This ppt will give you an idea about types of grammar in TOC. Learn from it and share it to share knowledge

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INSTITUTE OF TECHNOLOGY AND MANAGEMENT
TOPIC: TYPES OF GRAMMAR
CS-501(A):Theory of computation
Presented to- Presented by-
Dr . Deepak Gupta Abhay Dhupar 0905CS191001
Associate Professor Abhay Singh 0905CS191002
(Dept. of CSE) Abhinav Goyal 0905CS191003
Abhinav Gupta 0905CS191004

2. GRAMMARS
• Noam Chomsky gave a mathematical model of grammar.
This model is used to write computer languages effectively.
• Grammar in theory of computation is a finite set of formal
rules that are generating syntactically correct sentences.
• The formal definition of grammar is that it is defined as four
tuples
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3. CONT.
 G=(V,T,P,S)
 G is a grammar, which consists of a set of production rules. It is used to generate
the strings of a language.
 T is the final set of terminal symbols. It is denoted by lower case letters.
 V is the final set of non-terminal symbols. It is denoted by capital letters.
 P is a set of production rules, which is used for replacing non-terminal symbols
(on the left side of production) in a string with other terminals (on the right side
of production).
 S is the start symbol used to derive the string.
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4. CONT.
• V = { S , A , B } => Non-Terminal symbols
• T = { a , b } => Terminal symbols
• P = { S → ABa , A → Ba , B → ab} => Production rules
• S = { S } => Start symbol
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7. DIFFERENT TYPES OF GRAMMAR
Grammar can be divided on basis of –
 Type of Production Rules
 Number of Derivation Trees
 Number of Strings
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8. CONT.
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9. TYPES OF GRAMMAR
Grammar language Automata Production
Rules
Type 0 Recursively
enumerable
Turning machine No restriction
Type 1 Context-
sensitive
Linear-bounded Non-
deterministic machine
αAβ → αγβ
Type 2 Context-free Non-deterministic push down
Automata
A→γ
Type 3 Regular Finite Automata data A→αB
A→α
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10. CONT.
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11. TYPE 0
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Type 0 grammar language are recognized by turing machine.
Grammar Production in the form of
where
α is ( V + T)* V ( V + T)*
β is ( V + T )*.
In type 0 there must be at least one variable on Left side of production.
Ex -
Sab –> ba
A –> S.

12. TYPE 1
Type-1 grammars generate the context-sensitive languages.
The language generated by the grammar are recognized by the Linear
Bound Automata
In Type 1,
I. First of all Type 1 grammar should be Type 0.
II. Grammar Production in the form of
|α | <= | β |
i.e count of symbol in α is less than or equal to
Ex S –> AB
AB –> abc
B –> b
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13. TYPE 2
Type-2 grammars generate the context-free languages. The language
generated by the grammar is recognized by a Pushdown automata.
In Type 2,
1. First of all it should be Type 1.
2. Left hand side of production can have only one variable.
|α| = 1.
Their is no restriction on β .
Ex -
S –> AB
A –> a
B –> b
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14. TYPE 3
Type-3 grammars generate regular languages. These languages are
exactly all languages that can be accepted by a finite state automaton.
Type 3 is most restricted form of grammar.
It should be in the given form only :
V –> VT / T (left-regular grammar)
(or)
V –> TV /T (right-regular grammar)
Ex -
S –> a
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15. APPLICATION OF GRAMMAR
• For defining programming languages
• For parsing the program by constructing syntax tree
• For translation of programming languages
• For describing arithmetic expressions
• For construction of compilers, etc.
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16. THANK YOU
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