# Tag Info

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### Are LR(k) languages and DCFLs equivalent?

According to Wikipedia: For every fixed $k \geq 1$: A language has an LR($k$) grammar iff it is DCFL. A language has an LR(0) grammar iff it is DCFL and has the prefix property (no word is a prefix ...
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### Need for an augmented grammar

Yes, if you follow the canonical conversion of augmented grammars, a first step is adding a new start symbol $S'$ and the production $S' \to S$, since the algorithm may later "change" $S$. However, ...
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### Is $\{a^nb^n\}\cup\{a^nb^{2n}\}$ LR(k)?

Propbably you should read the citation as: "The problem is that the c (which separates the two parts of the language) is at the extreme right and not at the extreme left, where we start parsing." ...
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### Is THEADS the same as FIRST?

I recently had the same question in mind when reading Pager's work. I found the paper The Edge-Pushing LR(k) Algorithm by Chen and Pager, which seems to say that the two terms are indeed the same. ...
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### How to remove empty strings a.k.a (lambda, epsilon) from a LR(0) grammar

Find all nullable variables. In this case only E' is nullable. Let me illustrate the second step with an example: Replace a production A -> BCD with a family of productions like this (assuming B, C &...
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### An intuitive explanation for LR grammars?

A language is $LR(k)$ if looking at the right side of a production, and looking $k$ symbols ahead, one can determine the left hand side of the production. This is quite incomplete, but intuitively ...

### Are shift and goto moves for all LR parsers ( LR(0), SLR(1),CLR(1),LALR(1) ) same?

Every reduce action corresponds to a production; the action "undoes" the production by replacing its right-hand side with the non-terminal which produced it. That can only happen in one way; the ...
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### Merging states in LALR parser

No, you can't do that. The definition of LALR parsers is that it has combined(union of lookaheads) states having the same cores but different lookaheads. So what would happen if you were to combine ...
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### How does LALR(1) parser behave compared to LR(1) paser?

The explanation is given in the following paragraphs. Given a correct input, the LALR parser produces exactly the same sequence of reduce and shift actions as would an LR parser for the same grammar. ...
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### What are cases where we cannot perform LR parsing without augmented grammar?

Once we have a parsing table, we can parse (or reject) any sentence without any reference to the grammar. So at that point, the fact that the grammar was or was not augmented is essentially moot. (It ...
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### Equivalence of LR(k) and LL(k′) parsers

Yes, $\{a^i b^j c \mid i \ge j \ge 0\}$ can be parsed by a $LR(0)$ parser but not by any $LL(k')$ parser for any $k'$. See How does $LL(n)$ languages compare with $LR(0)$, for $n>0$?. See also ...
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### How to disambiguate CFG with unary/binary minus and binary prefix operator

I'm going to limit myself, at least for now, to the question actually asked here: how to deal with the ambiguity between an operator which could be prefix or infix (such as unary negation) and a ...
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### Edit distance into a DCFL

It would appear the language edit distance problem for the class of deterministic context-free languages requires cubic time. In Language Edit Distance Approximation via Amnesic Dynamic Programming (...
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### Analysis of a LALR shift-reduce conflict

This conflict arises because when the parser is at the beginning of a line and the lookahead is VAR, it can't tell whether or not to reduce an empty ...
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### What is the time complexity of SLR and LALR parsers?

They all run linear time with regards to input length ($O(n)$). The different algorithms have different memory trade offs for making it easier to write grammar for. That is not all grammars that work ...
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### Reduce-reduce conflict in SLR vs LALR

Note: I'm assuming that when you wrote $SLR$ and $LALR$ that you actually meant $SLR(1)$ and $LALR(1)$. It is certainly the case that if a grammar shows a conflict in an $LALR(1)$ automaton, that ...
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### Why can't a LR(0) parser have GOTO and Reduce Items in the same canonical set?

This isn't what you asked, but let me start by saying that I suspect the answer they're looking for in the question you link is (D), "A LR(0) parser can parse any regular grammar". That ...
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### How to create a LR(k) grammar for an arbitrary k

Here's one pattern for an LR(k) grammar which is not LR(k-1). I didn't fill in the definition of $A$; there's nothing particularly special about it. It might have an empty right-hand side, or it might ...
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Before applying the LR algorithm to a grammar, the grammar must be "augmented" by adding the rule $S' \to S \$$where S is the original start symbol and S' and \$$ are symbols not in the ... 1 vote ### LR parsers and ambiguous and non deterministic grammars The grammar is really ambiguous.$\textbf{ if } expr \textbf{ then if }expr \textbf{ then } stmt \textbf{ else } stmt$has two possible parses with that grammar. (The$ \textbf{ else }\$ can ...

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