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Copyright @ 2009 Ananda Gunawardena
Lecture 18
Regular Expressions
Many of today’s web applications require matching patterns in a text document to look
for specific information. A good example is parsing a html file to extract <img> tags of a
web document. If the image locations are available, then we can write a script to
automatically download these images to a location we specify. Looking for tags like
<img> is a form of searching for a pattern. Pattern searches are widely used in many
applications like search engines. A regular expression(regex) is defined as a pattern
that defines a class of strings. Given a string, we can then test if the string belongs to this
class of patterns. Regular expressions are used by many of the unix utilities like grep,
sed, awk, vi, emacs etc. We will learn the syntax of describing regex later.
Pattern search is a useful activity and can be used in many applications. We are already
doing some level of pattern search when we use wildcards such as *. For example,
> ls *.c
Lists all the files with c extension or
ls ab*
lists all file names that starts with ab in the current directory. These type of commands
(ls,dir etc) work with windows, unix and most operating systems. That is, the command ls
will look for files with a certain name patterns but are limited in ways we can describe
patterns. The wild card (*) is typically used with many commands in unix. For example,
cp *.c /afs/andrew.cmu.edu/course/15/123/handin/Lab6/guna
copies all .c files in the current directory to the given directory
Unix commands like ls, cp can use simple wild card (*) type syntax to describe specific
patterns and perform the corresponding tasks. However, there are many powerful unix
utilities that can look for patterns described in general purpose notations. One such utility
is the grep command.
The grep command
Grep command is a unix tools that can be used for pattern matching. Its description is
given by the following.

.
The grep (Global Regular Expression Print) is a unix command utility that can be used to
find specific patterns described in “regular expressions”, a notation which we will learn
shortly. For example, the “grep” command can be used to match all lines containing a
specific pattern. For example,
grep “a href” guna.html output.txt
writes all lines containing the matching substring “a href” to the file output.txt
grep unix command can be an extremely handy tool for searching for patterns. If we do
grep “foo” filename
it returns all lines of the file given by filename that matches string foo.
Unix provide the | command (pipe command) to send an input from one process to
another process. Say for example, we would like to find all files that have the pattern
“guna”. We can do the following to accomplish that task.
ls | grep guna
We note again that Pipe command | is used to send the output from one command as
input to another. For example, in the above command, we are sending the output from ls
as input to grep command.
If we need to find a pattern a.c in a file name (that is any file name that has the substring
a.c, where dot(.) indicates that any single character can be substituted) we can give the
command
ls | grep a.c
So we can find file name that has the substring aac, abc, a_c etc.
grep
NAME
grep, egrep, fgrep - print lines matching a pattern
SYNOPSIS
grep [options] PATTERN [FILE...]
grep [options] [-e PATTERN | -f FILE] [FILE...]
DESCRIPTION
grep searches the named input FILEs (or standard input if no files are
named, or the file name - is given) for lines containing a match to
the given PATTERN. By default, grep prints the matching lines.
Source: unix manual

Text Processing Languages
There are many scripting languages that can be used to process textual data to extract and
manipulate patterns of interest. Among some of the popular languages are awk, sed and
perl. In this course, we will not go in detail into awk and sed, but will encourage students
to read and understand some of the use cases of these utilities as a general topic of
interest. We will however, later focus on perl, a popular programming language for
parsing textual data. Before we learn perl programming, we will focus on learning regular
expressions, a powerful way to describe general string patterns in perl. With the
understanding of regular expressions and perl syntax, we can write powerful programs to
accomplish interesting tasks.
Regular expressions
Regular expressions, that defines a pattern in a string, are used by many programs such
as grep, sed, awk, vi, emacs etc. The PERL language (which we will discuss soon) is a
scripting language where regular expressions can be used extensively for pattern
matching.
The origin of the regular expressions can be traced back to formal language theory or
automata theory, both of which are part of theoretical computer science.
A formal language consists of an alphabet, say {a,b,c} and a set of strings defined by the
language. For example, a language defined on the alphabet {a,b,c} could be all strings
that has at least one ‘a’. So “ababb” and “abcbbc” etc are valid strings while “ccb” is not.
An automaton (or automata in plural) is a machine that can recognize valid strings
generated by a formal language. A finite automata is a mathematical model of a finite
state machine (FSM), an abstract model under which all modern computers are built. A
FSM is a machine that consists of a set of finite states and a transition table. The FSM
can be in any one of the states and can transit from one state to another based on a series
of rules given by a transition function.
Example: think about a FSM that has an alphabet {a,b} and 3 states, Q0, Q1, and Q2
Define Q0 as the initial state, Q1 as intermediate and Q2 as the final or accepting state.
Complete the transitions so that the machine accepts any string that begins with zero or
more a’s immediately followed by one or more b’s and then ending with an ‘a’. So the
strings accepted by this FSM would include “aba”, “aaba”, “ba”, “aaaaaabbbbbbbbba”
etc.
Q0 Q1 Q2

