Questions tagged [context-free]

Questions about the set of languages (equivalently) described by context-free grammars or accepted by (non-deterministic) pushdown automata.

198 questions with no upvoted or accepted answers
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22
votes
2answers
448 views

Machines for context-free languages which gain no extra power from nondeterminism

When considering machine models of computation, the Chomsky hierarchy is normally characterised by (in order), finite automata, push-down automata, linear bound automata and Turing Machines. For the ...
21
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4answers
2k views

Algorithm to test whether a language is context-free

Is there an algorithm/systematic procedure to test whether a language is context-free? In other words, given a language specified in algebraic form (think of something like $L=\{a^n b^n a^n : n \in \...
14
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1answer
484 views

Is the language of words that are unbalanced in the first half context-free?

(Practice exam question in computational models) Definition: A word $w\in \{0,1\}^*$ is called balanced if it contains the same number of $0$s as $1$s. Let $L = \{w\in \{0,1\}^*\mid |w|$ is even and ...
10
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1answer
368 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 ...
6
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0answers
179 views

Is it decidable if this zipping operation gives a context-free language?

Motivation Consider the following languages, are they context-free? $\{x \# y: x \neq y\}$ $\{x y: |x|=|y|, x \neq y\}$ $\{x \# y: |x|=|y|, x \neq y\}$ $\{x y: |x|=|y|,d(x,y)>1\}$ $\{x x\}$ The ...
6
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0answers
681 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 ...
6
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1answer
524 views

Using the Chomsky-Schutzenberger theorem to prove a language is not context-free?

The Chomsky-Schutzenberger representation theorem states that a language $L$ is context-free iff there is a homomorphism $h$, a regular language $R$, and a paired alphabet $\Sigma = T \cup \overline{T}...
4
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0answers
111 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
92 views

is it decidable whether a grammar in Chomsky normal form has useless rules?

Given a context-free grammar in Chomsky normal form, is it decidable whether that grammar has any useless rules? By "useless", I mean a rule that can be omitted from the grammar without ...
3
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1answer
69 views

A language that is not context free

I working through some textbook exercises, and came across a problem that I'm struggling with. Give a CFL $L$ such that $\{x|\forall y \in \Sigma^* \space xy \in L\}$ is not a CFL. I've got the idea ...
3
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0answers
39 views

BNF rule to regular expression

I'm looking for a way to find out whether a specific rule in a BNF grammar can be converted to a regular expression. (With "regular expression" (RE), I mean the simple mathematical kind. I'm ...
3
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0answers
53 views

Are there context free grammars for all restricted Dyck paths?

A Dyck path is a finite list of $1$'s and $-1$'s whose partial sums are nonnegative and whose total sum is $0$. For example, [1, 1, -1, -1] is a Dyck path. Rather ...
3
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0answers
51 views

Conditions that imply closure under intersection of context-free languages

Context-free languages are not closed under intersection. Suppose $L_1, L_2 \in CF \setminus REG$ (i.e., $L_1,L_2$ are context-free but not regular). Are there well-known theorems (and/or whole ...
3
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0answers
96 views

Generating valid sentence with respect to attribute grammar

Given a context free grammar, both the algorithm for determining whether a given string is grammatical and the algorithm for producing a grammatical string in that language are well understood. To ...
3
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0answers
295 views

CFG for $\lambda$-calculus with minimal parentheses

The typical presentation of the syntax of the $\lambda$-calculus is as an ambiguous CFG (or BNF) like the following: $$T \rightarrow \lambda X . T \mid T ~ T \mid X \mid (T)$$ Where we permit $X$ to ...
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
264 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 ...
3
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0answers
79 views

Can we define CFL without grammars or automata?

The set of regular languages $R$ over an alphabet $\Sigma$ can be defined as the smallest set satisfying these 5 axioms: Empty language: $\{\} \in R$ Singleton languages: $\forall a \in \Sigma : \{a\}...
3
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0answers
273 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
334 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
101 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
15 views

Unparsing an operator grammar in the face of ambiguity

I'm using the grammar scheme of Danielsson and Norell ("Parsing Mixfix Operators"). The short version is: user defined mixfix operators such as _+_ or <...
2
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0answers
23 views

closure property violated by palindrome language

It is well established that palindrome language is non-regular. The one way to prove it is by means of pumping lemma. The other way is violating the closure properties of regular language. The ...
2
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0answers
226 views

Pumping lemma for L = {a^i b^j c^k: i < j < k}

I had a question regarding a specific proof I found online that I had some concerns with, I have quoted it below. Show that the language L = {a^i b^j c^k: i < j < k} is not a context-free ...
2
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0answers
2k views

Turing machine VS Push Down Automaton in CFL

I want to ask that between turing machine and pushdown automaton: which abstract machine can handle context-free language (CFL) in a more efficient way, and why? I know that a pushdown automaton can ...
2
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0answers
41 views

Is the language $L$ of coded CFG's Turing decidable?

