Context-Sensitive Grammar (CSG) & Language (CSL)

# Context-Sensitive Grammar (CSG) & Language (CSL) - Theory of Computation - Computer Science Engineering (CSE)

### Context-Sensitive Grammar –

A Context-sensitive grammar is an Unrestricted grammar in which all the productions are of form –

α → β
where α, β ∈ (V u T)+ and |α| ≤ |β|
Where α and β are strings of non-terminals and terminals.
Context-sensitive grammars are more powerful than context-free grammars because there are some languages that can be described by CSG but not by context-free grammars and CSL are less powerful than Unrestricted grammar. That’s why context-sensitive grammars are positioned between context-free and unrestricted grammars in the Chomsky hierarchy.

Context-sensitive grammar has 4-tuples. G = {N, Σ, P, S}, Where

N = Set of non-terminal symbols

Σ = Set of terminal symbols

S = Start symbol of the production

P = Finite set of productions

All rules in P are of the form α1 A α2 –> α1 β α2
Context-sensitive Language: The language that can be defined by context-sensitive grammar is called CSL. Properties of CSL are :

• Union, intersection and concatenation of two context-sensitive languages is context-sensitive.
• Complement of a context-sensitive language is context-sensitive.

Example – Consider the following CSG.

S → abc/aAbc

Ab → bA
Ac → Bbcc
bB → Bb
aB → aa/aaA
What is the language generated by this grammar?
Solution:
S → aAbc
→ abAc
→ abBbcc
→ aBbbcc
→ aaAbbcc
→ aabAbcc
→ aabbAcc
→ aabbBbccc
→ aabBbbccc
→ aaBbbbccc
→ aaabbbccc
The language generated by this grammar is {anbncn | n≥1}.

The document Context-Sensitive Grammar (CSG) & Language (CSL) | Theory of Computation - Computer Science Engineering (CSE) is a part of the Computer Science Engineering (CSE) Course Theory of Computation.
All you need of Computer Science Engineering (CSE) at this link: Computer Science Engineering (CSE)

## Theory of Computation

18 videos|56 docs|44 tests

## FAQs on Context-Sensitive Grammar (CSG) & Language (CSL) - Theory of Computation - Computer Science Engineering (CSE)

 1. What is a context-sensitive grammar (CSG) and how is it related to context-sensitive language (CSL)?
Ans. A context-sensitive grammar (CSG) is a formal grammar in computer science that allows the rules of a grammar to be applied in a context-sensitive manner, meaning that the rules can be based on the surrounding context. A context-sensitive language (CSL) is a language that can be generated by a context-sensitive grammar. In other words, a CSG is used to describe the syntax or structure of a CSL.
 2. How is a context-sensitive grammar different from a context-free grammar?
Ans. A context-sensitive grammar (CSG) allows the rules of a grammar to be applied in a context-sensitive manner, meaning that the rules can be based on the surrounding context. On the other hand, a context-free grammar (CFG) has rules that are applied without considering the context. In a CFG, the rules are applied solely based on the current non-terminal being expanded. This difference in rule application makes CSGs more expressive than CFGs and allows them to define more complex languages.
 3. What are some practical applications of context-sensitive grammars and languages?
Ans. Context-sensitive grammars and languages have various practical applications in computer science and natural language processing. Some examples include: - Syntax analysis and parsing of programming languages - Natural language understanding and processing - Speech recognition and synthesis - Compiler design and optimization - Formal language theory and linguistics research
 4. Can a context-sensitive language be recognized by a finite automaton?
Ans. No, a context-sensitive language (CSL) cannot be recognized by a finite automaton. Finite automata, such as deterministic finite automata (DFAs) and non-deterministic finite automata (NFAs), have a fixed number of states and cannot keep track of the necessary context information required to recognize a CSL. Instead, more powerful computational models such as pushdown automata or Turing machines are needed to recognize and generate context-sensitive languages.
 5. Are all natural languages context-sensitive languages?
Ans. Yes, all natural languages are considered to be context-sensitive languages (CSLs). This is because natural languages exhibit context-sensitivity in their syntax and meaning. The interpretation of words, phrases, and sentences in natural languages often depends on the surrounding context and the intended meaning. For example, the word "run" can have different meanings depending on the context, such as "to jog" or "to manage." Therefore, natural languages require context-sensitive grammars to accurately describe their syntax and semantics.

## Theory of Computation

18 videos|56 docs|44 tests

### Up next

 Explore Courses for Computer Science Engineering (CSE) exam

### Top Courses for Computer Science Engineering (CSE)

Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Track your progress, build streaks, highlight & save important lessons and more!
Related Searches

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

;