Implementing Bead-Sort with P Systems

Abstract

In this paper, we implement Bead-Sort, a natural sorting algorithm that we introduced in [1], with the new, biochemically inspired P systems. In Bead-Sort, positive integers are represented by a set of beads (like those used in an Abacus). The beads representing integers to be sorted are allowed to slide through the rods of the Abacus. In this process, the smaller “numbers” always emerge above the larger ones and this creates a natural comparison and thus a natural sorting action. This natural sorting phenomenon is “implemented” with a special type of P system —::::::::::::::::::::::; a tissue P system that computes by means of communication (using symport/antiport rules) only. Beads are represented by objects placed within membranes of a tissue P system; a rod is represented by a “group” of membranes that can communicate with one another by means of symport/antiport rules. The “flow” of objects between the group of membranes representing a rod (using communication rules) reflects the actual flow of beads in the physical system.