Master the fundamentals of regular expressions with these detailed lecture notes for COMP11212. Understand their syntax, semantics, and applications in pattern matching and text processing. These notes offer clear explanations, practical examples, and helpful diagrams, making it easier to grasp the...
Language
Human using complex systems of language Examples :
capacity for acquiring and communication , and a
is
any specific example of such a system
.
Gab ,
aa , ba , bby
In mathematics , computer science and linguistics a Eb aa aba, cbc, abobal
, formal language consists of words whose letters ,
, ,
taken from an alphabet and are well-formed according to a specific set of rules.
are
Sa ,
ab , abb , abbb, ...
3
Formal Language
Symbols Alphabet Word (or strings
concatenation with
· a
,
b, c, 0 ,
1 [a
·
,
b,
ch ·
abc , ana bbbbbca , a,
·
abc .
e = abc
, empty word
· r , 9, ·
40 , 13 · abc . bc =
abobes concatenation
·
(a) = aa
11 Caba)
· = abaaba aba
·
,
·
E < empty word
⑧
11 (
· red , green ,
blue
Now languages from old (set theory ( Kloone Star
Sab babuda, , by =
Sa ,
b , ab , bay L . La = (s t . s th , t t(z] ↳* =
(5 32
, ...
Sn nEIN
,
Sitt for all 0 bi
In]
2
lab , bay e gab by ,
=
(ab] ↳ =
L L .
** =
(2) =
10
3
Cab bas sab by =
[ba) ↳ = W L L .
.
, ,
L =
u(E) L Lu = L d h . .
... L
-
n times
Examples
[ = (a b, c) alphabet For given alphabet [we define language L( *)
,
a can a
such that
Lo =
(a , b)
Li =
Laa ,
ab
,
ac
,
ba bb , be ca ob
, , , , ] L( E) =
[7 ,
X2 ... In nEIN , Vie for all 0<i < n]
ha = Lo Lo . =
Gaa ,
ab , ba , bby
Le =
[V x ,
...
En neI
,
ne3
,
i ] all the words that are a
sequence on n characters such that
u is natural number and less than equal to
Sa is
a n or 3 and
=
,
bab , a
,
b
, c, a ,
...
] &i is in the alphabet I .
↳ G =
my ↳ Gha
ha = Cave ...
In NEI
,
Vie I ] < all the words that are a
sequence on n characters and
· xplicitely start with an 'a' Such thata is a natural number and
= Sabc , ada
,
aba
, a
,
...
Y &i is in the alphabet I .
↳ nhn = Saa ,
ab , acs
↳ (n = (ba ,
bb
,
bc , ca
,
(b
, <)
Li =
Slab)"nEIN] all the words that are a sequence of 'ab' concatenated to itself
n times such that n is a natural number
.
=
[2 ,
ab
,
abab
,
ababab
, ....
Regular Expressions
Definition 1: Let I be an alphabet. A pattern or
regular expression over I is any word over
Examples
Joat = v (0 ,
3
,, *, ( , 13 Operators > [0 ,
2
,
X
, 1 ,
*
]
*
generated by the
following recursive definition .
· I =
(a by , (a(b)
Empty pattern : The character I is a pattern
·
I = (a , b, 2) ((alb) (c) or (a)(b(c)) or
Calblc)
Empty word : The character a is a pattern
Letters : Every letter from I is a pattern
Concatenation : if p , and pe are patterns then so is (pipe)
Alternative If :
p, and pe are patterns then so is (p /Pc)
,
if pattern then (p )
*
Kleene star : p is a so is
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