Simple techniques
for plagiarism detection
in student programming projects
Szymon Grabowski, Wojciech Bieniecki
Computer Engineering Dept.,
Tech. Univ. of Łódź, Poland
{SGrabow, WBieniec}@kis.p.lodz.pl
We plagiarized it...
Sieci i Systemy Informatyczne, Łódź, październik 2006
What is plagiarism?
http://library.kcc.hawaii.edu/main/images/plagiarism_cartoon.gif
Sz. Grabowski & W. Bieniecki, Simple techniques for plagiarism detection...
2
Plagiarism everywhere
• text (articles, scientific papers
(also self-plagiarisms), essays
...or just plot ideas in fiction books)
• music (melodies, “sampling”)
• images (copy/paste e.g. from web pages)
Our interest: text plagiarism.
Sz. Grabowski & W. Bieniecki, Simple techniques for plagiarism detection...
3
Text plagiarism
• stealing natural language (NL) texts
• stealing software code
Sz. Grabowski & W. Bieniecki, Simple techniques for plagiarism detection...
4
Previous work (1/3)
Faidhi & Robinson (1987):
six levels of program modification in a plagiarism attempt:
(i) changing comments,
(ii) changing identifier names,
(iii) reordering variable positions,
(iv) procedure combination,
(v) changing program statements,
(vi) changing control logic.
Changes in the program control logic are most
laborious (and vulnerable to hard-to-detect errors)
but also hardest to properly identify as plagiarism.
Sz. Grabowski & W. Bieniecki, Simple techniques for plagiarism detection...
5
Previous work (2/3)
Irving (2004):
finding local similarity with a variant of
the Smith-Waterman classic algorithm (1982).
Aim: taking care of both precision/recall and speed.
Pretchelt et al. (2000):
JPlag online system.
Basic technique: find a set of indentical substrings
of strings A and B, adhering to a few simple rules.
Quite robust to reordering parts of the text.
Sz. Grabowski & W. Bieniecki, Simple techniques for plagiarism detection...
6
Previous work (3/3)
Many algorithms based on various
code complexity measures
(like e.g. the number of execution paths through a program).
(See [Clough, 2000] for details.)
Mozgovoy et al. (2005):
Suffix array based alg.
to decrease the computation complexity of
all-against-all file comparison.
Sz. Grabowski & W. Bieniecki, Simple techniques for plagiarism detection...
7
Our motivation
Some say that laziness is a professional feature...
Therefore we wanted to keep things simple
(as opposed to many algs from the literature).
Our task: find plagiarisms in student homeworks.
Namely, in Java projects.
Small projects: not more than a few hundred lines expected.
Sz. Grabowski & W. Bieniecki, Simple techniques for plagiarism detection...
8
Our approach
We conjecture that the relative order and frequency of
the keywords of a given language
is quite a good indicator
if two documents were created independently or not.
Because it is not easy to find synonymous constructs
without some understanding of the code.
Why keywords? Maybe operators instead?
Rather not. Examples (in C and similar lang.):
x = y / 2;  x = y * 0.5;
x-=2;  x--, x--;
Sz. Grabowski & W. Bieniecki, Simple techniques for plagiarism detection...
9
Java keywords
http://java.sun.com/docs/books/tutorial/java/
nutsandbolts/_keywords.html
Sz. Grabowski & W. Bieniecki, Simple techniques for plagiarism detection...
10
Three variants
Extracting keywords, that’s easy. What then?
What similarity measure?
We propose 3 variants:
• based on the context-free counts of the keywords,
i.e., order-0 statistics;
• based on the similarity of the statistics of pairs
of successive keywords in the source files,
i.e., order-1 rather than order-0 statistics;
• based on the similarity between the whole sequences of
used keywords, in the order of their appearances, with aid of
the LCS (longest common subsequence) measure.
In all variants we measure pair-wise file similarity.
Sz. Grabowski & W. Bieniecki, Simple techniques for plagiarism detection...
11
Algorithm I (order-0 statistics)
1. For both files we create a dictionary (Dict1 and Dict2,
respectively) of occurring keywords with the number of
occurrences (a histogram).
2. We calculate the total number of keywords C.
C
 count1 k    count2 k  
kDict1\ Dict 2

