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When you tell AppleScript exactly what to do, and it is able to interpret each of your commands correctly, your script runs perfectly But all too often, you ll run into a problem that causes an error When you do, AppleScript displays an error message telling you that a problem has occurred You ll then need to correct the code to make the script run correctly

s 0 This s is called the slack variable for the inequality As justi cation, observe that a vector (x1 , , xn ) satis es the original inequality constraint if and only if there is some s 0 for which it satis es the new equality constraint 2b To change an equality constraint into inequalities is easy: rewrite ax = b as the equivalent pair of constraints ax b and ax b 3 Finally, to deal with a variable x that is unrestricted in sign, do the following: Introduce two nonnegative variables, x + , x 0

Part II:

Try dealing with an error that occurs in a script Follow these steps:

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Replace x, wherever it occurs in the constraints or the objective function, by x + x This way, x can take on any real value by appropriately adjusting the new variables More precisely, any feasible solution to the original LP involving x can be mapped to a feasible solution of the new LP involving x + , x , and vice versa By applying these transformations we can reduce any LP (maximization or minimization, with both inequalities and equations, and with both nonnegative and unrestricted variables) into an LP of a much more constrained kind that we call the standard form, in which the variables are all nonnegative, the constraints are all equations, and the objective function is to be minimized For example, our rst linear program gets rewritten thus: max x1 + 6x2 x1 200 x1 + x2 400 x1 , x 2 0 x2 300 min x1 6x2

CONNECTION_TYPE AUTHENTICATION_METHO CLIENT_IP -------------------- -------------------- -------------------CORPORATE_PASSWORD PASSWORD 1921680200 1 row selected mary@aos> -- query MARY's OLS authorization and mary@aos> -- the effective OLS session label mary@aos> SELECT sa_sessionlabel('CUSTOMER_POLICY') "EFFECTIVE_SESSION_LABEL" FROM DUAL; EFFECTIVE_SESSION_LABEL ----------------------HIGH 1 row selected mary@aos> -- query the SHCUSTOMERS table mary@aos> SELECT cust_credit_limit , count(*) FROM shcustomers GROUP BY cust_credit_limit ORDER BY cust_credit_limit / CUST_CREDIT_LIMIT COUNT(*) ----------------- ---------1500 11334 3000 7975 5000 7724 7000 8634 9000 9093 10000 5935 11000 2935 15000 1870 8 rows selected

to the specified position, and changes to your chosen view but then an error occurs (see Figure 3-4)

The original was also in a useful form: maximize an objective subject to certain inequalities Any LP can likewise be recast in this way, using the reductions given earlier 194

Next we want to examine how our policy behaves when MARY is querying the SHCUSTOMERS table from outside the corporate network In this scenario, we expect MARY to be able to see only customers with a credit limit of LOW In addition, we expect the effective OLS session label to be the maximum label MARY is authorized to see LOW

Figure 3-4

mary@aos> -- show the Connection_Type factor and session context mary@aos>SELECT DVSYSGET_FACTOR('Connection_Type') Connection_Type , DVSYSGET_FACTOR('Authentication_Method') Authentication_Method , DVSYSGET_FACTOR('Client_IP') Client_IP FROM DUAL; CONNECTION_TYPE AUTHENTICATION_METHO CLIENT_IP -------------------- -------------------- -------------------OTHER PASSWORD 10101010

A linear function like x1 + 6x2 can be written as the dot product of two vectors c= 1 6 and x = x1 , x2

5:

(continued)

denoted c x or cT x Similarly, linear constraints can be compiled into matrix-vector form: 1 0 200 x1 200 x1 = 0 1 300 x2 300 x2 1 1 400 x1 + x2 400 A x b Here each row of matrix A corresponds to one constraint: its dot product with x is at most the value in the corresponding row of b In other words, if the rows of A are the vectors a1 , , am , then the statement Ax b is equivalent to ai x bi for all i = 1, , m With these notational conveniences, a generic LP can be expressed simply as max cT x Ax b x 0

mary@aos> -- query MARY's OLS authorization and mary@aos> -- the effective OLS session label mary@aos> SELECT sa_sessionlabel('CUSTOMER_POLICY') "EFFECTIVE_SESSION_LABEL" FROM DUAL; EFFECTIVE_SESSION_LABEL ----------------------LOW 1 row selected mary@aos> -- query the SHCUSTOMERS table mary@aos> SELECT cust_credit_limit , count(*) FROM shcustomers GROUP BY cust_credit_limit ORDER BY cust_credit_limit / CUST_CREDIT_LIMIT COUNT(*) ----------------- ---------1500 11334 3000 7975 2 rows selected

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