2.1 & 2.2 grammar introduction – types of grammar
- 1. Grammar an Introduction & Types of Grammar -Sampath Kumar S, AP/CSE, SECE
- 2. Grammar an Introduction Noam Chomsky gave a mathematical model of grammar in 1956 which is effective for writing computer languages. Grammar A grammar G can be formally written as a 4-tuple (N, T, S, P) where 1. N or VN is a set of Non-terminal symbols 2. T or ∑ is a set of Terminal symbols 3. S is the Start symbol, S ∈ N 4. P is Production rules for Terminals and Non- terminals 11/21/2017 Sampath Kumar S, AP/CSE, SECE 2
- 3. Example 1: Grammar G1 − ({S, A, B}, {a, b}, S, {S → AB, A → a, B → b}) Here, S, A, and B are Non-terminal symbols; a and b are Terminal symbols S is the Start symbol, S ∈ N Productions, P : S → AB, A → a, B → b 11/21/20173 Sampath Kumar S, AP/CSE, SECE
- 4. Example 2: Grammar G2 − ({S, A}, {a, b}, S,{S → aAb, aA →aaAb, A → ε } ) Here, S and A are Non-terminal symbols. a and b are Terminal symbols. ε is an empty string. S is the Start symbol, S ∈ N Production P : S → aAb, aA → aaAb, A → ε 11/21/20174 Sampath Kumar S, AP/CSE, SECE
- 5. Chomsky Classification of Grammars According to Noam Chomosky, there are four types of grammars 1. Type 0 2. Type 1 3. Type 2 and 4. Type 3. 11/21/2017 Sampath Kumar S, AP/CSE, SECE 5
- 6. Chomsky Classification of Grammars The following table shows how they differ from each other 11/21/2017 Sampath Kumar S, AP/CSE, SECE 6 Grammar Type Grammar Accepted Language Accepted Automaton Type 0 Unrestricted grammar Recursively enumerable language Turing Machine Type 1 Context-sensitive grammar Context-sensitive language Linear - Bounded automaton Type 2 Context-free grammar Context-free language Pushdown automaton Type 3 Regular grammar Regular language Finite state automaton
- 7. Illustration 11/21/2017 Sampath Kumar S, AP/CSE, SECE 7
- 8. Type - 3 Grammar Type-3 grammars generate regular languages. Type-3 grammars must have a single non-terminal on the left-hand side and a right-hand side consisting of a single terminal or single terminal followed by a single non-terminal. The productions must be in the form X → a or X → aY where X, Y ∈ N (Non terminal) and a ∈ T (Terminal) The rule S → ε is allowed if S does not appear on the right side of any rule. Example X → ε X → a X → aY 11/21/2017 Sampath Kumar S, AP/CSE, SECE 8
- 9. Type - 2 Grammar Type-2 grammars generate Context - Free Languages. The productions must be in the form A → γ where A ∈ N (Non terminal) and γ ∈ (T∪N)* (String of terminals and non-terminals). These languages generated by these grammars are be recognized by a non-deterministic pushdown automaton. Example S → X a X → a X → aX X → abc X → ε 11/21/2017 Sampath Kumar S, AP/CSE, SECE 9
- 10. Type - 1 Grammar Type-1 grammars generate Context- Sensitive Languages. The productions must be in the form α A β → α γ β where A ∈ N (Non-terminal) and α, β, γ ∈ (T ∪ N)* (Strings of terminals and non-terminals) The strings α and β may be empty, but γ must be non-empty. The rule S → ε is allowed if S does not appear on the right side of any rule. The languages generated by these grammars are recognized by a Linear Bounded Automaton. Example AB → AbBc A → bcA B → b 11/21/2017 Sampath Kumar S, AP/CSE, SECE 10
- 11. Type - 0 Grammar Type-0 grammars generate recursively enumerable languages. The productions have no restrictions. They are any phase structure grammar including all formal grammars. They generate the languages that are recognized by a Turing machine. The productions can be in the form of α → β where α is a string of terminals and non-terminals with at least one non-terminal and α cannot be null. β is a string of terminals and non-terminals. Example S → ACaB Bc → acB CB → DB aD → Db 11/21/2017 Sampath Kumar S, AP/CSE, SECE 11
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- 13. நன்றி 11/21/2017 Sampath Kumar S, AP/CSE, SECE 13
Editor's Notes
- #2: School of EECS, WSU