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What would you get if you add parameters to context free grammars?

Affix grammars (parameterised context-free grammars) were studied extensively by the eminent Dutch computer scientist Cornelis HA Koster, starting with his 1962 paper "Basic English, a generative ...
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14 votes
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Why separate lexing and parsing?

You don't have to separate them. People combine them into scannerless parsers. The key disadvantage of scannerless parsers appears to be that the resulting grammars are rather complicated -- more ...
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14 votes

For every 'evil' regex, does there exist a non-evil alternative, or is the devil in the grammar?

It depends upon whether you've got a regular expression or a regexp: regexps are evil, but regular expressions are a thing of beauty and will never turn evil on you. By regexp, I mean a modern ...
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13 votes
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Removing left-recursion in grammar while maintaining left-association of operator

Compatibility of left associativity and LL(1) parsing You just hit one of the major inconsistencies in the use of context-free (CF) syntax. People want to choose grammars so that the parse-tree will ...
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12 votes

What was Robert Floyd's algorithm for inserting brackets?

The seminal paper referred to is "Syntactic Analysis and Operator Precedence" (1963), which describes the operator precedence algorithm still used by many simple expression parsers today. ...
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11 votes

Correct name for a recursive descent parser that uses loops to handle left recursion?

It is just an LL(1) parser implemented with recursive descent. Starts with: ...
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11 votes

Representing "but not" in formal grammar

For context-free grammars (I guess your question concerns this type of formal grammars), it would be not only painful, but also impossible in general. Suppose we have an algorithm that provides such "...
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10 votes
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How do I reconstruct the forest of syntax trees from the Earley vector?

I am using terminology and notations from Earley's paper. It is possible that the description you read is different. It seems frequent that general CF parsing algorithms are first presented in the ...
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10 votes

any hope for a universal automatic parser?

You might be interested in learning about grammar induction: given a set of examples of strings from a context-free language, there are algorithms to learn a context-free grammar that generates those ...
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9 votes
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Is CYK still relevant today?

CYK is still relevant, afaik, as the simplest example of a family of general parsing algorithm based on dynamic programming, ranging over all parsing technique (that I know of) and many syntactic ...
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9 votes

Representing "but not" in formal grammar

In the case of regular languages (and in your examples, we're just talking about character classes, which are an especially simple form of regular language), they are closed under set difference. Not ...
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8 votes
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Are LALR tables equal to SLR tables if the grammar is SLR modulo precedence/associativity of operators?

If a grammar is SLR(1), then: [Note 1] The SLR(1) and LALR(1) state machines will have the same states The set of shift transitions in the two machines will be identical (as will the goto actions). ...
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8 votes
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Can an Earley Parser be made into a fuzzy parser similar to the Levenshtein Automata Algo for DFA?

The answer is yes. However I would not do that with an Earley parser because there are simpler ones with the same capabilities. Basically, Earley parser belongs to a family of general context-free ...
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8 votes
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How can I check that the language of one context-free grammar is a subset of a second context-free grammar?

Here you have a couple of salient points. Firstly, the grammars are right linear (strictly $G_{1}$ needs some small changes, but they're trivial). This means that the two languages are regular. Given ...
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8 votes

How to find unambiguous grammar for palindromes

First, I believe you are looking for a different word than 'unambiguous'. A grammar is ambiguous if some string in its language has two or more derivations; I'm sure that a palindromic string must ...
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7 votes
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What is an IELR(1)-parser?

The IELR(1) Parsing Algorithm The IELR(1) parsing algorithm was developed in 2008 by Joel E. Denny as part of his Ph.D. research under the supervision of Brian A. Malloy at Clemson University. The ...
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7 votes

Check for balanced parentheses in an expression in log-space

The Dyck language on any fixed number of symbols can be recognised by a marking automaton, which is a two-way finite automaton that can mark a fixed number of input tape squares. The automaton simply ...
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7 votes
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Is there a different resolution of the "dangling else" problem other than "match closest"?

This problem is an exact analogue of the problem of matching parentheses in an expression in which some of the close parentheses have been omitted. Here an "if" (or $a$ in the representative grammar) ...
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7 votes
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Finding the number of distinct strings in regular expression

In your example, think of the result as having filled four slots: _ _ _ _, each of which can take one or three substrings, namely 0, 1, or the empty string. Ignoring the empty strings, it's clear that ...
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7 votes

Representing "but not" in formal grammar

The particular grammar formalism used in the grammar you cite is defined in Appendix A of that document, which includes in section A.3, a precise definition: A grammar production may specify that ...
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6 votes

Parsing arbitrary context-free grammars, mostly short snippets

My company (Semantic Designs) has used GLR parsers very successfully to do exactly what OP suggest in parsing both domain specific languages, and parsing "classic" programming languages, with our DMS ...
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6 votes

Recursive descent parser with backtracking for the grammar $S \rightarrow aSa\ |\ aa$

This is not much of an answer, but the parse trees do not fit the normal comments. Your grammar $S \rightarrow aSa\ |\ aa$ should parse the string $aaaaaa$. But the parse tree has the following form:...
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6 votes
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Why we use context-free grammar for parsing?

Because regular expressions are too weak and context-sensitive languages are too difficult to parse. More specifically, regular expressions can't specify that the brackets in your program match up; ...
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6 votes
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What is the point of delimiters and whitespace handling

Now, is it right that only identifiers and literals have to be separated by delimiters or whitespace? How do I ensure that? If by "right" you mean it is the case in every programming ...
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6 votes

Correct name for a recursive descent parser that uses loops to handle left recursion?

You want to look into LL($k$) parsing. The Wikipedia article is mostly useless, but it's basically recursive descent with $k$ symbols lookahead. There is also LL($*$) which permits unbounded ...
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6 votes

What would you get if you add parameters to context free grammars?

Take the pumping lemma for CFGs: Take the grammar S -> A("") A(p) -> p | p '\n' A(p"*") '\n' p This describes a star triangle: ...
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6 votes
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Is there a LL(K) Grammar which is not LALR(K) Grammar?

Every $LL(k)$ grammar is $LR(k)$, but there are $LL(k)$ grammars which are not $LALR(k)$. There's a simple example in Parsing Theory by Sippu&Soisalon-Soininen $$\begin{align}S &\to a A a \...
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5 votes

BNF and Simultaneous Parsing

If the grammar is amenable to limited-lookahead bottom-up parsing, then the parallelism is more or less implicit in the parsing algorithm, and there is little to be gained from parallel computing, at ...
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5 votes
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When did $LR(k)$ acquire the meaning "left-to-right scan, rightmost derivation?"

I went and asked Don Knuth about this. He mentioned that he first used the new terminology in his 1972 paper Top-Down Syntax Analysis (link here) to provide a consistency between the terminology in $...
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5 votes

Lookahead in LL(k) parsing

No, you still consume one symbol at a time. However, you are allowed to consult the next $k$ symbols in order to decide what to do before consuming the symbol. Here's a simple example: the grammar of ...
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