Consider the following language $L$ = {$<G><w>$ | $G$ is a CFG and $w\in L(G)$} Now, I wish to prove that $L$ is Turing decidable. My gut tells me to construct a Turing machine that ...
2
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0answers
87 views

What strategies exist for handling/resolving ambiguity in parsers?

I define a parser as a context-free grammar with semantic actions for each production. It is not defined in what order the semantic actions run, just that the semantic actions of the non-terminals in ...
2
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0answers
103 views

What is the simplest automaton that can compute the sum of two integers of arbitrary length?

It should be obvious that a Turing machine is capable of computing the sum of two integers. However, what is the simplest automaton that can compute the sum of two integers of arbitrary length? I ...
2
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0answers
36 views

How to know a certain grammar is parse-able

Is it possible to parse all kinds of structured data and give them a semantic meaning? For example, C++ is a really complicated language and I could never imagine a parser would be possible for it. ...
2
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0answers
43 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
87 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
93 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
58 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-...
2
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0answers
87 views

Examples of context-free grammars with worst-case complexity

What are some examples of context-free grammars that necessarily trigger cubic worst-case complexity for GLR parsers? I have seen a mention of the example S $\rightarrow$ SSS | SS | "a" but I would ...
2
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0answers
546 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
586 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-...
2
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1answer
134 views

Language of CFG: $S \to aS | aSbS | \varepsilon$

I'm trying to prove that the language L generated by the CFG $S \to aS | aSbS | \varepsilon$ is the language $L=\{ w \in \{a,b\}^*: \text{every prefix of $w$ has at least as many $a$'s as $b$'s} \}$.I ...
2
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0answers
168 views

Intuitive Explanation on Converting BNF Grammar to LR(1)

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

Is the problem that intersection of two cfl is a cfl or not undecidable?

I am trying to use the computation histories argument to fit this. But I am unable to find this as yet.
2
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0answers
68 views

Correct bracketing check with rotate operation on position i

Given sequence (length $N$) of brackets like $($ and $)$. The task is to implement data structure which supports following operations: Check whether the sequence is correctly bracketed Rotate bracket ...
2
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0answers
254 views

Context free grammar as minimal solution of a system of equations

It is a well-known fact that language generated by a context-free grammar is the minimal solution of a particular system of equations, for example: $$\begin{align*} X &=\{{\epsilon}\} \cup Y\\ X ...
2
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0answers
77 views

Proof $\{u\colon |u| \text{ is odd and $b$ is in the middle}\}$ is not deterministic

Without using pumping lemma for deterministic context-free languages I need to prove that the language $\{u\colon |u| \text{ is odd and $b$ is in the middle}\}$ is not deterministic. Someone ...
2
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0answers
6k 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
68 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
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0answers
186 views

The grammar of the GeoQuery language

GeoQuery is a dataset used for benchmarking semantic parsers. It contains 880 queries about USA geography. The queries are in Prolog format, for example: answer(A,longest(A,(river(A),traverse(A,B),...
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0answers
26 views

How to generate a context-free grammar that defines a regex expression

As the title says, I have been asked to generate a grammar that defines the language of regular expressions. The symbols are: + . * | ? char I tried and came up with this but it doesn't work when ...
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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 ...
1
vote
1answer
514 views

How to convert regular expression to CFG?

How can I convert the regular expression (ab*)*b to a context-free grammar? When I look for examples I keep seeing plus signs in the expression but I don’t have any. Is that just a different way of ...
1
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0answers
48 views

How to interpret this context free language?

$S \to aAA$ $A \to aS \mid bS \mid a$ Trivial thing: starting and ending with a Atleast 3 a's are definitely present (These are very layman observations...but seriously I am unable to figure out what ...