# Software Quality Exercise 1

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2 Simulate a model (append -p -g for more verbose output) spin model.pml Verify a property on a model. spin -a -F property.ltl model.pml gcc -o pan pan.c./pan -a Replay a trace found by the verifier (append -p -g for more verbose output). spin -t model.pml Note: In some MacOSX and Linux distributions SPIN has problems to process LTL files given with the -F modifier. This issue can be avoided by specifying the LTL formula directly in the command line within double quotes after the -f modifier. For example: spin -a -f " [] greenlight" model.pml The LTL formula can then be saved in an LTL file before submitting the solution. Colony of Chameleons A friend of yours is the director of a zoo. He has described you the latest acquisition he was considering for his zoo: a rare colony of chameleons. This colony of chameleons includes 4 red, 5 blue, and 0 green individuals. Whenever two chameleons of different colors meet, each changes to the third color. The color mutation is an unique feature and your friend expects to attract many visitor with this colony. Still, the director has a doubt: if, by any chance, all 99 chameleons are in the same color, there will not be any color change any more and the colony would loose its value.. State Space a) Give a rough estimation of the number of states in which the colony can be. b) How many states present the undesired property?. Promela Model of the Colony Download the file Colony.pml.txt on the website of the exercises and rename it to Colony.pml. Study this model with the help of Promela documentation. a) What are the main components of a Promela model? b) The behavior of chameleons is not deterministic, in the sense that they meet each other randomly. How is this non-determinism expressed in the Promela model of the colony? c) Which other aspect of Promela is not deterministic? d) Explain briefly what are d step blocks and the reason of their presence in the Promela model of the colony. In which sense is the first instruction of such a block different than the others? e) Despite their relation with the color change phenomenon, the duration of a color change and the probability of a change have not been modeled. Explain, in maximum 5 sentences, why they are not relevant for the problem at hand.

3 . Simulation and Verification a) Run a few simulations of the model. Have you ended up in a state where all chameleons are of the same color? b) Express the property there are always at least two chameleons of different color in an LTL formula using the variables defined in the Promela model of the colony. Save this formula in a textfile named ColorChange.ltl. Note that you cannot define predicates in an ltl file; you have to define them as macros in the Promela model. For example: #define noredchameleonleft (!nred) c) Is it a safety or a liveness property? Why? d) Using spin, investigate whether the colony can reach a state where this property does not hold. Note that spin looks for executions that satisfy an LTL property, so, you have to negate the formula in ColorChange.ltl. What will you recommand to your friend? e) In the report of pan, the number of states stored is the number of reachable states. How many states were reachable? Compare with your answer in...a). f) In the report of pan, the number of transitions is the number of transitions that have been visited during the search. How many transitions were investigated by pan? g) A few days later, the director of the zoo informs you: a green chameleon escaped during the delivery. Has he any reason to worry? h) What is the depth of the trace (that is, the number of steps) found by pan?.4 Extending the Model After a few weeks, you visit the zoo. Looking at this chameleon colony, you feel a strong relief: there are still chameleons of every color and they change colors happily. Still, by observing them, you figure out that your friend did not describe the behavior of the chameleons very precisely. You make the following additional observations: When chameleons of different colors meet, they argue violently and kill eachother. When chameleons of the same color meet, they give birth to a new chameleon of their color. At the day of your visit, there were 0 red, 8 blue, and 6 green individuals. a) Extend the Promela model of the colony with processes so that it reflects your new observations. b) Run a few simulations of this model. What happens? Explain. c) Let s make an assumption here: chameleons only give birth if there are less than N chameleons of that color in the colony ( N = 5). Modify the model accordingly. d) Express the property soon or later, there will be no chameleon left in an LTL formula. Save this formula in a textfile named Extinction.ltl. e) Is it a safety or a liveness property? Why? f) Using spin, investigate whether the colony can die off. Are chameleons threatened with extinction? g) Modify you model again so that chameleons only give birth if there are in total less than N chameleons in the colony (initially, set N to 0). Are chameleons still threatened with extinction? h) Change the the number N to 50 instead of 0. As you did previously, investigate whether the colony can die off. What happens? Why?

4 p₃ t₂ p₁ t₁ p₂ cap(p₂) = 5 Figure : Example of Petri net i) Set the max search depth to steps when performing the verification. Do you obtain a different result? What is the depth of the trace? Which depth has been reached during the search? j) Change the order of process declarations in the Promela model by swapping the fight process with the birth process and re-verify the model. What is the depth of the trace and which depth has been reached during the verification? Explain the difference with your previous results. Your explanation must account the fact that the behavior of the model remains unchanged by your modification..5 Scalability This exercise is based on the extended model of the colony built in the exercise..4. No LTL property will be checked on the model. While keeping the max search depth to steps, perform an exhaustive search on the model for N = 60, N = 0, N = 80, N = 0 and N = 400. Note that you have to invoke pan without the option -a, since no LTL property was specified. For every execution of pan, report the following information in a table: the time spent for the verification. the number of transitions explored. the length of the longest trace explorated. the number of reachable states. the memory used for the verification. Petri Nets Petri nets can easily be translated into Promela models. For example, the Petri net in figure can be translated in the following Promela code: byte p, p, p; /* assumption: at most 56 tokens on each place */ init { p = ; p = 0; p = ; /* initial marking */ do /*t*/ :: d_step {p >= && p <= 4; p = p - ; p = p + ;} /*t*/ :: d_step {p >= ; p = p - ; p = p + ;} od } 4

5 Create a Promela model based on the Petri net depicted in figure. Using spin, verify whether (a) this Petri net is free of deadlock, (b) the transition t 4 can be fired at least once, (c) the transition t can be fired an infinite number of times and whether (d) as soon as p 4 receives a token, it never gets empty again. If applicable, give an execution trace to justify your answer. In each case, explain briefly how you did the verification with spin. cap(p₁) = 6 cap(p₄) = p₁ p₄ t₁ p₂ t₃ t₂ cap(p 5 ) = 4 p 5 5 t 5 t₄ Figure : Petri net to be translated in Promela 5

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