Chomsky Classification of Grammar || GATECSE || TOC

[@KaushalBeniwal_]

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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[@RohitKumar-gx5zx]

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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[@panvirsingh9428]

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[@technopal7969]

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[@anishsingh9043]

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

[@fukrajvd]

Wait till end you get better understanding and tackle with question❤

[@omthorat4962]

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[@tanishqyadav9379]

sir aB--> AB i also Type 0

[@nishantkumar1360]

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[@subhash07092]

Y€ vT*/T* Then Y€ V, means y belongs to single variable only S-> A , is it true

[@THEGATEHUB]

Yes

[@subhash07092]

Then how it is left linear or right linear

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