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This overview explains how a proved Boolean rewrite can preserve
policy decisions while changing the work needed to compute them.

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Finding a match, admitting its proof, updating identities,
and handling fallback can cost more than the rewrite saves.

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Finding a match, admitting its proof, updating identities,
and handling fallback can cost more than the rewrite saves.

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Both routes require authorized staff.

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One route accepts allowed hours; the other accepts an explicit exception.

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The two branches therefore share A, while B and C are alternatives.

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Factor the common staff condition outside the or.

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When A is zero, both forms deny access.

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When A is one, both forms return B or C.

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These two cases prove the equality for every combination of the other conditions.

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For authorized staff outside normal hours with an exception, the original branches return

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zero and one.

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Their or allows access.

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The factored form first finds B or C true, then combines it with A one

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and also allows access.

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and also allows access.

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A proved Boolean identity can preserve decisions while reducing structure.

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Profitability also includes finding the match, admitting
the proof, updating identities and handling fallback.

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Use allow equals role AND region, OR role AND resource.

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Factor it to role AND the OR of region and resource.

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Exhaustive evaluation over the three inputs confirms equality.

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In the revision example, the resource clause changes.

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The matching record and proof instance depend on that clause.

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They require invalidation or revalidation; an old
cache name alone cannot establish validity.

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The factorization is a conceptual proof example.

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It is not asserted to be a deployed rule or a measured D-series winner.

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A smaller expression can still lose whole-task
time after matching and cache overhead.

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Preserve an exact no-rewrite path when advice is rejected.

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Work a second complete case with A 0, B 1, C 1.

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Keep this assignment fixed throughout the calculation.

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Each symbol retains the meaning already introduced; a new value does not

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create a new logical rule.

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Although both alternative conditions are true, the shared

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authorized-staff condition is false.

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Both original branches contain that false requirement and return zero.

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The factored form keeps A outside the or and also returns zero.

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Factoring has preserved the permission boundary.

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This case establishes a specific contrast.

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A remains required in both forms.

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Do not replace the policy with B OR C alone.

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Keep the input, intermediate values, and conclusion together when comparing

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it with the previous case.

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The calculated answer belongs to this complete assignment under the stated rule.

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Suppose the exception route now requires D rather than A.

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The earlier factorization does not automatically apply, because the two branches no longer

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share the same required condition.

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The meaning of the revised clause matters.

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With A zero, B zero, C one, and D one, the revised policy allows access

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through the second branch.

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The old factored expression returns zero because it still requires A.

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This single complete assignment disproves that proposed rewrite of the revised policy.

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Apply exact checking to the current rule version.

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After correctness is established, count or measure the work of recognizing, preparing, and

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executing the rewrite.

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A safe transformation can still cost more than evaluating the original

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policy for the requested lifetime.

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Check correctness independently of profitability.

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Check correctness independently of profitability.

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Charge the complete request and retain an exact no-rewrite fallback.