Finite automata can be built to recognize valid strings defined by a formal language. For
example, we can use a machine as defined above to find all substrings that begins with
zero or more a’s immediately followed by one or more b’s and then ending with an ‘a’.
One important feature of a finite state machine is that it cannot be used to count. That is,
FSM’s have no memory. For example, we can build a machine to accept all strings that
has even number of a’s, but cannot build a FSM to count the a’s in the string.
Our discussion on FSM’s now leads to regular expressions. A regular expressions and
FSM’s are equivalent concepts. Regular expression is a pattern that can be recognized by
a FSM.
Regular Expression Grammar
Regular expression grammar defines the notation used to describe a regular expression.
We discuss here the basic concepts of regular expression grammar including
alternation, grouping and quantification. It should be noted that these grammar may
not work exactly as is in every system. The grammar defined here are applicable to strong
regex based languages such as perl.
Alternation
The vertical bar is used to describe alternating choices among two or more choices. For
example, the notation a | b | c indicates that we can choose a or b or c as part of the string.
Another example is that “(c|s)at” describes the expressions “cat” or “sat”.
Grouping
Parenthesis can be used to describe the scope and precedence of operators. In the
example above (c|s) indicates that we can either begin with c or s but must immediately
follow by “at”.
Quantification
Quantification is the notation used to define the number of symbols that could appear in
the string. The most common quantifiers are ?, * and +
The ? mark indicates that there is zero or one of the previous expression. For example
“aab?b” would represents the strings “aab” and “aabb” etc. Color and Colour can be
described by the regex “Colou?r”.
The “*” indicates that zero or more of the previous expression can be accepted. For
example: “a(ab)*b” indicates any string that begins with a, ends with a b, but can have
any number of the substring “ab” in the middle. The strings “ab”, “aabb”, “aababb” are
all valid strings described by the regex a(ab)*b.
The “+” indicates at least one of the previous expression. For example
“go+gle” would describe the expressions “gogle” , “google” , “gooogle” etc.

Other Facts
• . matches a single character
• .* matches any string
• [a-zA-Z]* matches any string of alphabetic characters
• [ag].* matches any string that starts with a or g
• [a-d].* matches any string that starts with a,b,c or d
• ^ab matches any string that begins with ab. In general, to match all lines that
begins with any string use ^string
grep command used with regular expression notation can make a powerful scripting
language. When using grep, be sure to escape special characters with .
Eg: grep ‘b(a | c ) b’ looks for patterns bab or bcb specifically
Example
1. Find all subdirectories within a directory
Answer: ls –l | grep “^d”
Character Classes
Character classes such as digits (0-9) can be described using a short hand syntax such as
d. A PERL(a language we shortly learn) programmer is free to use either [0-9] or d to
describe a character class.
• d digit [0-9]
• D non-digit [^0-9]
• w word character [0-9a-z_A-Z]
• W non-word character [^0-9a-z_A-Z]
• s a whitespace character [ tnrf]
• S a non-whitespace character [^ tnrf]
Note: we will not use these shorthand notations with grep
Other more general regex grammar includes
1. {n,m} at least n but not more than m times
2. {n,} – match at least n times
3. {n} – match exactly n times
Examples:
Find all patterns that has at least one but no more than 3, ‘a’s
(ans: grep “a{1,3}” filename)
Finding non-matches
To exclude patterns we can use [^class]. For example, to exclude patterns that may
contain a numeric digit, write [^0-9]. For example, we can exclude all lines that begins
with a-z by writing
grep “^[^a-z]” filename

