ContextFree Languages 1 Regular Languages 2 ContextFree Languages
- Slides: 74
Context-Free Languages 1
Regular Languages 2
Context-Free Languages Regular Languages 3
Context-Free Languages Context-Free Grammars Pushdown Automata stack automaton 4
Context-Free Grammars 5
Grammars express languages Example: the English language 6
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A derivation of “the dog walks”: 8
A derivation of “a cat runs”: 9
Language of the grammar: L = { “a cat runs”, “a cat walks”, “the cat runs”, “the cat walks”, “a dog runs”, “a dog walks”, “the dog runs”, “the dog walks” } 10
Notation Production Rules Variable Terminal 11
Another Example Grammar: Derivation of sentence : 12
Grammar: Derivation of sentence : 13
Other derivations: 14
Language of the grammar 15
More Notation Grammar Set of variables Set of terminal symbols Start variable Set of Production rules 16
Example Grammar : 17
More Notation Sentential Form: A sentence that contains variables and terminals Example: Sentential Forms sentence 18
We write: Instead of: 19
In general we write: If: 20
By default: 21
Example Grammar Derivations 22
Example Grammar Derivations 23
Another Grammar Example Grammar : Derivations: 24
More Derivations 25
Language of a Grammar For a grammar with start variable : String of terminals 26
Example For grammar : Since: 27
A Convenient Notation 28
Example A context-free grammar : A derivation: 29
A context-free grammar : Another derivation: 30
Describes parentheses: (((( )))) 31
Example A context-free grammar : A derivation: 32
A context-free grammar : Another derivation: 33
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Example A context-free grammar : A derivation: 35
A context-free grammar : A derivation: 36
Describes matched parentheses: () ((( ))) (( )) 37
Definition: Context-Free Grammars Grammar Variables Terminal symbols Start variable Productions of the form: Variable String of variables and terminals 38
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Definition: Context-Free Languages A language is context-free if and only if there is a context-free grammar with 40
Derivation Order Leftmost derivation: Rightmost derivation: 41
Leftmost derivation: Rightmost derivation: 42
Derivation Trees 43
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Derivation Tree 48
Derivation Tree yield 49
Partial Derivation Trees Partial derivation tree 50
Partial derivation tree 51
sentential form Partial derivation tree yield 52
Sometimes, derivation order doesn’t matter Leftmost: Rightmost: Same derivation tree 53
Ambiguity 54
leftmost derivation 55
leftmost derivation 56
Two derivation trees 57
The grammar is ambiguous: string has two derivation trees 58
The grammar is ambiguous: string has two leftmost derivations 59
Definition: A context-free grammar if some string is ambiguous has: two or more derivation trees 60
In other words: A context-free grammar if some string is ambiguous has: two or more leftmost derivations (or rightmost) 61
Why do we care about ambiguity? take 62
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Correct result: 65
• Ambiguity is bad for programming languages • We want to remove ambiguity 66
We fix the ambiguous grammar: New non-ambiguous grammar: 67
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Unique derivation tree 69
The grammar : is non-ambiguous: Every string has a unique derivation tree 70
Another Ambiguous Grammar IF_STMT if EXPR then STMT else STMT 71
If expr 1 then if expr 2 then stmt 1 else stmt 2 IF_STMT if expr 1 if then expr 2 STMT then stmt 1 else STMT else stmt 2 IF_STMT if expr 1 if then expr 2 then stmt 1 72
Inherent Ambiguity Some context free languages have only ambiguous grammars Example: 73
The string has two derivation trees 74
- Regular grammars generate regular languages
- Right linear grammar to left linear grammar
- Decision properties of regular languages
- Properties of regular languages
- Closure under intersection
- Regular and irregular languages
- Pumping lemma non regular languages examples
- Decision properties of regular languages
- Proof by contradiction examples
- Decision properties of regular languages
- Decision properties of regular languages
- A method to make regular saving easier is ____.
- Aturan produksi
- Malha estrutural irregular
- Regular polyhedra
- Regular language
- Best feature articles
- Dense regular ct
- 10 3 areas of regular polygons
- Regular expressions wikipedia
- Triangulo equilatero caracteristicas
- Examples of irregular adverbs
- A regular polygon is equiangular
- Unit 11 homework 4 area of regular figures
- Pentagon shape
- Geo algebra
- Cuales son los verbos regulares
- Anlogos
- Regular quadrilaterals
- Secular franciscan clothing
- Algebraic properties of regular expression
- Oabc is a parallelogram p is the point on ac
- Ordinary speech with no regular pattern of accentual rhythm
- Affirmative past simple tense
- Fui di vi
- Fixed connective tissue
- Chop regular or irregular verb
- Escondidas es un verbo
- Reloj es regular o irregular
- Regular expression
- Enjambment
- Create length and height in hair design.
- A pentagonal plate of side 30mm
- Notasi ekspresi reguler
- Regular language properties
- Erection
- Vital signs according to age
- Total surface area of pyramid
- Irregular past tense of blow
- Principal parts of regular and irregular verbs
- Espelho física
- Concave polygon
- Area of a regular nonagon
- Principal parts of regular and irregular verbs
- Symmetry of regular octagon
- Rhythm is the of visual movement colors shapes or lines
- Regular and irregular verbs play
- Polygon properties
- Cepillarse preterite
- Regular expression symbols
- Nome de todas as pirâmides
- Area de un trapecio regular
- Bien mal regular
- Expressao regular
- Fluido espinhal
- Que son las emociones ?
- 11-4 area of regular polygons
- Calibri regular
- Modifying comparatives
- Polígonos convexos
- Malo regular bueno excelente
- Cdef is a quadrilateral
- Regular vs irregular dense connective tissue
- Grab minulý čas
- Sentences with regular and irregular verbs