Lemma 2: a Symmetric Maximal-pool System Preserves Property A1

Proof: We present here only a sketch of the proof. Consider a symmetric maximal-pool system X m (DB), and a single-paging 1 system with a buffer-pool of size m and a buffer replacement policy that is the same as that of the symmetric system. Let F(s,m) denote the number of faults experienced by the single-paging system when it encounters a reference string s. We can show that X m (DB) preserves the Hence, X m (DB) preserves property A1. t Theorem 1: A symmetric maximal-pool system preserves the DP property if the fault-ratio is less than or equal to 1. Proof: Follows directly from Lemma 1 and Lemma 2. t 1 Recall that, a single-paging system is equivalent to a double paging system whose buffer-pool is fully allocated.