TOC Introduction Of Grammer
TOC Introduction Of Grammer
Contents [hide]
- 1 Introduction to Grammar in Theory of Computation (TOC)
- 2 What is Grammar in TOC?
- 3 Example of a Grammar
- 4 Types of Grammar (Chomsky Hierarchy)
- 5 Importance of Grammar in TOC
- 6 Summary
- 7 Introduction to the Theory of Computation Languages, …
- 8 Introduction to the Theory of Computation, 3rd ed.
- 9 Introduction to Theory of Computation
- 10 theory of computation lecture notes
- 11 TOC Introduction Of Grammer
Introduction to Grammar in Theory of Computation (TOC)
In Theory of Computation (TOC), Grammar is a set of rules that defines how strings in a language are formed. It is mainly used to generate and analyze formal languages.
What is Grammar in TOC?
A Grammar (G) in TOC is formally defined as:
G = (V, T, P, S)
Where:
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V (Variables/Non-terminals): Set of symbols that can be replaced.
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T (Terminals): Set of symbols that appear in the final string.
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P (Production Rules): Rules that define how variables can be replaced by terminals or other variables.
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S (Start Symbol): The initial variable from which derivations begin.
Example of a Grammar
Consider a simple grammar:
G = ({S}, {a, b}, {S → aSb | ab}, S)
Production Rules:
S → aSb
S → ab
Generated Strings:
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ab(using rule 2) -
aabb(using rule 1 followed by rule 2) -
aaabbb(using rule 1 twice and then rule 2)
This grammar generates a language of balanced a and b pairs (like ab, aabb, aaabbb, etc.).
Types of Grammar (Chomsky Hierarchy)
Noam Chomsky classified grammars into four types:
| Type | Grammar Name | Rules Format | Example |
|---|---|---|---|
| Type 0 | Unrestricted Grammar | No restrictions | AI-generated texts |
| Type 1 | Context-Sensitive Grammar | α → β ( | α |
| Type 2 | Context-Free Grammar (CFG) | A → γ (Single Non-terminal → String) | `{aⁿbⁿ |
| Type 3 | Regular Grammar | A → aB or A → a | {a*, b*} |
Importance of Grammar in TOC
Used in Compilers for parsing programming languages.
Helps in designing automata (Finite Automata, Pushdown Automata, Turing Machines).
Forms the basis of syntax analysis in Natural Language Processing (NLP).
Summary
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Grammar defines the structure of languages in TOC.
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It consists of V (Variables), T (Terminals), P (Productions), and S (Start Symbol).
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Chomsky Hierarchy classifies grammars into four types.
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It is widely used in Compilers, NLP, and Automata Theory.
Do you need more examples or explanations on any type of grammar?