Chaos Theory for Software Evolution Rui Gustavo Crespo Technical University of Lisbon

Chaos Theory for

Software Evolution

Rui Gustavo CrespoTechnical University of Lisbon

2/22Software Evolution Behaviours

Laws of Software Evolution (1)

MM Lehman informal laws of software evolution1

Continuing change: a program used in a real-world environment must change.

Increasing entropy: the program structure becomes more complex, unless efforts are made to avoid the complexity.

Statistically smooth growth: the global system metrics appear locally stochastic in time and space but are self-regulating and statistically smooth.

1Lehman, M.M.: Programs, Life Cycles and Laws of Software Evolution. IEEE Special Issue on Software Engineering, 68(9), 1060-1076


Laws of Software Evolution (2)

Valid laws must be:-1. Unambiguous: the underlying system model must be

clear (better formally).2. Falsifiable: model predictions are checked against

collected data and the law remains valid until tests fail.

Thesis: Program organization plays a role in maintenance,

and may be measured with LRC (“Long-range correlation”) metrics.

Program evolution follows Verhulst population model.


F2(l) = [BW(l,l0)]2 - [BW(l,l0)]2

BW(l,l0) = BW(l0+l)-BW(l0)

LRC metrics (1)

1. Encode symbols (data types int, struct,... and instruction keywords if, while,...) with a balanced numeric code.

2. Identify the Brownian walk graph BW

BW(0) = 0

BW(n) = BW(n-1) + Code(Sn)

3. Evaluate the root of mean square flutuation about the average of displacement.


LRC metrics (2)

10 0

10 1

10 2

10 3

10 4

10 0

10 1

10 2

10 3

F(l) l

= 0.5, random programs

0.5<<1, meaningful programs


0

0.2

0.4

0.6

0.8

1

0 5 10 15 20 25 30 35 40

Number

Alp

ha

LRC metrics (3)

[A] values for 36 compilers, coded in C

Average: 0,82


LRC metrics (4)

for 36 random programs, same keyword distribution (similar results for same number of lines)

0

0.2

0.4

0.6

0 5 10 15 20 25 30 35 40

Number

Alp

ha

Average: 0,48


0

0.2

0.4

0.6

0.8

1

0 5 10 15 20 25 30 35 40

Number

Alp

ha

LRC metrics (5)

values for 36 random C programs, same number of lines, same keyword distribution

Average: 0,62


LRC metrics (6)

values for source and object files are strongly correlated

y = 0.1802x + 0.5713

R2 = 0.8212

0.6800

0.6900

0.7000

0.7100

0.7200

0.7300

0.7400

0.0000 0.2000 0.4000 0.6000 0.8000 1.0000

Source program Alpha

Ob

ject

pro

gra

m A

lph

a


Process dynamics (1)

Pierre Verhulst, Belgian mathematician, studied models of human population growth in the 19th century Growth with unlimited resources

du/dt=u, >0

Solution is an exponential function u(t)=u(t0)e(t-t0)

Growth with limited resourcesdu/dt=(-u)u, is the upper limit

Xt+1 = Xt(1-Xt) Xt \in [0,1], \in [0,4]

Verhulst model, or logistic map



=1.1

0

0.2

0.4

0.6

0.8

1

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58



=2.9

0

0.2

0.4

0.6

0.8

1

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58



=3.4

0

0.2

0.4

0.6

0.8

1

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58

Oscilation period is 2n



BTW, predator and prey populations (e.g., wolves and rabbits), are ruled by the same kind of equations dr/dt=(- w)r

dw/dt=(r - )w

Solution of the differential equations are sinusoidal functions, with different phases

-1.5

-1

-0.5

0

0.5

1

1.5

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31

Rabbit

Wolf



=3.8

0

0.2

0.4

0.6

0.8

1

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58

The behaviour is cahotic



Software processes also “compete” for resources (time, man-power, …)

Interaction between components is non-linear: small changes in a module may stop other modules to work properly

Proposal: link Verhulst values toProgram organization, and Ideas formation



norm = 2|-0.5|; = t+1/t(1-t)

Ideas formation Ideas covergence Single Idea Implementation

Time

Pro

duct

Att

ribu

tes

InformationCriativity

Pro

cess

For

m

Chaos Bifurcation Normal

3,4 03,0



BeanMetaData.java versions in JBOSS (Jul 2000-Oct 2002)

Chaotic Normal

0

1

2

3

4

5

6

1.1

1.4

1.7

1.10

1.13

1.15

.2.1

1.18

1.21

1.23

.2.1

1.23

.2.4

1.26

1.29

1.32

1.35

1.38

1.39

.2.2

1.40

Version

Bifurcation



0100200300400500600700800

1.1

1.4

1.7

1.10

1.13

1.15

.2.1

1.18

1.21

1.23

.2.1

1.23

.2.4

1.26

1.29

1.32

1.35

1.38

1.39

.2.2

1.40

Version

LO

C



EJBVerifier20.java versions in JBOSS (May 2000-Sep 2002)

Chaotic

Normal

00.5

11.5

22.5

33.5

4

1.1

1.3

1.5

1.7

1.9

1.11

1.13

1.15

1.17

1.17

.2.2

1.18

1.20

1.22

1.24

1.25

1.27

Version

Bifurcation



0

500

1000

1500

2000

2500

3000

1.1

1.3

1.5

1.7

1.9

1.11

1.13

1.15

1.17

1.17

.2.2

1.18

1.20

1.22

1.24

1.25

1.27

Version

LO

C


It is possible to measure program organization and automatically highlight version behaviours

Next steps:Check LRC validity and Verhulst model in other

applications / languages / process phases Improve Verhulst model (sometimes, >4) Identify faster algorithms

Cardoso,AI; Kokol,P.; Lenic,M.; Crespo,R.G.; Complexity-based Evaluation of Systems Evolution; in Advances in UML/XML Based Software Evolution;IRM Press; 2004 (in print)

Conclusions

Documents

Chaos Theory for Software Evolution Rui Gustavo Crespo Technical University of Lisbon