Questions tagged [lr-k]
LR(k) is a common type of parser for context-free grammars
37
questions
-1
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18 views
Formal proof that if a grammar is LR then it isn't ambiguous
Title says it all. I'm looking for a formal proof that there can't be two parse trees for a same sentential form if the grammar is LR.
Can you help me?
0
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1answer
16 views
How to create a LR(k) grammar for an arbitrary k
Is there a simple procedure for constructing a grammar that is LR(k) but not LR(k-1) for any k?
0
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1answer
34 views
Is following grammar LR(0)?
I know how to verify whether grammar is LR(0) or not. But this particular case is little tricky and hence the question.
Grammar:
$SL \rightarrow SL ; S \space | \space \epsilon$
$S \...
0
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0answers
24 views
question about LL(1) and LR(0)
If grammar is an $LL(1)$ and does not contain any null production (i.e $V \rightarrow \epsilon$) then does that grammar necessarily be an $LR(0)$ grammar?
I have tried to find counterexample for ...
0
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1answer
72 views
Analysis of a LALR shift-reduce conflict
I have created an extremely simple byacc grammar (ok, it's not really that simple but I simplified purposefully to be a minimal complete verifiable example):
...
0
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2answers
131 views
Are shift and goto moves for all LR parsers ( LR(0), SLR(1),CLR(1),LALR(1) ) same?
I understand the difference in the parsing tables of the above 4 parsers.
I understand that CLR>LALR>SLR>LR(0) in terms of power.
Are shift and goto moves for all LR parsers ( LR(0), SLR(1),CLR(1),...
1
vote
1answer
46 views
Wikipedia says this grammar is LR(0), but Grammophone says it is not; is it?
E -> E * B .
E -> E + B .
E -> B .
B -> 0 .
B -> 1 .
I am confused because Wikipedia cites this grammar as an example of an LR(0) grammar ...
0
votes
1answer
80 views
Is there a LL(K) Grammar which is not LALR(K) Grammar?
It is easy to know that there are LALR(K) grammars which are not LL(K) because any grammar with left recursion which is LALR(K), is not LL(K) because all LL(K) grammar must be left recursion free. And ...
0
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0answers
168 views
Understanding handle, viable prefix and valid item in the context of LR(0) and LR(1) items
Dragon book gives definition of handle, viable prefix and valid item at various different places. I am trying to understand these definitions in each other's context. Various definitions given are as ...
1
vote
1answer
279 views
When will SLR(1) parser fail but CLR(1) will not
Dragon book says following about where SLR(1) parser can fail but CLR(1) wont:
Recall that in the SLR method, state $i$ calls for reduction by $A→α$ if the set of items $I_i$ contains item $[A→α.]$...
0
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1answer
201 views
LR parsers and ambiguous and non deterministic grammars
Dragon book says:
An ambiguous grammar can never be LR.
And then immediately further it says:
For example, consider the dangling-else grammar:
$\begin{align} stmt \rightarrow & \textbf{...
2
votes
1answer
369 views
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 ...
1
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0answers
540 views
Are LL(1) grammars a subset of LR(0) grammars?
As far as I've understood it seems that LL1 are a subset of LR0, but studying the following grammar I end up in a contraddiction.
Grammar :
S -> (S) | [S] | {S} | ε
This is an LL1 while it seems ...
1
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1answer
89 views
3
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1answer
550 views
can every LR(k) grammer be transformed to LR(1)
when i was studying compilers i came across this in Wikipedia every DCFL has a corresponding unambiguous grammar and hence can be parsed by an LR(1) parser which is the most powerful parser then what ...
1
vote
0answers
194 views
Is the Java 8 Grammar still a LALR(1) grammar?
As I found out here: http://www.eclipse.org/jdt/core/howto/generate%20parser/generateParser.html , the Java Version of 2005 (might be Java 6, I'm not sure) is a LALR(1) grammar. However, I couldn't ...
2
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0answers
150 views
7
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2answers
1k views
DCFL with prefix property have LR(0) grammar?
There are two important theorems about LR(k) grammars and DCFL. Mentioned here.
A language has an LR(1) grammar iff it is DCFL.
A language has an LR(0) grammar iff it is DCFL and has prefix property.
...
4
votes
1answer
598 views
Are LR(k) languages and DCFLs equivalent?
In the familiar book of Theory of Computation by M. Sipser, the author proved that for endmarked context-free languages, the set of languages having a LR(k) grammar for a predefined $k \in \mathbb{N}$ ...
0
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1answer
46 views
Can I mix LL and LR parsing?
