Questions tagged [formal-grammars]

Questions about formal grammars, generative descriptions of formal languages.

131 questions with no upvoted or accepted answers
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10
votes
1answer
307 views

Shift-resolve parsing - questions

I've recently came across a paper describing the parsing technique mentioned in the title. Unfortunately, the terminology used in said paper is somewhat beyond my comprehension, so I've been ...
8
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0answers
243 views

Can any PEG grammar be parsed in linear time?

On the Wikipedia for PEG it is claimed: Any PEG can be parsed in linear time by using a packrat parser, as described above. However, packrat parsers can't handle left recursion. You can eliminate ...
6
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0answers
64 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 ...
4
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0answers
577 views

Which programming languages have a syntax that can be described by deterministic context-free grammars?

This question asks which programming languages have a syntax that cannot be described by deterministic context-free grammars - the answer is "Many [...] including Algol 60, C, and C++". Until ...
3
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0answers
99 views

Simple description of circularities in Knuth original attribute grammar paper

Knuth's original attribute grammar paper (title: Semantics of Context-Free Languages) introduced three types of circularity. More specifically section "Testing for circularity" page 134-5 figures 3.1-...
3
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0answers
119 views

Semantic parsing with Grammatical Framework - is this possible?

So far I have learned about categorial grammars, type logical grammars and formal semantics of natural language, the relevant tools are Cornell Semantic Parsing Framework https://github.com/clic-lab/...
3
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0answers
27 views

How to model grammar ambiguity

Say you have a (context-free) grammar, and you wish to mathematically model the magnitude of the ambiguity possible under this grammar, across the space of all possible** input strings. Practically, ...
3
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0answers
99 views

Unambiguous context-free language that can't be parsed in linear time by backtracking recursive descent?

Is there a context-free language that can be expressed with an unambiguous grammar but can't be expressed with a grammar that would result in linear-time backtracking recursive descent parsing? The ...
3
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0answers
226 views

How to refactor a grammar to be suitable for recursive descent?

I'm trying to learn how to use a recursive descent parser, and reading on this page I find this example: $S \rightarrow AB \\ A \rightarrow a \\ A \rightarrow SA \\ B \rightarrow b \\ B \rightarrow ...
3
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0answers
221 views

Context-free grammar for DAGs?

I'm looking for a "safe" representation of DAGs. With "safe" representation I mean that it can be described by a context-free grammar. Ideally, this grammar would be suitable for a simple LR parser. ...
3
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0answers
84 views

What kind of formal language is generated by Parsing Expression Grammars?

I've been unable to find what class of languages is recognized by PEGs. The original paper [1] only conjectures that there are some Context-Free Grammars that are unrecognizable by PEGs. It also ...
3
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0answers
113 views

Is there a grammar type for deterministic LBA?

Contextsensitive grammars define exactly the langauges acceptable by nondeterministic LBA. But how about deterministic LBA - is there a grammar type capturing exactly the languages acceptable by this ...
3
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0answers
50 views

Tree Languages are Word Languages on an Infinite Alphabet of Contexts

I have been reading the book Tata (Tree Automata Techniques and Applications), and there is a sentence I have read thousands of times, yet still don't quite understand. In the beginning of Chapter 2, ...
3
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0answers
282 views

Recursive-descent parser for the grammar S -> S(S)S | ε

I'm studying (for self-betterment - I don't go to school) the 2nd edition of Compilers: Principles, Techniques and Tools by Aho et al. I'm not sure how to do Exercise 2.4.1 (b), which is to construct ...
3
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0answers
97 views

Prove or disprove that every $L$ in this class is a CFL iff $L$ is equivalent to a substitution

Let $L$ be a language with every string of the form $(w_i\#)^*$ with $w_i\in\{0,1\}^*$. Set $w'\sim w$ if there is a permutation $\pi_1$ such that $w_i=w'_{\pi_1(i)}$ for all $i$. If additionally $\...
2
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0answers
34 views

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).....
2
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0answers
33 views

Give LL grammar for this language?