Group Matching
If we group a match by using ( ) then the matching groups are given by 1, 2 etc..
For example a regex
h([1-4]).*h([1-3])
Returns 1 as the number that matched with the first group ([1-4]) and
2 as the number that matched with the second group ([1-3])
This can be useful in looking for patterns based on previous patterns found. For example
The regex
h[1-4] can match to h1, h2, h3, or h4.
Suppose later in the expression we need to match the same index. We can do this by
grouping [1-4] as ([1-4]) --- note we need ( to make sure that ( is not used as a literal
match ---
Now the match is saved in a variable 1 (must refer to as 1) it can be used later in the
expression to match similar indices. An application of this would be to look for
h1 …. h1 but not h1 …. h2
Here is how you do that.
grep “h([1-4]).*h1” filename
In general, the back-reference n, where n is a single digit, matches the substring
previously matched by the nth parenthesized sub expression of the regular expression.
This concept is sometimes called back reference. We will expand these ideas later in
Perl programming.
Summarized Facts about regex
• Two regular expressions may be concatenated; the resulting regular expression
matches any string formed by concatenating two substrings that respectively
match the concatenated subexpressions.
• Two regular expressions may be joined by the infix operator | the resulting
regular expression matches any string matching either subexpression.
• Repetition takes precedence over concatenation, which in turn takes precedence
over alternation. A whole subexpression may be enclosed in parentheses to
override these precedence rules.
• The backreference n, where n is a single digit, matches the substring previously
matched by the nth parenthesized subexpression of the regular expression.

• In basic regular expressions the metacharacters ?, +, {, |, (, and ) lose their
special meaning; instead use the backslashed versions ?, +, {, |, (, and ).
Source: Unix Manual
Exercises
1. Build a FSM that can accept any string that has even number of a’s. Assume the
alphabet is {a,b}.
2. Using grep command and regular expressions, list all files in the default directory
that others can read or write
3. Write a regex that matches the emails of the form userid@domain.edu. Where
userid is one of more word characters or ‘+’ and the domain is one or more word
characters.
4. Construct a FSM and a regular expression that matches patterns
containing at least one “ab” followed by any number of b’s.
5. Write the grep commands for each of the following tasks
a. Find all patterns that matches the pattern “ted” or
“fred”
b. Find all patterns that matches ed, ted or fed
c. Find all patterns that does not begin with “g”
d. Find all patterns that begins with g or any digit from
0-9
e. Find all patterns that begins with “guna”
f. Find lines in a file where the pattern “sam” occurs at
least twice
g. Find all lines in a file that contain email addresses
6. Write a regex that matches any number between 1000 and 9999
8. Write a regex that lists all the files in the current directory
that was created in Nov and are txt files.

ANSWERS
1. Build a FSM that can accept any string that has even number of a’s. Assume the
alphabet is {a,b}.
2. Using grep command and regular expressions, list all files in the default directory
that others can read or write
Ans: ls –l | grep ‘.{7}rw’
3. Write a regex that matches the emails of the form userid@domain.edu. Where
userid is one of more alpha characters or ‘+’ and the domain is one or more alpha
characters.
Ans: grep [a-z+]+@[a-z]+.edu
4. Construct a FSM and a regular expression that matches patterns
containing at least one “ab” followed by any number of b’s.
Ans: grep ‘(ab)+b*’
5. Write the grep commands for each of the following tasks
a. Find all patterns that matches the pattern “ted” or
“fred” [t/fr]ed
b. Find all patterns that matches ed, ted or fed
[t|f]?ed
c. Find all patterns that does not begin with “g”
^[^g]
d. Find all patterns that begins with g or any digit from
0-9
^(g|[0-9])
e. Find all patterns that begins with “guna”
^(guna)
f. Find lines in a file where the pattern “sam” occurs at
least twice
(sam).*1
g. Find all lines in a html file that contain email
addresses (hint: mailto)
Ans: [1-9][0-9]{3}

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