Chomsky Classification of Grammar || GATECSE || TOC
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- เผยแพร่เมื่อ 10 ม.ค. 2025
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chomsky classification of grammar || chomsky hierarchy || chomsky hierarchy of formal languages || chomsky hierarchy of languages in theory of computation || type 0 grammar || type 1 grammar || type 2 grammar || type 3 grammar || context free grammar || computer science lectures for gate || automata lecture for gate || chomsky hierarchy in toc || chomsky classification in toc || chomsky classification of formal language || chomsky hierarchy of languages
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This video discusses the Chomsky Hierarchy, a classification system used in automata for grammar. It identifies three types of grammar: Unrestricted Grammar (Type 0), Context Sensitive Grammar (Type 1), Context Free Grammar (Type 2), and Regular Grammar (Type 3). The hierarchy categorizes languages accepted by different machines into three types: Unrestricted, Context Sensitive, Context Free, and Regular.
Type 0 grammar, also known as Unrestricted grammar, allows for the efficient modeling of languages with no restrictions on their grammar rules.
Type 1 grammar, also known as Context Sensitive Grammar, is used to represent context-sensitive language. It follows rules such as having multiple symbols on the left side of production rules, not exceeding the right-hand side's number of symbols, and not allowing the rule A → ε unless A is a start symbol. Type 1 grammar should be Type 0, with production in the form of V → T.
Type 2 Grammar, also known as Context Free Grammar, is a type of language that can be represented by the context free grammar (CFG). Its production rule is based on the form A → α, where A is a single non-terminal or a combination of terminals and non-terminals.
Type 3 Grammar, also known as Regular Grammar, describes languages using regular expressions and can be modeled using NFA or DFA. It is the most restricted form of grammar, requiring Type 2 and Type 1 and forming the form of V → T*V / T* or V → VT* / T*.
03:17 Chomsky classification of grammar
06:34 Chomsky Classification of Grammar
09:51 Type 0 grammar is defined using 4 tuples: V, T, P, S
13:08 Chomsky classification of grammar
16:25 Chomsky classification of type 1 grammar
19:42 Representation of grammar and Chomsky Classification
22:59 Chomsky classification defines type 2 and type 3 grammar
26:13 Chomsky classification of grammars involves left linear and right linear grammars.
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right sir
Context-Free Languages (CFLs) are Type 2 in the Chomsky hierarchy. They sit above Regular Languages (Type 3) but below Context-Sensitive Languages (Type 1) and Recursively Enumerable Languages (Type 0).
Type 3 (Regular Languages) are simpler than context-free languages and can be recognized by finite automata, which have no memory stack.
Type 2 (Context-Free Languages) can be recognized by pushdown automata, which have an additional stack for memory, making them more powerful than finite automata. This allows CFLs to handle nested structures, like balanced parentheses or recursion in programming languages, which regular languages cannot.
Type 1 (Context-Sensitive Languages) are more powerful than context-free languages. These languages require a more complex computational model (linear-bounded automaton), and their grammar allows rules where the left side of a production can be longer than the right side.
Type 0 (Recursively Enumerable Languages) are the most powerful and can be recognized by Turing machines, which can simulate any computation. These languages encompass all others but are much more complex and less efficient to parse.
Key Differences:
Context-Free Languages (CFLs) can handle recursion and nested structures (e.g., matching parentheses in programming languages), but they can't handle some constructs that require context (e.g., matching an equal number of as, bs, and cs in the string "a^n b^n c^n").
Context-Sensitive Languages (CSLs) are more powerful than CFLs and can handle certain dependencies between different parts of a string that context-free grammars cannot. For example, CSLs can describe languages where the number of symbols from different sets must match (e.g., "a^n b^n c^n").
Summary of Chomsky Hierarchy:
Type 3: Regular Languages (RL)
Simple rules, recognized by finite automata.
Example: a*, valid phone numbers.
Type 2: Context-Free Languages (CFL)
One non-terminal on the left side of each production rule, recognized by pushdown automata.
Example: Arithmetic expressions, programming languages syntax.
Type 1: Context-Sensitive Languages (CSL)
Rules can have context-dependent production, recognized by linear-bounded automata.
Example: Some programming languages and more complex syntactic structures.
Type 0: Recursively Enumerable Languages (RE)
Unrestricted grammar, recognized by Turing machines.
Example: Complex natural languages and certain computations.
Conclusion:
Context-Free Languages are an important class of languages in the Chomsky hierarchy because they describe many of the syntactical structures in programming languages. They are more powerful than regular languages but less powerful than context-sensitive languages. Understanding where CFLs fit in the hierarchy helps in designing compilers, interpreters, and understanding the complexity of different languages.
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G = {V,T,P,S}
Type 0 : Unrestricted Grammar : Turing machine
Rule : NT -> (NT+T)*
Note : There should be a non terminal defining a set of terminal or non terminal
a->S fail
Type 1 : Context Sensitive Grammar : Linear bounded Automata
Note : There should be no null production in NT->(NT+T)+
|LHS|a/e; If this is done then S should not come on the RHS at any time.
Type 2 : Context Free Grammar : Push Down Automata
Note : |LHS|=1
Null production is allowed anywhere
Type 3 : Regular Grammar : Finite Automata
Note : It should be either RLG or LFG, right/left linear grammar, it shouldnt be a combination
S->aS/Sb is wrong,so it is not type 3
Wait till end you get better understanding and tackle with question❤
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sir aB--> AB i also Type 0
Bhaishab pair kaha h aapke🙌
Y€ vT*/T*
Then Y€ V, means y belongs to single variable only
S-> A , is it true
Yes
Then how it is left linear or right linear
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