I need to give the LL grammar for the language below and explain why the grammar is LL and what the value of $k$ should be: $$L = \{ a^n c^m c^{n+m} : n \ge 1, m \ge 1 \}. $$ I have the following, ...
2
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0answers
81 views

Looking for a subclass of deterministic context-free languages, other than the subclass of regular languages

Let $X=\{x_1,\ldots,x_n\}$ be a finite set of alphabet and $X^\ast$ denote the set of all words (including empty word) over $X$. Clearly, $X^\ast$ is a regular language. Is there a subclass, say $C$, ...
2
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0answers
15 views

Induction / (machine learning) of Resource Grammars for Grammatical Framework?

Grammatical Framework is based in Abstract Categorial Grammars. It is known that Combinatory Categorial Grammars have grammar induction/learning capabilities see e.g. https://link.springer.com/article/...
2
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0answers
80 views

How to prove that a language created from a context-free gramar's left side is regular(or left-linear)?

Given a context-free grammar $G$, let $\longrightarrow_G$ be the (one-step) rightmost derivation relation, and $\longrightarrow^*_G$ its reflexive and transitive closure. Let $S$ be the start symbol ...
2
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0answers
232 views

Is the complement of $L = \{a^nb^mc^p \, n= m= p\}$ context free language?

Is the complement of $L = \{a^nb^mc^p \ , n= m= p\}$ a context free language. I believe that we can write $L^{'} \ as \ L1 \cup L2$ where $L1=(a^*b^*c^*){'} \ $ $L2={{a^nb^mc^p \ m\ne n \ or \ n\...
2
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0answers
158 views

How would I build a parser generator for a context free grammar using Pushdown Automata?

I am building a parser generator, not for any project in particular, just for fun to improve my understanding of parsing, grammars, languages, etc. I am at the point where I have lexer generation ...
2
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0answers
141 views

Intuitive Explanation on Converting BNF Grammar to LR(1)

Consider the following BNF Grammar G: ...
2
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0answers
47 views

Effectively compute bound and period of regular expression on single alphabet

It is known that an infinite language $L\subseteq \{a\}^*$ is regular iff the set $U:=\{x|a^x\in L\}$ is ultimately periodic. (A set $U\subseteq\mathbb{N}$ is said to be ultimately periodic if there ...
2
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0answers
48 views

How to lexically list sentences in peano arithmetic?

I am working on building a toy automated theorem prover, What I want to do is to efficiently generate sentences in peano arithmetic, that I can attempt to verify as True/False/requires-more-resources ...
2
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0answers
189 views

Is asking a LL(1) parsing table for this grammar a trap?

I'm trying to solve some exercises for the upcoming Compilers' exam. Teacher gave us some sheets from previous exams to practice with - no answers provided. Let $\mathcal{G}$ be the following ...
2
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0answers
248 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
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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 ...
2
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0answers
4k views

Converting CNF to GNF

I'm studying context free grammars and I can grasp how to create context free grammars given a set notation, and now to convert these context free grammars to Chomsky Normal form but I am utterly ...
2
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0answers
2k views

Converting Chomsky Normal Forms to Greibach Normal Form

Here is a passage from Kozen's Automata and Computability (pages 145-146) that I'm confused about: Now we show how to convert an arbitrary grammar to an equivalent one (except possibly for $ \...
2
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0answers
561 views

Removing hidden ambiguity in grammar using left factoring

I am trying to reduce the grammar to LL(1) for a hypothetical language we created. I have removed most of the left factoring issues in the grammar, using the general rule of introducing new non-...
2
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0answers
66 views

What kind of structural features of strings can be described by regular grammars?

Context-free grammars, as well as other types of grammars, can naturally associate structure with the strings of the defined language, for example tree structures in the case of context-free language. ...
2
votes
1answer
196 views

Negative lookahead in LR parsing algorithm

Consider such a rule in grammar for an LR-family parsing generator (e.g YACC, BISON, etc.): Nonterminal : [ lookahead not in {Terminal1, ..., TerminalN} ] Rule ; ...
2
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0answers
565 views

Parsing family of grammars, determine if LR(k)

Consider the family of grammars $G_n,~n\geq2$. $$S \rightarrow A_ib_i~,~for~~1\leq i \leq n$$ $$A_i \rightarrow a_jA_i~|~a_j~,~for~~1 \leq i,j \leq n~~and~~i \neq j$$ where multiple alternative right ...
1
vote
1answer
38 views

