Insertion Sort with Self-reproducing Comparator P System

We present in this paper a self-reproducing comparator P system that simulates insertion sort. The comparator Πc is a degree–2 membrane and structured as μ = [h0 [h1 ]h1 [h2 ]h2 ]h0 . A maximizing Πc compares two multisets a and b where min(|a|, |b|) is stored in compartment h1 while max(|a|, |b|) is stored in compartment h2. A conditional reproduction rule triggers Πc to clone itself out via compartment division followed by endocytosis of the cloned compartment. We present the process of sorting as a collection of transactions implemented in hierarchical levels where each level has different concurrent or serialized steps.