# Questions tagged [formal-grammars]

Questions about formal grammars, generative descriptions of formal languages.

1,023 questions
Filter by
Sorted by
Tagged with
161 views

### Is there any other computation theory besides the one in automata theory?

I'm a bit confused at a fundamental level. In Computer Science, maybe some of us mostly use discrete mathematics since our computer is digital (like during studying operating system, algorithms, ...
539 views

### Removing lambda-productions when it's at the start symbol

I had a question regarding removing lambda-productions from context-free grammars. I understand that the basic theorem or process for removing lambda-productions is to find nullable productions and ...
2k views

### Unrestricted grammar to generate $a^{n^2}$

I have been asked to find a grammar that will generate the language $\{a^{n^2}:n \ge0\}$ in an exercise. So far I tried to replicate the previously written characters with my grammar rules but it didn'...
20k views

### Steps to convert regular expressions directly to regular grammars and vice versa

I came across following intuitive rules to convert basic/minimal regular expressions directly to regular grammar (RLG for Right Linear Grammars, LLG for Left Linear Grammars): Then I came across many ...
271 views

### Closure under intersection of context free binary trees

Some sets of ordered binary trees can be represented as a CFG with rules of the form A -> aBC A -> b Where A,B,C are ...
334 views

### Generative power and classification of matrix grammars

[Edited] I am reading about matrix grammars from several sources and got confused about its generative power and classification to the Chomsky hierarchy. In here it is stated that: A matrix grammar ...
3k views

### Equivalence of two context free grammars [for the given example]

I know that in general it is undecidable whether two context free grammars generate the same language, but I have to do this exercise and I am finding myself somewhat stuck: G1: S->e|aB|bA B->bS|...
2k views

### Difference between substitution, morphism, and homomorphism

In closure properties, I got confused between substitution and morphism. 1) According to Wikipedia, string substitution means to map letters in a set of alphabets to languages (possibly in a ...
898 views

7k views

### Why do grammars in Chomsky Normal Form have derivations of length 2n-1?

I would like to know how they obtained the expression $2n-1$ as said from the excerpt of article (p.3): The key advantage is that in Chomsky Normal Form, every derivation of a string of n letters ...
86 views

### What is examples of languages to prove the inclusions between families of languages generated by matrix grammars?

$\lambda M_{ac}$ = family of languages generated by matrix grammar with appearance checking and with erasing rules $\lambda M$ = family of languages generated by matrix grammar without appearance ...
107 views

### Anatomy of a production rule

Production is said to be of the form $u \to v$. I want to know if you distinguish $u$ from $v$ giving them some distinguishing names, like LHS/RHS or something alike.
108 views

### How to give a context-sensitive grammar for a^nba^nba^nb?

I am struggling on this problem since days: $L = \{a^nba^nba^nb \mid n \in \Bbb N\}$. I have to give for this language a context-sensitive grammar.
558 views

### How to find unambiguous grammar for palindromes

I am trying to figure out how to make an unambiguous grammar for palindromes over the alphabet {a, b}. I have the following, but it is ambiguous and causes conflicts in yacc. ...
268 views

### Semantic readings of the Lambek sequent calculus

I am reading Categorial Grammar: Logical Syntax, Semantics, and Processing by Glyn Morrill and I am stuck with the Fig. 3.9: Can someone explain this set of formulas and |.| function specifically? ...
104 views

### How to express modalities in lambda calculus - are some extensions required?

Lambda calculus can be used for encoding semantics of natural language, e.g. http://yoavartzi.com/tutorial/ contains full details about semantic parsing of natural language: converting natural ...
472 views

### Meta-grammar for context-free grammars

Formal grammars like regular expressions (REs) or context-free grammars (CFGs) specify languages, i.e. sets of strings over an alphabet. Grammars themselves can be seen as languages, e.g. the set of ...
50 views

### How to make sense of this context-sensitive production in a textbook? (a typo perhaps?)

In Chapter 1 of Kenneth Slonneger and Barry L. Kurtz's Formal Syntax and Semantics of Programming Languages: A Laboratory Based Approach, an example of its production is given to illustrate the nature ...
72 views

### Language of walks in a grid – context-free?

Consider the infinite two-dimensional grid with integer co-ordinates. A walk in the grid can be represented by a string over the alphabet $\{u,d,l,r\}$, where the letters stand for moving one square ...
5k views

### Defining a context-free grammar for $\{w \in \{0, 1\}^* : \#_0(w) = \#_1(w)\}$ [duplicate]

I have a language where each string in the language has even amount of $0$'s as $1$'s (e.g., $0101$, $1010$, $1100$, $0011$, $10$ are all in the language). I was hoping to define a context-free ...
78 views

### Why are four context sensitive grammar (CSG) rules needed to represent AB -> CD?

In Wikipedia of Kuroda normal form, it says A straightforward technique attributed to György Révész transforms a grammar in Kuroda's form to Chomsky's CSG: AB → CD is replaced by four context-...
1k views

### Converting REGEX to BNF grammar

Say I have a bunch of regex expressions which are used as filtering rules. (Any special extraction capabilities are unnecessary here, the set of regular expressions I have is only used for filtering ...
265 views

### Do an ambiguous grammar and its corresponding unambiguous version generate the same language?

If I have an ambiguous grammar G and its disambiguated version D. Then which one is true L(D) ⊂ L(G) , L(G) ⊂ L(D) or L(G)=L(D)? As I tried with some examples to transform a grammar to it ...
1k views

### Syntax and formal grammar of a formal language

For a formal language, I wonder what differences and relations are between its syntax and its formal grammar. A formal grammar is a set of formation rules that describe how to generate the strings ...
157 views

### Gyorgy E. ReveszExercise 1.1: Show the grammar $G$ generates the language $L$ [duplicate]

The exercise says "Show that the grammar $G = \langle\{S\}, \{a, b\}, S, \{S \to \lambda, S \to aSb\}\rangle$ generates the language $L = \{a^i b^i \mid i = 0, 1, 2, \ldots\}$." Now, I'm new to ...
277 views

### Priority in formal grammar

From my recitation class, I have the following exercise: $\mathrm{EXP} = 0 \mid 1 \mid b \mathrm{EXP} \mid \mathrm{EXP} a \mid \mathrm{EXP} m \mathrm{EXP}$ The above grammar is ambiguous. ...
62 views

327 views

### Is it decidable whether a linear language contains a square?

A square is a word of the form $ww$. A linear grammar is a CFG that has productions of the form $A\to uBv$ or $A\to u$ (with lower case symbols corresponding to terminal strings). Question: Is it ...
139 views

### Arden's lemma applicability on context free grammars

The Arden's lemma states that there exists a solution to the equation between regular expressions r = sr + t, with r unknown, and it is s*t. I went through some other topics on the forum and I always ...