Final exam to Modellierung

Transcription

1 Name: First name: Matr.Nr: Universität Duisburg-Essen WS 2008/09 Ingenieurwissenschaften / Informatik 4. August 2009 Professor: Prof. Dr. Barbara König Klausur Final exam to Modellierung The exam consists of 5 questions, worth 40 points in total. You have two hours to finish the exam. You pass the exam, if you get 50% of the points (that is 20 points). On the last two pages of the exam, there are a small English-German word list and some definitions about Petri nets. Exercise 1 Eigenschaften eines Petri-Netzes (7 Punkte) Let the following Petri net be given: p 1 p 2 t 2 t 3 t 4 p 3 (a) Give the reachability graph of the Petri net. (b) Indicate which properties hold for the Petri net by filling in the following table: Strongly live Weakly live Deadlock-free Yes/No Safe Bounded Unbounded Yes/No (2 Punkte) (c) Give all sets of transitions which are concurrent under the initial marking. You only need to mention the sets of transitions which contain two transitions or more. (2 Punkte)

2 Exercise 2 Building Petri nets (8 Punkte) (a) Let the following structure of a reachability graph be given. m 0 t 2 t 4 t 3 t 3 t 2 m 1 m 2 m 3 m 4 t 3 t 4 t 4 t 2 m 5 All of the markings m 0 m 5 are different. The names of the fired transitions are given in the graph. The Petri net, whose reachability graph is given, has three places and its initial marking is (1, 0, 1). Give a Petri net with three places, which has the graph above as reachability graph. Also indicate which markings coincide with m 0 m 5. (b) Give a Petri net with the following coverability graph: t 2 (1, 0, 0) (0, 1, 1) (1, ω, 0) (0, ω, 1) t 2 Hint: There are infinitely many possible solutions. It is only required to give one! (c) Give a loop-free Petri-net with the following incidence matrix: (2 Punkte)

3 Exercise 3 Reachability and invariants (7 Punkte) Let the following Petri net be given: p 1 t 4 p 3 p 4 t 2 p 2 t 3 2 (a) Give the incidence matrix of the Petri net. (1 Punkt) (b) Give all S-invariants of the Petri net. Also show how the S-invariants were obtained. For solutions without justification no points will be given. (c) Show, with the help of an S-invariant, that the marking (1, 1, 23, 45) is not reachable.

4 Exercise 4 UML class diagram of an exam correction system (9 Punkte) Correcting exams costs us lecturers a lot of time and leads to stress. Therefore, we need a computer program in order to make this task a little easier. In this exercise, you will help us to model the desired system. (a) The structure of the system is described as follows: There are two types of person: lecturers and students. Of all persons, the name is stored. Furthermore, the room number of lecturers is stored as well as the student number and current semester of students are stored. An exam consists of at least one exercise. The lecture that is tested by the exam, and the date on which it takes place, are stored. Of all exercises, the name of the exercise and the maximum amount of points are stored. The exercises are divided over the lecturers: each exercise is corrected by at least one lecturer. A student who participates in the exam hands in an answer sheet. An answer sheet consists of the answers to the corresponding exercises. For each answer, the amount of points the student got for it is stored. The class AnswerSheet has an operation calculatetotal, which calculates the total points, and an operation haspassed, which calculates whether or not the student got half of the points and passed the exam. Give a uml class diagram for this system. Think about which multiplicities should be written at the arrows. You may assume, that the following standard classes are available: Boolean (for truth values), Date (for dates), Double (for real numbers), Integer (for whole numbers), String (for texts) und Time (for times) You do not need to draw these classes in the class diagram. You may use them as data types, however. (5 Punkte) (b) Also the gnomes make use of the modeled system. This morning, August 4th,2009, the exam to the lecture Knocking on bath burners took place. The exam consisted of two exercises, which were called Exercise 1 and Exercise 2, respectively. De lecturers of the lecture were Ada Langmütze and Björn Hochhut. Second semester student Carsten Riesenkäppi took part in the exam, and go7 points for the first and 12 points for the second exercise. Give a uml object diagram, which is compatible to the class diagram you gave in part (a) and which models the above situation. (4 Punkte)

5 Exercise 5 Sequence diagrams (9 Punkte) (a) Consider the sequence diagram below, in which send and receive events are identified by letters. How many possible runs, that is, how many possible sequences of events, are there for this sequence diagram? :X :Y par X1 Y1 X2 Y2 (2 Punkte) (b) Anna has three friends: Boris, Christine and David. She wants to organise a joint meeting with them by sms. To this end, she sends an sms containing an invitation to each of her three friends. Thereupon Boris, Christine and David answer by sms, and agree with the appointment. After Anna has received all the answers, she sends her friends a confirmation that the meeting will take place. Model this scenario with a sequence diagram. The order of the events must only be fixed insofar this is absolutely necessary. That is, the diagram should be modeled in such a way, that the maximal amount of parallelism is obtained. In particular: Anna sends her invitations in arbitrary order. The answers of Boris, Christine and David arrive in arbitrary order. It is also possible that answers arrive before all invitations were sent. Of course, the three friends send their answer only after they received their own invitation. Anna sends the confirmations only after all friends have answered. The confirmations are also sent in arbitrary order. (5 Punkte) (c) Describe the difference between synchronous and asynchronous communication. How can the two types of communication be distinguished in a sequence diagram? (2 Punkte) End of the exam For word list and Petri net definitions, see next sheet

6 Some Petri net definitions Definition 1. A Petri net is bounded, if there exists a constant c N, such that for each reachable marking m and each place p, it holds that m(p) c. A Petri net is unbounded, if it is not bounded. Definition 2. A Petri net is safe, if all weights are 1 or less, and for each reachable marking m and place p, it holds that m(p) 1. Definition 3. A set T = {,..., t n } T of transitions is called concurrent under the marking m, if t n m. That is, m contains enough tokens, to fire all transitions at the same time. Definition 4. A Petri net is (strongly) live, if for each transition t and each reachable marking m, there is a marking m, which is reachable from m, such that t is activated under m. A Petri net is weakly live, if for each transition t there is a reachable marking m (reachable from the initial marking), such that t is activated under m. Definition 5. A deadlock is a reachable marking m, under which no transition is activated. A Petri net is called deadlock-free, if it does not have any deadlock. Hinweis 1. In an incidence matrix the rows correspond to places and the columns to transitions. That is, the incidence matrix of a Petri net with three places and four transitions has three rows and four columns. Short English-German Word List activated aktiviert bounded beschränkt class diagram (das) Klassendiagramm concurrent nebenläufig deadlock (die) Verklemmung free verklemmungsfrei to fire schalten incidence matrix (die) Inzidenzmatrix live lebendig strongly stark weakly schwach marking (die) Markierung object diagram (das) Objektdiagramm place (die) Stelle reachable erreichbar reachability graph (der) Erreichbarkeitsgraph safe sicher sequence diagram (das) Sequenzdiagramm token (die) Marke unbounded unbeschränkt