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Oct 30, 2023

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Fall CIS Assured programming with formal methods Act. 04 solution Class student number: SU email: Introduction In this activity, we will study two examples of Kripke structures. By completing this activity successfully, you will be able to explain, via examples, each features of a Kripke structure and illustrate the use of kripke’s structures in the interpretation of access control formulas. ACST Example . For each simple principal P in the Kripke model given in Example 2 . 8 , draw a di- agram for the relation J ( P ) . Label all the features in the diagram to fully describe the structure. Discuss, for each given propositions, when will it be true with respect to the model. Answer Let M 28 = h W 1 , I 1 , J 1 i be the model where the primitive principals are Alice and bob, and PropVar = { q , r , s } . The graph of the relations J (Alice) and J (Bob) are shown below: Figure : The graph of the relation J ( Alice ) Figure : The graph of the relation J ( Bob ) Andrew C. Lee EECS Dept, Syracuse University
Fall CIS Assured programming with formal methods Act. 04 solution ACST Example . With respect to Example 2 . 9 in our text, draw a diagram for the relation J ( Obs ) . Labelallthefeaturesinthediagramtofullydescribethestructure. Discuss, foreachgivenpropo- sitions, when will it be true with respect to the model. Note : The Kripke model in this example is h W 2 , I 2 , J 2 i , where W 2 = { A , B , C , D } and the primiti- ive propositions are p , q , r and s . The interpretation function I is defined via the following: I 2 ( p ) = { A , C } , I 2 ( q ) = { A , B , D } , I 2 ( r ) = , I 2 ( S ) = { A , B , C , D } . In addition, there is an observer Obj (a primitive principal) where J 2 ( Obj ) = {( A , A ) , ( B , B ) , ( C , D ) , ( D , D )} . Answer Let M 29 = h W 2 , I 2 , J 2 i be the model. The graph of the relations J (Obs) is shown below: Figure : The graph of the relation J ( Obs ) Remark Table 2 . 2 given in the supplement (select from ACST) illustrates that two different observers can have different “perceptions” in the model. For example, one’s view is specified according to the x = 0 column whereas another’s view is specified by x = 1 column. Andrew C. Lee EECS Dept, Syracuse University
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