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## From Ill-formed to Well-formed

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**From Ill-formed to Well-formed**• One of the most important skills in research is problem formulation – transforming an interesting idea/question into something that can be analyzed. • To shed light on the questions that we have raised in last class, we need to • postulate a logical relation between the effort we spent in software engineering and the resulting reliability • this logical relationship should ground in factual observation. But idealization is fine.**Assumptions Grounded in Observations**• 1) The more complex the software project is, the harder it is to make it reliable. For a given degree of complexity, the more effort that we can devote to software engineering, the higher the reliability. • 2) The obvious errors are spotted and corrected early during the development. As time passes by, the remaining errors are subtler, more difficult to detect and correct. • 3) There is only a finite amount of effort (budget) that we can spend on any project.**C=1**C = 2 Figure 1: Reliability and Complexity From Assumptions to Model • These observations suggest that, for a normalized mission duration t = 1, the reliability of a software system can be expressed as an exponential function of the software complexity, C, and available development effort, E, in the form of R(E, C) =e-C /E. As we can see, R(E, C) rises as effect E increases and decreases as complexity C increases. There is, however, another way to model it.**Analysis**• For 3-version programming: • the reliability of each version when efforts are equally allocated is R = exp( – c/(E/3)) • The system works if all of 3 works or any 2 out 3 works. Thus, the reliability of the system Rs = R3 + 3(R2*(1-R)). Note that this analysis assumes faults in different versions are independent, a favorable assumption. • For recovery block with a perfect acceptance test (favorable assumption), if any version works the system works. • For the case of 3 alternatives without complexity reduction and with equal effort allocation, we have R = exp( –c/(E/3)) and Rs = 1 – (1 – R)3 • if you divide the effort equally among 2 alternatives but one has only 0.5c complexity, then R1 = exp(–c/(E/2)) and R2 = exp(–0.5c/(E/2)) and system reliability Rs = 1 – (1 – R1)(1–R2). • You can try out different effort allocation methods and different complexity reductions and see the results (plot them and try to find a qualitative pattern).**Single version programming**3-version programming Figure 2: Effect of Divided Efforts in 3-version Programming From Assumption to Model - 3 • Single version vs 3 version (equal allocation)**RB**Single version programming RB: Recovery Block Figure 3: Effect of Dividing Effort in Recovery Block Single version vs Recovery Block • Single version vs Recovery Block (3 alternatives, equal allocation, no complexity reduction)**RB2**RB10 RB3 Figure 4: Degree of Diversity Degree of Diversity • RBn, where n is the number of alternatives. (n-way equal allocation, no complexity reduction) Adding diversity to system is kind of liking adding salt to a bowl of soup. A little improves the taste. Too much is counter-productive.**RB2L10**RB2 RB2L2 Single version programming Figure 5: Effect of Complexity Reduction Keep it Simple, Stupid! • RB2Ln, where n is the complexity reduction in the alternative to the primary with full functionality. (2-way equal effort allocation, n times complexity reduction in the simple alternative)**Using Simplicity to Control Complexity**• Ok, simplicity leads to reliability. But we want fancy features that require complex software. Worse, most applications do not have high coverage acceptance tests. • The solution is to use simplicity to control complexity. • use a simple and reliable core that provides the essential service. • Ensure that the reliable core will not compromised by the faults in the bells-and-whistles. • Leverage the reliable core to ensure the overall system integrity in spite of faults in the complex features, even WHEN THERE IS NO EFFECTIVE ACCEPTANCE TESTS.**Homework for Next Lecture**• In next lecture, we will investigate the idea of forward recovery that embodies the idea of using simplicity to control complexity. • Each team shall give 1 single slide that gives an example in everyday life, other fields of engineering or CS that embodies the idea of using simplicity to control complexity. • Think and think creatively • The class presentation will go on after the mini-lecture.