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

2/22Software Evolution Behaviours Laws of Software Evolution (1)  MM Lehman informal laws of software evolution 1  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. 1 Lehman, M.M.: Programs, Life Cycles and Laws of Software Evolution. IEEE Special Issue on Software Engineering, 68(9),

3/22Software Evolution Behaviours 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.

4/22Software Evolution Behaviours F 2 (l) = [  BW(l,l 0 )] 2 - [  BW(l,l 0 )] 2  BW(l,l 0 ) = BW(l 0 +l)-BW(l 0 ) 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(S n ) 3. Evaluate the root of mean square flutuation about the average of displacement.

5/22Software Evolution Behaviours LRC metrics (2) F(l)  l   = 0.5, random programs  0.5<  <1, meaningful programs

6/22Software Evolution Behaviours LRC metrics (3) [A]  values for 36 compilers, coded in C Average: 0,82

7/22Software Evolution Behaviours LRC metrics (4)  for 36 random programs, same keyword distribution (similar results for same number of lines) Average: 0,48

8/22Software Evolution Behaviours LRC metrics (5)  values for 36 random C programs, same number of lines, same keyword distribution Average: 0,62

9/22Software Evolution Behaviours LRC metrics (6)  values for source and object files are strongly correlated

10/22Software Evolution Behaviours Process dynamics (1) Pierre Verhulst, Belgian mathematician, studied models of human population growth in the 19 th century  Growth with unlimited resources du/dt=  u,  >0 Solution is an exponential function u(t)=u(t 0 )e  (t-t0)  Growth with limited resources du/dt=  (  -u)u,  is the upper limit X t+1 =  X t (1-X t ) X t \in [0,1],  \in [0,4] Verhulst model, or logistic map

11/22Software Evolution Behaviours Process dynamics (2)

12/22Software Evolution Behaviours Process dynamics (3)

13/22Software Evolution Behaviours Process dynamics (4) Oscilation period is 2 n

14/22Software Evolution Behaviours Process dynamics (5) 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

15/22Software Evolution Behaviours Process dynamics (6) The behaviour is cahotic

16/22Software Evolution Behaviours 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  values to  Program organization, and  Ideas formation

17/22Software Evolution Behaviours Process dynamics (8)  norm = 2|  -0.5|;  =  t+1 /  t (1-  t ) Ideas formation Ideas covergenceSingle Idea Implementation Time Product Attributes Information Criativity Process Form Chaos Bifurcation Normal  3,4 0 3,0

18/22Software Evolution Behaviours Process dynamics (9) BeanMetaData.java versions in JBOSS (Jul 2000-Oct 2002) ChaoticNormal Bifurcation

19/22Software Evolution Behaviours Process dynamics (10)

20/22Software Evolution Behaviours Process dynamics (11) EJBVerifier20.java versions in JBOSS (May 2000-Sep 2002) Chaotic Normal Bifurcation

21/22Software Evolution Behaviours Process dynamics (12)

22/22Software Evolution Behaviours  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