kDict 2 \ Dict1
 max count1 k ; count2 k 
kDict1 Dict 2
3. We calculate the number of keyword repetitions R:
R
 max count1 k ; count2 k 
kDict1 Dict 2
4. We evaluate the similarity S = R / C.
Sz. Grabowski & W. Bieniecki, Simple techniques for plagiarism detection...
12
Algorithm II (order-1 statistics)
1. For both files create a sequence of keywords
(List1 and List2).
2. For each element i of List1 (except from the last one)
take its successor List1(i+1) and add the pair to
the list lp1. Delete the repeated records from lp1.
3. Analogously for lp2.
4. Evaluate the similarity measure S:
S
lp1  lp2
min lp1 , lp2 
Sz. Grabowski & W. Bieniecki, Simple techniques for plagiarism detection...
13
Longest Common Subsequence (LCS)
Given strings A, B, |A| = n, |B| = m,
find the longest subsequence shared by both strings.
Sometimes we are interested in a simpler problem:
finding only the length of the LCS (LLCS), not the
matching sequence.
LCS example
A=matter
B=brothers
LLCS(A, B) = 3.
LCS(A, B) = t e r
Sz. Grabowski & W. Bieniecki, Simple techniques for plagiarism detection...
14
Algorithm III
LCS on strings where the “characters”
are keywords
1. Denote the sequence of keywords in file1 and file2
with Word1, Word2, respectively.
2. Use the formula for similarity measure S:
S
LCS W ord1, W ord2
min W ord1 , W ord2 
Sz. Grabowski & W. Bieniecki, Simple techniques for plagiarism detection...
15
Implementation / test setup
All codes in Python 2.4
(perfect language for reluctant coders).
Test machine: Pentium4 3 GHz, 512 MB of RAM,
Windows XP SP2.
Input files:
15 student Java projects (single source files)
solving the same task: displaying time on an analog clock,
using a client-server technology
(a server provides the system time,
and many clients can be connected to the server).
Sz. Grabowski & W. Bieniecki, Simple techniques for plagiarism detection...
16
Test files
Files that
in fact are
plagiarisms
are in the
positions:
5 → 1,
8 → 15,
7 → 10
and 7 → 13.
Sz. Grabowski & W. Bieniecki, Simple techniques for plagiarism detection...
17
Alg I (order-0 stats), similarity measure
...But the
4th thief
was not
detected.

Sz. Grabowski & W. Bieniecki, Simple techniques for plagiarism detection...
18
Alg II (order-1 stats), similarity measure
Not
perfect
but not
bad
either...
Sz. Grabowski & W. Bieniecki, Simple techniques for plagiarism detection...
19
Alg III (LCS), similarity measure
All
four
thieves
at the
top!

Sz. Grabowski & W. Bieniecki, Simple techniques for plagiarism detection...
20
Conclusions
All the presented algorithms seem to
indicate the plagiarized codes properly.
But in practice it is impossible to set the threshold similarity
value for each algorithm above which the files are plagiarisms.
In Algorithm I the values of similarity vary from 0.75 to 1
and all below 0.98 don’t indicate a plagiarism.
This algorithm is the most resistant to changing the
order of instructions and functions.
Sz. Grabowski & W. Bieniecki, Simple techniques for plagiarism detection...
21
Conclusions, cont’d
Algorithm II is pretty resistant to changing the
order of functions and blocks of instructions.
The range of obtained similarity measure values
is much wider comparing to the first case.
Algorithm III, based on the LCS measure, is vulnerable to
changing the order of functions and instructions in the file.
In the inspected case, however, students stealing
the code did not bother to mix the functions
so the results are comparable to Algorithm II.
All presented algorithms should work properly
if a stolen homework is only a part of the original code.
Sz. Grabowski & W. Bieniecki, Simple techniques for plagiarism detection...
22
Future plans
Making it more robust to function reordering
(even Algorithm II).
Idea: convert a source file to a cannonical form,
sorting functions according to their signatures.
Use not only keywords but
standard library function names too?
More experiments (also for sources in C++, PHP...).
Handling multi-file projects.
Several independent similarity measures and the detection
based on training?
Sz. Grabowski & W. Bieniecki, Simple techniques for plagiarism detection...
23