8.9 Exercises

1:	Draw the lattice described in the first example in Section 8.1.1.
2:	Prove Lemma 8–2.
3:	Consider the systems Louie and Dewey in Section 8.2.4. Suppose the sends and receives for the buffers are nonblocking. Is the composition of Hughie, Dewey, and Louie still noninterference-secure? Justify your answer. Suppose all buffers are unbounded. Is the composition of Hughie, Dewey, and Louie still noninterference-secure? Justify your answer.
4:	Modify the two-bit system in the first example in Section 8.3 as follows. Whenever a High operation is performed, the High state bit is output. Whenever a Low operation is performed, the Low state bit is output. The initial state is not output (in contrast to the example). Is this version of the two-bit system noninterference-secure with respect to Lucy? Why or why not?
5:	In the second example in Section 8.3, Lucy sees the output sequence as 011011. Given that she knows the low-level input sequence, list all possible input sequences that match the known low-level input sequence and produce the desired output.
6:	Prove that a system that meets the definition of generalized noninterference security also meets the definition of deducible security.
7:	Suppose composite machine catdog (see Section 8.4.1) emits the same value from the left and the right. Show that it has received no inputs from the left.
8:	Prove Theorem 8–5.