In the framework of tissue P systems with cell division, the length of communication
rules provides a frontier for the tractability of decision problems. On the
one hand, the limitation on the efficiency of tissue P systems with cell division and
communication rules of length 1 has been established. On the other hand, polynomial
time solutions to NP–complete problems by using families of tissue P systems with cell
division and communication rules of length at most 3 has been provided.
In this paper, we improve the previous result by showing that the HAM-CYCLE problem
can be solved in polynomial time by a family of tissue P systems with cell division by
using communication rules with length at most 2. Hence, a new tractability boundary is
given: passing from 1 to 2 amounts to passing from non–efficiency to efficiency, assuming
that P ̸= NP.Ministerio de Ciencia e Innovación TIN2009-13192Junta de Andalucía P08 – TIC 0420
