Cfg part i

Recap
Applications of minimum edit distance, calculating minimum edit
distance.
•1

Today’s Agenda
 Context Free Grammar,
 Terminals,
 non-terminals,
 productions,
 CFG,
 context Free language,
 examples.
•2

Context Free Grammar (CFG)
The earliest computers accepted no
instructions other then their own
assembly language. Every procedure,
no matter how complicated , had to
be encoded in the set of instructions,
LOAD, STORE, ADD the contents of two
registers and so on. The major problem
was to display mathematical formulas
as follows
•3
2
)1011()107()08( 222
−+−+−
=S
or

CFG continued …
So, it was necessary to develop a way
of writing such expressions in one line of
standard typewriter symbols, so that in
this way a high level language could
be invented. Before the invention of
computers, no one would ever have
dreamed of writing such complicated
formula in parentheses e.g. the right
side of formula can be written as
((1/2)+9)/(4+(8/21)+(5/(3+(1/2))))
•4
2
1
3
5
21
8
4
9
2
1
+
++
+
=A

CFG continued …
The high level language is converted into
assembly language codes by a program
called compiler.
The compiler that takes the user’s
programs as its inputs and prints out an
equivalent program written in assembly
language.
Like spoken languages, high level
languages for computer have also, certain
grammar. But in case of computers, the
grammatical rules, don’t involve the
meaning of the words.
•5

CFG continued …
It can be noted that the grammatical rules
which involve the meaning of words are
called Semantics, while those don’t
involve the meaning of the words are
called Syntactics.
e.g. in English language, it can not be
written “ Buildings sing ”, while in computer
language one number is as good as
another.
e.g. X = B + 10, X = B + 999
Following is a remark
•6

Remark
In general, the rules of computer language grammar,
are all syntactic and not semantic. A law of grammar
is in reality a suggestion for possible substitutions.
•7

CFG terminologies
Terminals: The symbols that can’t be replaced by
anything are called terminals.
Non-Terminals: The symbols that must be replaced by
other things are called non-terminals.
Productions: The grammatical rules are often called
productions.
•8

CFG
CFG is a collection of the followings
1. An alphabet ∑ of letters called terminals
from which the strings are formed, that will
be the words of the language.
2. A set of symbols called non-terminals, one of
which is S, stands for “start here”.
3. A finite set of productions of the form
A Non-terminal  finite string of terminals
and /or non-terminals.
Following is a note in this regard
•9

Note
The terminals are designated by small letters, while the
non-terminals are designated by capital letters.
There is at least one production that has the non-
terminal S as its left side.
•10

Context Free Language (CFL)
The language generated by CFG is called Context Free
Language (CFL).
Example:
∑= {a}
productions:
1. S aS
2. S^
Applying production (1) six times and then
production (2) once, the word aaaaaa is
generated as
•11

•12
S aS
aaS
aaaS
aaaaS
aaaaaS
aaaaaaS
aaaaaa^
= aaaaaa
⇒
⇒
⇒
⇒
⇒
⇒
⇒

Example continued …
It can be observed that prod (2)
generates ^, a can be generated
applying prod. (1) once and
then prod. (2), aa can be
generated applying prod. (1)
twice and then prod. (2) and so
on. This shows that the grammar
defines the language expressed
by a*
.
•13

Example
∑ = {a}
productions:
1. SSS
2. Sa
3. S^
This grammar also defines the language
expressed by a*
.
Note: It is to be noted that  is considered to be
non-terminal. It has a special status. If for a
certain non-terminal N, there may be a
production N. This simply means that N can be
deleted when it comes in the working string.
•14

Example
∑ = {a,b}
productions:
1. SX
2. SY
3. X^
4. YaY
5. YbY
6. Ya
7. Yb
•15

Example continued …
All words of this language are of
either X-type or of Y-type. i.e. while
generating a word the first
production used is SX or SY.
The words of X-type give only ,
while the words of Y-type are
words of finite strings of a’s or b’s or
both i.e. (a+b)+
. Thus the language
defined is expressed by (a+b)*
.
•16

Example
∑ = {a,b}
productions:
1. SaS
2. SbS
3. Sa
4. Sb
5. S^
This grammar also defines the language
expressed by (a+b)*
.
•17

Example
∑ = {a,b}
productions:
1. SXaaX
2. XaX
3. XbX
4. X^
This grammar defines the language
expressed by (a+b)*
aa(a+b)*
.
•18

Summing Up
Context Free Grammar, Terminals, non-terminals,
productions, CFG, context Free language, examples.
•19

Cfg part i

More Related Content

What's hot (19)

Similar to Cfg part i (20)

Recently uploaded (20)

Cfg part i