers
18 views
Show {𝑎^i𝑏^j𝑐^k, i!=j!=k} is context free or not, how can we prove it? [duplicate]
I stuck on this question for a long time and cannot figure out how to prove it?
0
votes
0answers
29 views
Show {𝑎^i𝑏^j𝑐^k, 𝑖!= j and 𝑗 != 𝑘} is a context-sensitive language, what is the grammar? It is context free or nor?
I've been pondering this question for a long time, that 𝑎^i𝑏^j𝑐^k, 𝑖!=j and 𝑗 != 𝑘 is a context-sensitive language, how we can prove it to be context sensitive or which grammar can generate such ...
4
votes
1answer
631 views
Is every unambiguous grammar regular?
While searching for an answer to this question I found out that there is an unambiguous grammar for every regular language.
But is there a regular language for every unambiguous grammar? How can I ...
