# ContextFree Languages 1 Regular Languages 2 ContextFree Languages

- Slides: 48

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

Example A context-free grammar : A derivation: 6

A context-free grammar : Another derivation: 7

Example A context-free grammar : A derivation: 9

A context-free grammar : Another derivation: 10

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Example A context-free grammar : A derivation: 12

A context-free grammar : A derivation: 13

Definition: Context-Free Grammars Grammar Variables Terminal symbols Start variables Productions of the form: is string of variables and terminals 15

Definition: Context-Free Languages A language is context-free if and only if there is a grammar with 16

Derivation Order Leftmost derivation: Rightmost derivation: 17

Leftmost derivation: Rightmost derivation: 18

Derivation Trees 19

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Derivation Tree 24

Derivation Tree yield 25

Partial Derivation Trees Partial derivation tree 26

Partial derivation tree 27

sentential form Partial derivation tree yield 28

Sometimes, derivation order doesn’t matter Leftmost: Rightmost: Same derivation tree 29

Ambiguity 30

leftmost derivation 31

leftmost derivation 32

Two derivation trees 33

The grammar is ambiguous: string has two derivation trees 34

The grammar is ambiguous: string has two leftmost derivations 35

Definition: A context-free grammar if some string is ambiguous has: two or more derivation trees 36

In other words: A context-free grammar if some string is ambiguous has: two or more leftmost derivations (or rightmost) 37

Why do we care about ambiguity? take 38

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Correct result: 41

• Ambiguity is bad for programming languages • We want to remove ambiguity 42

We fix the ambiguous grammar: New non-ambiguous grammar: 43

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Unique derivation tree 45

The grammar : is non-ambiguous: Every string has a unique derivation tree 46

Inherent Ambiguity Some context free languages have only ambiguous grammars Example: 47

The string has two derivation trees 48

- Every linear grammar generates a regular language
- 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
- Right linear grammar to left linear grammar
- Decision properties of regular language
- Properties of regular languages
- Closure properties of regular languages
- Perl
- Lateral area of a regular pyramid
- Convex polygon example
- Right regular solids
- 9-2 developing formulas for circles and regular polygons
- Irregular verbs principal parts
- The trampoline shown is shaped like a regular dodecagon
- Geometry area of regular polygons
- Define regular polyhedron
- Deseja se cimentar um quintal quadrado com lados medindo 8m
- Surface area of regular tetrahedron
- Areas of regular polygons and composite figures
- Preterite regular verbs
- Symmetry of regular octagon
- Technical drawing isometric projection
- Polygram theorem
- World history semester 2 exam review
- Simple squamos
- Modifying comparatives
- Polygon with 4 sides
- Present simple ed
- Conjugation of ir verbs in french
- Area de un trapecio regular
- Qué son emociones
- Present simple regular
- Ekivalensi
- Formas naturais e artificiais
- Fsmtoregexheuristic algorithm
- Present perfect regular
- Cuerpo
- Dense irregular connective tissue
- Parthenocarpic fruit
- Preterite pronounce
- Aturan produksi
- Traçado urbano irregular
- Irregular verbs 50
- Regular language
- A language is regular if and only if *