6. In the second example in Section 9.3, 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.

Section 9.3 Example:

EXAMPLE: Revisit the two-bit system. When operations are executed by HIGH, only the HIGH state bit changes, and the same is true for LOW. Let ₀ = (0, 0). The commands are (Holly, xor1), (Lucy, xor0), (Lucy, xor1), (Lucy, xor0), (Holly, xor1), and (Lucy, xor0), and both bits are output after each command. So, the output string (which includes the initial state) is 00101011110101, the even-numbered bits being LOW and the odd-numbered bits being HIGH.

These functions are not noninterference-secure with respect to Lucy. Because Lucy is cleared only for LOW, she sees the output string as 0001111. But deleting the HIGH commands would produce the string 00111 for Lucy, which is different (and thereby violates Definition 94).

However, given the string 00111, Lucy cannot deduce what instructions were deleted because they do not affect the values in the output string; the deletions only affect its length. Hence, this version of the two-bit system is secure with respect to the property described above.

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