I want to go RD parsing with Shunting Yard for expression (for the sake of easier operator precedences and less left-recusion), is that considered no-good because nobody did that before?
3
votes
1answer
137 views
Is $\{a^nb^n\}\cup\{a^nb^{2n}\}$ LR(k)?
I was reading Knuth's paper "On The Translation of Languages from Left to Right", my particular interest being on RL($k$) languages (not a typo). By the end of the paper, he puts the grammar:
$$
S \...
1
vote
1answer
2k views
Need for an augmented grammar
The question is under the concept of LR parser.
Suppose the original grammar is
S->AA
A->aA|b
Is it necessary to add an additional rule S'->S to make it as augmented grammar?
In short, I want to ...
1
vote
0answers
159 views
Upper bound of automaton states for SLR parsing
How do I tell, given a specific grammar, which is the upper bound for the number of states of a LR(0) or LR(1) automaton for its SLR parsing?
My guess is that generating the canonical item collection ...
2
votes
0answers
282 views
How to find conflicts in LALR parser?
I have a LR analyser and I can't find out how to know whether the grammar is or is not LALR(1).
I think that I have to merge states with the same rules. So I have to merge states: $2 - 12, 3 - 13, 4 -...
2
votes
0answers
24 views
Determine if two LR(1) action/goto tables always produce the same derivation
I am experimenting with implementing minimal LR(1) algorithms/techniques, but I find it very difficult to verify the correctness of what I've implemented.
Is there a fast algorithm to determine if ...
6
votes
0answers
67 views
Is THEADS the same as FIRST?
I'm reading the paper "A Practical General Method for Constructing LR(k) Parsers" by David Pager, and it contains the following paragraph:
We will first of all briefly review the LR(1) parsing and ...
0
votes
1answer
488 views
How to remove empty strings a.k.a (lambda, epsilon) from a LR(0) grammar
Say I have the following grammar:
E -> TE'
E' -> +TE'| -TE' | λ
T -> (E) | id
I need to build the finite state machine with the LR(0) items,
But I ...
2
votes
1answer
62 views
Item lookaheads versus dot lookaheads for $LR(k)$ with $k \gt 1$?
I was reading "Parsing Techniques: A Practical Guide, Second Edition" by Grune and Jacobs, which details a bunch of different parsing algorithms. In the section on $LR(2)$ parsing, they mention that ...
4
votes
1answer
144 views
An intuitive explanation for LR grammars?
With LL grammars, there seems to be a very intuitive explanation, in terms of first and follow tables.( The first letter/s encountered in a particular state, can only mean a particular rule). With LR ...
2
votes
1answer
192 views
Use DFA minimization on LR(1) states
I have recently started reading more about context-free parsing techniques, in particular LR parsing.
As I have read, LR state transition graph (or table(s)) used for finding handles in sentential ...
1
vote
0answers
23 views
How equality of item (production state) is defined in LR parser?
Whenever I read about equality I took it for granted, but few days ago I wondered if my understanding is not too shallow. Consider such example (taken from: http://david.tribble.com/text/honalee.html):...
0
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1answer
157 views
Chomsky NF or Greibach NF benefits for LR parser?
Are there any benefits of having grammar in CNF/GNF for LR parser? I have those in mind:
total speed of creating a parser (that is time for creating CNF/GNF out of the grammar, and then creating ...
4
votes
1answer
140 views
Are there automatic transformation of grammar algorithms?
From time to time you can write a grammar that creates shift/reduce conflict (for example) but after reading the grammar you notice that if you rewrite the productions the conflict will go away, ...
10
votes
2answers
520 views
How much bigger can an LR(1) automaton for a language be than the corresponding LR(0) automaton?
In an LR(0) parser, each state consists of a collection of LR(0) items, which are productions annotated with a position. In an LR(1) parser, each state consists of a collection of LR(1) items, which ...
1
vote
1answer
335 views
Is this grammar LR(1)?
A bit confused about whether this grammar is ambiguous or not
C' -> C
C -> d C u C
C -> d C
C -> ε
I tried building the DFA for this but I get this ...
0
votes
1answer
164 views
How to create an LR($k$) grammar for a given language?
How can I construct an LR($k$) grammar (which $k$ is not really of interest for now) for a given language, say:
$$L=\left\{w \in \{a, b\}^\star \ | \ \exists u \in \{a, b\}, v \in \{a, b\}^\star: w = ...
12
votes
2answers
5k views
Is there any way to distinguish between LL(k) and LR(k) grammar?
I am recently studying about Compilers designing. I came to know about two types of grammar one is LL grammar and other is LR grammar.
We also know the facts that every LL grammar is LR that is LL ...
