formal grammars real
DESCRIPTION
Formal Grammars RealTRANSCRIPT
-
REYNALD JAY F. HIDALGO, MS Computer ScienceProfessor
-
A set of atomic/non-divissible symbols
Eg. A = {a,b,c,d,e,f,g,h,I,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}A = {a,b,c}A = {0, 1}A = {+,-,*,/}
-
A sequence of symbol/s from a given alphabet
Eg.A = {a,b,c}w = aw = bw = cw = aaw = abcw = ccc
-
Denotes the empty string
w=
-
Denotes the length of a given string (an integer value)
w = abcd/w/ = 4w = 0/w/ = 1w = 12/w/ = 2w = /w/ = 0
-
Fundamental operation on strings
Let be the first string and be the 2nd stringThe concatenation of and is denoted by = .
-
= .
Where is the prefix of and is a proper prefix if while is the suffix of and is a proper suffix if
-
Any string concatenated with will result to the same string
-
denotes k copies of w
Given w = abcw3 = 3 copies 0f w = abcabcabc
-
Is a subset of the powerset W
-
S L EL V :=E if B then A else EE AB A < AB A = AA T + AA TT VT 0T 1T (E)V xV yV w
1. Generate the Algol statement w:= if x < y then 0 else x + y + 1
Prove that the following Algol statement is valid
x:= ( 1 + ( 0 + x ) )
Generate the Algol Statement
y := if ( x + y ) = 1 then 0 else ( if x < 0 then x else 0 )
-
NTP
-
It is a four-tupleG = (N, T, P, )Where N is a finite set of nonterminal symbolsT is a finite set of terminal symbolsN and T are disjoint: N T = P is a finite set of productions is the sentence symbol; (NT)
-
Each production P is an ordered pair of strings (,) = = In which ,, are possible empty strings in (NT)* and A is or a nonterminal letter. We usually write production () as
-
Let G1 have N = {A,B,C}, T =(a,b) and the set of productions A A aABC A abC CB BC bB bb bC bIdentify the Language L generated by G1
-
Let G2 have N = {A,B,C}, T (a,b,c) and the set of productions AA aABCA abCCB BCbB bbbC bccC ccIdentify the Language L generated by G2
-
Let G3 have N = {S}, T= (a,b) and the set of productions SS aSbS abdentify the Language L generated by G3
-
The Language L(G) generated by a formal grammar G is the set of terminal strings derivable from
-
Given a G an L can be derived
-
1. Let G4 have N = {A,B}, T= (1,0) and the set of productions 1B 1 A 1B B 0A A 1 Identify the Language L generated by G4
2. Let G5 have N = {A,B}, T= (1,0) and the set of productions B1 1 A B1 B A0 A 1 Identify the Language L generated by G5
-
Occurs when 2 or more derivation trees can be drawn from a single w
-
StructuralLabeling
-
Let G6 have N = {A}, T (0,1) and the set of productions AA A0AA 1Draw a derivation tree for the string 10101
-
Let G7 have N = {A,B}, T (1,0) and the set of productions A A B0 A A0 B B0 A 1 B 1Draw a derivation tree for the string 100
-
S S ScS S c 2. A B A A a A b A c B + B * Prove that the following Grammars are ambiguous. How? ConceptsN = {A,B,S}
-
AN {}, , and (N T)*, B N, a T
TYPEFORMAT OF PRODUCTIONSREMARKS0AUnrestricted Substitution RulesContracting1A, Context SensitiveNon-Contracting2A , Context FreeNon-Contracting
3A aBA aA BaA aRegular, Right Linear
Regular, Left LinearNon-Contracting