Proving that the set of grammars generating L or L complement is undecidable

Let $X$ be a regular language, I need to prove that either $\{G \mid L(G) = X\}$ or $\{G \mid L(G) = \overline{X} \}$ is undecidable using the following hint: Use reduction to absurdity supposing that ...
1
vote
1answer
157 views

Prefix/suffix property of language containing only empty word

Does language $L ={\varepsilon}$, where $\varepsilon$ - empty word has suffix/prefix property? The definition says that language has prefix/suffix property requires that there is no code word in the ...
1
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0answers
50 views

Why full Chomsky hierarchy is so detailed, if there are decidable recursive languages?

One can have a look on the Chomsky hierarchy https://en.wikipedia.org/wiki/Chomsky_hierarchy , especially the inset named "Automata theory: formal languages and formal grammars" at the bottom of the ...
1
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0answers
22 views

Is there any difference in the expressiveness of boolean grammars versus definite clause grammars?

Definite clause grammars have been around a long time and are included in logic languages such as Prolog. They can be translated into (are just syntactic sugar for) Prolog programs and are therefore ...
1
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0answers
17 views

Clear definitions of various terms related to top down parsers and classification of the same

I am trying to clearly define various terms related to top down parser "so that I can relate them and come up with clear classification". Now this efforts might seem unnecessary as the terms I am ...
1
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0answers
22 views

Generalization of formal grammars - production rules with more general functions?

Usually formal grammars have production rules in the format N=tNt where simple concatenation function is used for the expansion of the nonterminal. https://www....
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0answers
34 views

Grammar for invertible functions

Has anyone ever come up with a grammar that only induces invertible functions, and does so in a way where it is possible to algorithmically construct the inverse function? It could be useful for ...
1
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0answers
107 views

Is star closure of reverse of grammar equivalent to reverse of closure of that grammar

I need to proof if that it's true or not. $ (G^R)^* = (G^*)^R $ If $G$ is a CFG and $ G = \langle V, \Sigma, \delta, S \rangle $ where $ V $ = Set of Variables or Non-Terminal Symbols $ \Sigma $ = ...
1
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2answers
99 views

CFG - Left factoring in recursive nested productions

I'm attempting to convert a CFG into an LL(1) grammar for predictive parsing in a compiler. I've been able to left factor and eliminate left recursion and ambiguity for every case in the grammar, with ...
1
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0answers
54 views

Constructing Context Free Grammar with 3 terminal symbols, with two dependent pairs

I am new to Context Free Grammars and am having trouble wrapping my head around how to approach writing a CFG for the following language: ...
1
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0answers
164 views

Unrestricted grammar is closed under intersection

I want to show that unrestricted grammar is closed under intersection and I don't want to use Turing machine or etc. So I think that we have two grammar $G_1$ and $G_2$ that are restricted for example ...
1
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0answers
50 views

Examples of context-free grammars whose ambiguity is unknown

Are there any examples of context-free grammars for which we simply do not know whether they are ambiguous? By examples I mean an actual specification for the grammar, not some kind of non-...
1
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0answers
300 views

Converting a non-deterministic context free grammar to deterministic

I have the non-deterministic context free grammar $$I \to abcX | abdY$$ $$X \to X d | \epsilon$$ $$Y \to XX |I$$ and i want to convert it into a deterministic. I know that the rules $I \to abcX | abdY$...
1
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0answers
235 views

Understanding definitions of Deterministic Context Free Grammar and Deterministic Pushdown Automaata

I read following here: Unambiguous grammars do not always generate a DCFL. Example: For example, the language of even-length palindromes on the alphabet of 0 and 1 has the unambiguous context-...
1
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0answers
25 views

CFG grammar with fixed number of “distinguished” terminals

I would like to know if there is a name for CFG grammars (or grammars in general) in which there is a fixed number of "distingushed" terminals or in which there is a terminal that appears a fixed ...
1
vote
2answers
297 views

Context-free grammar for binary words

I am supposed to create CFG for this languague: $L= \{w : w \in \{a, b\}^*, |w_b| = 3k, k \geq 0 \}$ where $|w_b|$ is count of terminals $b$ in $w$. For example: aa - OK, no 'b' abb - wrong, only ...