chapter 2 cf grammar and cf language-eng

8/3/2019 Chapter 2 Cf Grammar and Cf Language-Eng

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CF GRAMMARCF GRAMMAR

AND CFAND CFLANGUAGELANGUAGE

Chapter 2Chapter 2


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2.12.1CF GRAMMAR AND CFCF GRAMMAR AND CFLANGUAGELANGUAGE

Grammar can be divided into certaintype such :

Context-sensitive Grammar(csg) Context-free Grammar(cfg)

Right-linear Grammar


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Definition:Definition:

CFG. G represent with 4 tuples G =(V, , P, S):V is a set of variables(finite) or non-

terminal symbol is a set of terminal symbol (end),

where V =

S is a start symbol, where S V

P is a set (finite) of production rules thatis in a form of A for A V, (v )*.


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Context-free DefinitionContext-free Definition

Context-free Grammar (cfg) is asystem to generate a set of string oflanguage. This process is done by

changing a string using productionrules. Grammar is called context-freebecause of the general applicability

of the rules.


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Example:Examp

le:P : S uAv

A w

String derivation is:S => uAv => uwv

A string w can be derived from v if there are sequencial usedof rules that convert v to w:

v => w1 => w2 => ... => wn => w

Or writen as:*

v => w


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Let G = (V, , P, S) is cfg:

A string w(V )* is a sententialform of G if there is a derivation S=>*w in G.

A string w* is a sentence of G ifthere is a derivation S =>* w inG.

A language of G denoted L(G), is theset (w * S=>*w).


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Example:Example:

G = ({S}, {a,b}, P, S)P: S aS bS

String derivation :S => S => aS => a => aS => bS => b => bS => aS => aaS => aa => aaS => aS => abS => ab => ab

S => bS => bbS => bb => bb.................S => ... => combination of a and b


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Language is formed from certainword in a or b or combination of aand b, defined by regular expression:

L (G) = (a+b)*


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Derivation tree,DtDerivation tree,Dt

If G = (V, , P,S) is a cfg and S=>*w is aderivation. Derivation tree Dt for S=>*wis a process of building D.t as follows: Dt begin with S as root.

If A x1, x2, .... xn with xi(V) is the i rulefor string derivation uAv, then the addition x1,x2,..., xn is for the child of A tree.

If A is the i derivation in a string derivation

uAv, then the addition is a child for A tree.


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Contoh:Contoh:

G = ({S,.A}, {a, b}, P, S)P: S AA

A AAA bA Ab aThen string derivation for string formation ababaa is:S => AA => aA => aAAA => abAAA

=> abaAA => ababAA => ababaa

Figure ofderivation tree


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Cfg G called ambiguous, if there aren L(G), where n have more thanone method or different tree

derivation.

Cf language L is a naturalambiguous if every cfg generate L

is ambiguous.


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Example:Example:G = ({S}, {a,b}, P,S)

P : S aS Sa b Two derivation method for string aba is:

S =>aS > aSa => aba

or

S => Sa => aSa => aba

Production rules can be modified so that everyword in a language can be derived with only onemethod.


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Example:Example:P :S aS bB

B aB There only one way for string derivation for string formation aba:S => aS => abB => abaB => aba => aba

If there are n times derivation on the S

aS

bB rules, it willproduce,S => anS and then S => anbB

For derivation of m times doe on a rule of B aB it will produce:B => amB

andB => am => am

So,S => anbB => anbam {anbam n 0, m 0 } a*ba*


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Regular GrammarRegular GrammarDefinition:

Regular language is a language that can be generate byregular grammar.

Regular grammar is cfg. G consist of 4 tuples G = (V, , P,S), where every production rules in forms as below:

A aA aBA for A,BV and a. Grammar can also be classified into regular grammar and

non regular grammar.


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Example: RegularExample: RegularGrammarGrammar

L = a+b*

G1 = ({S,R}, {a,b}, P,S)

P = S

aS aRR bR L is a regular language because it

can be generate by regular grammarproduction rules.


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Example:non regularExample:non regular

L = a + b*

G1 = ({S,A,B}, {a,b}, P,S)

P : S AB

A aA aB bB

L is not regular language because itcannot be generate by regular grammarproduction rules.


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2.22.2Example of BNF inExample of BNF inPascal LanguagePascal Language

Cfg is in Backus Naur Form (BNF) ifevery variable writen in whereproduction writen as:

BNF usually being used to showsyntax for programming languagesuch as Pascal, C, ect.


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Example of BNF format forExample of BNF format fora simple language:a simple language:

:=

A B C

+

-

() *

where: var, exp, := A, B, C, +, *, -, ( , ) is asymbol used in grammar definition for a simple

phrase assign. Symbol Meaning

nonterminalor starting symbol

or:=,+,-,*,A,B,C, (.) terminal


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Example of BNF UsageExample of BNF Usage(Pascal language):(Pascal language):

A := B*(A+B) :=

A :=

A := *A := *()A := B* ()A := B*(+)

A := B*(A+)A := B*(A+)A := B*(A+B)


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contcontA := B*C(A+C) also represented inparse tree

form as below:

chapter 2 cf grammar and cf language-eng

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