Mini models EECS /74

Transcription

1 1/74 Mini models EECS

2 Mini source: Keld Gydum 2/74

3 Mini 3/74 source: Mike Bird

4 Model 4/74

5 Mini model 5/74

6 Hello World! 6/74 public class HelloWorld { public static void main(string[] args) { System.out.println("Hello World"); } } getstatic ldc invokevirtual return

7 Hello World! 7/74

8 Hello World! 8/74 target=helloworld classpath=. listener=gov.nasa.jpf.listener.statespacedot vm.max_transition_length=1

9 Hello World! 9/74 ====================================================== stat choice generators: thread=35 (signal=0,lock=1,sharedref=0,t ====================================================== sear elapsed time: 00:00:02 states: new=35,visited=0,backtracked=35,end=1 search: maxdepth=35,constraints=0 heap: new=348,released=11,maxlive=331,gccycles= instructions: 3198 max memory: 61MB loaded code: classes=56,methods=1220

10 Hello World! 10/74

11 One choice 11/74 Random random = new Random(); if (random.nextboolean()) { System.out.println("1"); } else { System.out.println("2"); }

12 One choice 12/74 target=onechoice classpath=. cg.enumerate_random=true listener=gov.nasa.jpf.listener.statespacedot

13 One choice 13/74

14 One choice 14/74 target=onechoice classpath=. cg.enumerate_random=true listener=gov.nasa.jpf.listener.statespacedot vm.max_transition_length=1

15 One choice 15/74

16 Two choices 16/74 Random random = new Random(); if (random.nextboolean()) { if (random.nextboolean()) { System.out.println("1"); } else { System.out.println("2"); } } else { if (random.nextboolean()) { System.out.println("3"); } else { System.out.println("4"); } }

17 Two choices 17/74 target=twochoices classpath=. cg.enumerate_random=true listener=gov.nasa.jpf.listener.statespacedot

18 Two choices 18/74

19 Two choices 19/74 target=twochoices classpath=. cg.enumerate_random=true listener=gov.nasa.jpf.listener.statespacedot vm.max_transition_length=1

20 Two choices 20/74

21 Many choices 21/74 Random random = new Random(); byte value = 0; while (random.nextboolean()) { value++; } System.out.println(value);

22 Many choices 22/74 How many different executions does the app ManyChoices

23 Many choices 22/74 How many different executions does the app ManyChoices Answer Infinitely many.

24 Many choices 22/74 How many different executions does the app ManyChoices Answer Infinitely many. How many different states does JPF encounter?

25 Many choices 22/74 How many different executions does the app ManyChoices Answer Infinitely many. How many different states does JPF encounter? Answer 257.

26 Not so many choices 23/74 Random random = new Random(); byte value = 0; while (random.nextboolean()) { value = (byte) ((value + 1) % 5); } System.out.println(value);

27 Many choices 24/74 How many different executions does the app ManyChoices

28 Many choices 24/74 How many different executions does the app ManyChoices Answer Infinitely many.

29 Many choices 24/74 How many different executions does the app ManyChoices Answer Infinitely many. How many different states does JPF encounter?

30 Many choices 24/74 How many different executions does the app ManyChoices Answer Infinitely many. How many different states does JPF encounter? Answer 6.

31 Not so many choices 25/74 target=notsomanychoices classpath=. cg.enumerate_random=true listener=gov.nasa.jpf.listener.statespacedot

32 Not so many choices 26/74 ====================================================== sear

33 Not so many choices 27/74

34 Not so many choices 28/74 target=nosomanychoices classpath=. cg.enumerate_random=true listener=gov.nasa.jpf.listener.statespacedot vm.max_transition_length=1

35 Not so many choices 29/74

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48 Not so many choices /74

49 Not so many choices /74

50 Not so many choices /74

51 Not so many choices /74

52 Not so many choices /74

53 Not so many choices 47/74 Does this remind you of an algorithm you have seen in the course EECS 2011 Fundamentals of Data Structures and EECS 3101 Design and Analysis of Algorithms?

54 Not so many choices 47/74 Does this remind you of an algorithm you have seen in the course EECS 2011 Fundamentals of Data Structures and EECS 3101 Design and Analysis of Algorithms? Answer Depth-first search of a directed graph.

55 Not so many choices 47/74 Does this remind you of an algorithm you have seen in the course EECS 2011 Fundamentals of Data Structures and EECS 3101 Design and Analysis of Algorithms? Answer Depth-first search of a directed graph. A labelled transition system is similar to a directed graph. state vertex transition edge

56 Depth-first search 48/74 Why do we have to keep track of the vertices that have been visited in depth-first search?

57 Depth-first search 48/74 Why do we have to keep track of the vertices that have been visited in depth-first search? Answer To ensure that the traversal terminates.

