Mtricas em Aplicaes Informticas

1
Rui Gustavo Crespo Technical University of Lisbon
2
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
3
Laws of Software Evolution (2)

• Valid laws must be-
• Unambiguous the underlying system model must be
  clear (better formally).
• 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.

4
LRC metrics (1)

• Encode symbols (data types int, struct,... and
  instruction keywords if, while,...) with a
  balanced numeric code.
• Identify the Brownian walk graph BW
• BW(0) 0
• BW(n) BW(n-1) Code(Sn)
• Evaluate the root of mean square flutuation about
  the average of displacement.

5
LRC metrics (2)

• F(l) ? la
• a 0.5, random programs
• 0.5ltalt1, meaningful programs

6
LRC metrics (3)

• A a values for 36 compilers, coded in C

Average 0,82
7
LRC metrics (4)

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

Average 0,48
8
LRC metrics (5)

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

Average 0,62
9
LRC metrics (6)

• a values for source and object files are
  strongly correlated

10
Process dynamics (1)

• Pierre Verhulst, Belgian mathematician, studied
  models of human population growth in the 19th
  century
• Growth with unlimited resources
• du/dtgu, ggt0
• Solution is an exponential function
  u(t)u(t0)eg(t-t0)
• Growth with limited resources
• du/dtb(?-u)u, ? is the upper limit
• Xt1 P Xt(1-Xt) Xt \in 0,1, P \in 0,4

11
Process dynamics (2)
12
Process dynamics (3)
13
Process dynamics (4)
Oscilation period is 2n
14
Process dynamics (5)

• BTW, predator and prey populations (e.g., wolves
  and rabbits), are ruled by the same kind of
  equations
• dr/dtb1(?1 - w)r
• dw/dtb2(r - ?2)w
• Solution of the differential equations are
  sinusoidal functions, with different phases

15
Process dynamics (6)
The behaviour is cahotic
16
Process dynamics (7)

• 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 P values to
• Program organization, and
• Ideas formation

17
Process dynamics (8)

• anorm 2a-0.5 P at1/at(1-at)

18
Process dynamics (9)

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

Bifurcation
Chaotic
Normal
19
Process dynamics (10)
20
Process dynamics (11)

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

Chaotic
Bifurcation
Normal
21
Process dynamics (12)
22
Conclusions

• 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, Pgt4)
• Identify faster a algorithms
• Cardoso,AI Kokol,P. Lenic,M. Crespo,R.G.
  Complexity-based Evaluation of Systems Evolution
  in Advances in UML/XML Based Software
  EvolutionIRM Press 2004 (in print)