Regular expression

A regular expression is a pattern that describes a set of strings.
WHY?
 Regular expressions are used in many situation in computer programming.
 Majorly in search, pattern matching, parsing, filtering of results and so on.
 In lay man words, its a kind of rule which programmer tells to the computer to
understand.
 You may see this in website forms, where you are only forced to enter ONLY
numbers or ONLY characters or MINIMUM 8 characters and so on, these are
controlled by REGEX behind the screen.

 American mathematician credited for
inventing Regular Expressions in the
1950’s using a mathematic notation called
regular sets.

 Union +
 Concatenation .
 Kleene Star *

 Concatenation:
 x = 010
 y = 1101
 x.y = 010 1101
 Language Union:
 L1 = {01, 00}
 L2 = {01, 11, 010}
 L1 +L2 = {01, 00, 11, 010}
 Kleene closure
 1*={ε,1,11,111,1111,……}

(0 + 1)* All strings of 0’s and 1’s
01* 0 followed by any number 1’s
0(0 + 1)* All strings of 0’s and 1’s, beginning with a 0
(0 + 1)*1 All strings of 0’s and 1’s, ending with a 1

 Nondeterministic finite automaton with ε-moves (NFA-ε) is a further
generalization to NFA.This automaton replaces the transition function with the one
that allows the empty string ε as a possible input.The transitions without
consuming an input symbol are called ε-transitions.

8
For E1
For E2
For E1 E2
ε
ε ε
ε

Convert a regular expression to NFA :
(ab ∪ a)*

 In DFA, for each input symbol, one can determine the state to which the machine
will move. Hence, it is called Deterministic Automaton. As it has a finite number
of states, the machine is called Deterministic Finite Machineor Deterministic
Finite Automaton.

 A Generalized Nondeterministic Finite Automaton is similar to an NFA but the
transition function takes a state and a regular expression in the alphabet instead of a
state and an alphabet element.
The idea is that in state q0 the transition to state q1 can be taken if the next input
matches the regular expression 1101.

 A generalized nondeterministic finite automaton is a 5-tuple, (Q,∑, δ, qstart, qaccept),
where
 Q is the finite set of states,
 ∑ is the input alphabet
 δ : (Q - {qaccept} x (Q - { qstart }) → R is the transition function, where R is the set of all
regular expressions over ∑
 qstart is the start state
 qaccept is the accept state

 1.Add a new start state and a new final state.
 2. Add epsi transitions to the new states.
 3. Remove 3
 4. Link between 2 and f is now b
 5. Remove 3
 6. Add a new link between 2 and 2 with bb∪a as a lop.
 7. Now link between 1 and 2 with ba.
 8. Remove 2
 9. Link 1 and f with (a∪b)(bb∪a)*b
 10. Link s and f with ((a∪b)(bb∪a)*ba)*((a∪b)(bb∪a)*b)
 This is the regular Expression from this NFA

CFG
WHAT IS CFG??
CFG MEANS CONTEXT –FREE GRAMMAR. IN FORMAL LANGUAGE THEORY, A CONTEXT-FREE GRAMMAR (CFG) IS A CERTAIN
TYPE OF FORMAL GRAMMAR: A SET OF PRODUCTION RULES THAT DESCRIBE ALL POSSIBLE STRINGS IN A GIVEN FORMAL LANGUAGE.
IN SIMPLE WORD IT’S A NOTATION OF DESCRIBING LANGUAGE.
[SOURCE : HTTPS://EN.WIKIPEDIA.ORG/WIKI/CONTEXT-FREEG_RAMMAR]

WHAT DOES CFG DO??
A CFG PROVIDES A SIMPLE AND MATHEMATICALLY PRECISE MECHANISM FOR DESCRIBING THE
METHODS BY WHICH PHRASES IN SOME NATURAL LANGUAGE ARE BUILT FROM SMALLER BLOCKS,
CAPTURING THE BLOCK STRUCTURE OF SENTENCES IN A NATURAL WAY.

CONTENTS OF DESCRIPTIONS
1. AMBIGUOUS GRAMMAR
2. DERIVATION
3. PARSE TREE

AMBIGUOUS GRAMMAR
GENERALLY REPRESENT BY ( V T P S )
VARIABLE TERMINAL PRODUCTION START SYMBOL
EXAMPLE:
S- AB
A AA
HERE ,
A = TERMINAL
V = VARIABLE

DERIVATION
TWO TYPE OF DERIVATION:
1. LEFT-MOST DERIVATION:
SAB
DERIVATION START FROM THE LEFT SIDE VARIABLE.
2. RIGHT-MOST DERIVATION:
SAB
DERIVATION START FROM THE RIGHT SIDE VARIABLE.

PARSE TREE
SAA
AA
FOR STRING AA PARSE TREE IS:
S
A A
A A

EXAMPLE OF CFG
A REGULAR EXPRESSION THAT START AND END WITH SAME SYMBOL
A(A+B)*A + B(A+B)*B +A +B +Ε
L={AA, BB, ABA, ABBA, AABA, BAAAB……..}
HERE GRAMMAR IS:
S AAA|BAB|A|B|Ε
A AA|BA|Ε
FOR STRING AABA THE DERIVATION IS:
S AAA
 AAAA
 AABAA
 AABΕAA
 AABA

PARSE TREE:
S
A
A
A
A A B Ε A

Wrote the regex library which is what Perl and Tcl
languages used for regular expressions

 PCRE
 POSIX
 BASIC & EXTENDED REGEX
 ECMA REGEX
 & LOADS more!

 RegEx flavors are not consistent in implementation
WHY USE IT?
 It makes changing large amounts of repetitive text trivial as long as you can see
patterns.
 It makes you awesome in a geeky way.

 Programming Languages: Javascript, PHP, PERL, C/C++
 Command-Line: grep, awk, sed
 Text-Editors:Vim, Emacas, Notepad++
 IDE’s: Netbeans,Visual Studio

 Standard Characters
 Letters: A to Z, a to z
 Numbers: 0 to 9
 Symbols: !, @, #, %, &, e.t.c.
 Meta Characters
 Special Characters: )(][^$.|?*+
 To use those special characters escape them with blackslash

 Matches one & only characters in a set of characters.
 [Aa] matches either ‘A’ or ‘a’
 [a-z] matches one lowercase letter among specified range
 [^Aa] matches anything but ‘A; and ‘a’

 d, [0-9] digits 0 t0 9
 w, [da-zA-Z_] alphanumeric or _
 s , [t(?:n|rn)] whitespace

 Matches any single character but the newline.

 Using a pipe | , match either the left or right side of the pattern.
 (You | Me) matches a string that contains either

 {n} Matches exactly n times
 {n,} Matches n or more times
 {n,m} Matches between n and m times
 * Same as {0,1}
 + Same as {1,}
 ? Same as {0,1}

 Matches positions instead of characters
 ^ matches beginning
 $ matches end
 b matches between token

 Positive Lookahead
 Iron(?=man) matches “Iron” if it is followed by “man”
 Negative Lookahead
 Iron(?!man) matches “iron” if it is not followed by “man”
 Positive Lookbehind
 (?<=Iron)man matches “man” if it is preceded by “Iron’
 Negative Lookbehind
 (?<!Iron)man matches “man” if it is not preceded by “Iron”

Regular expression

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Regular expression