58 Depth-first search 48/74 Why do we have to keep track of the vertices that have been visited in depth-first search? Answer To ensure that the traversal terminates. Similarly, when model checking we need to keep track of the states that have already been visited.

59 Exercise 49/74 Write a recursive method that for a given depth d chooses an integer in the range 1 2 d uniformly at random using random.nextboolean. Hint: provide the method with an additional parameter

60 Number of states 50/74 target=choice target.args=2 classpath=.

61 Number of states 51/74 d number of states , ,048,610

62 Number of states 51/74 d number of states , ,048,610 Can you express the number of states in terms of d?

63 Number of states 51/74 d number of states , ,048,610 Can you express the number of states in terms of d? Answer 2 d + 34.

64 Model 52/74 a b a b c a e b a a b c a d b a a b

65 Mini model 53/74 abab cadbaab caebaab

66 What do the model and the mini model in common? 54/74

67 54/74 What do the model and the mini model in common? Answer The initial state. The final states. The branching structure. The language: (finite and infinite) sequences of actions. a a Similar to the language accepted by a finite automaton, as discussed in EECS 2001 Introduction to Theory of Computation.

68 Model 55/74 a b c 3 e 5 d 4 f

69 Model 55/74 a b c 3 e 5 d 4 f Which is the initial state?

70 Model 55/74 a b c 3 e 5 d 4 f Which is the initial state? Answer State 0.

71 Model 56/74 a b c 3 e 5 d 4 f Which are the final states?

72 Model 56/74 a b c 3 e 5 d 4 f Which are the final states? Answer State 5.

73 Model 57/74 a b c 3 e 5 d 4 f Which are the branching states?

74 Model 57/74 a b c 3 e 5 d 4 f Which are the branching states? Answer State 2.

75 Model 58/74 a b c 3 e 5 d 4 f What is the language?

76 Model 58/74 a b c 3 e 5 d 4 f What is the language? Answer {abce, abdf }.

77 Mini model 59/74 What is the corresponding mini model?

78 Mini model 59/74 What is the corresponding mini model? ab ce df

79 Model 60/74 c a b

80 Model 60/74 c a b Which is the initial state?

81 Model 60/74 c a b Which is the initial state? Answer State 0.

82 Model 61/74 c a b Which are the final states?

83 Model 61/74 c a b Which are the final states? Answer There are none.

84 Model 62/74 c a b Which are the branching states?

85 Model 62/74 c a b Which are the branching states? Answer There are none.

86 Model 63/74 c a b What is the language?

87 Model 63/74 c a b What is the language? Answer {abcabcabc...}.

88 Mini model 64/74 What is the corresponding mini model?

89 Mini model 64/74 What is the corresponding mini model? abc 0

90 Model 65/74 c a b d 3 e 4

91 Model 65/74 c a b d 3 e 4 Which is the initial state?

92 Model 65/74 c a b d 3 e 4 Which is the initial state? Answer State 0.

93 Model 66/74 c a b d 3 e 4 Which are the final states?

94 Model 66/74 c a b d 3 e 4 Which are the final states? Answer State 4.

95 Model 67/74 c a b d 3 e 4 Which are the branching states?

96 Model 67/74 c a b d 3 e 4 Which are the branching states? Answer State 0.

97 Model 68/74 c a b d 3 e 4 What is the language?

98 Model 68/74 c a b d 3 e 4 What is the language? Answer {de, abcde, abcabcde,..., abcabcabc...}.

99 Mini model 69/74 What is the corresponding mini model?

100 Mini model 69/74 What is the corresponding mini model? abc 0 de 4

101 Model 70/74 e a b c d 3 4

102 Model 70/74 e a b c d 3 4 Which is the initial state?

103 Model 70/74 e a b c d 3 4 Which is the initial state? Answer State 0.

104 Model 71/74 e a b c d 3 4 Which are the final states?

105 Model 71/74 e a b c d 3 4 Which are the final states? Answer State 4.

106 Model 72/74 e a b c d 3 4 Which are the branching states?

107 Model 72/74 e a b c d 3 4 Which are the branching states? Answer State 2.

108 Model 73/74 e a b c d 3 4 What is the language?

109 Model 73/74 e a b c d 3 4 What is the language? Answer {abd, abcebd, abcebcebd,..., abcebcebce...}.

110 Mini model 74/74 What is the corresponding mini model?

111 Mini model 74/74 What is the corresponding mini model? ceb ab 0 2 d 4