Characterizing Tractability by Tissue-Like P Systems

Abstract

Summary. In the framework of cell-like membrane systems it is well known that the construction of exponential number of objects in polynomial time is not enough to efficiently solve NP-complete problems. Nonetheless, it may be sufficient to create an exponential number of membranes in polynomial time. In the framework of recognizer polarizationless P systems with active membranes, the construction of an exponential workspace expressed in terms of number of membranes and objects may not suffice to efficiently solve computationally hard problems.In this paper we study the computational efficiency of recognizer tissue P systems with communication (symport/antiport) rules and division rules. Some results have been already obtained in this direction: (a) using communication rules and forbidding division rules, only tractable problems can be efficiently solved; (b) using communication rules with length three and division rules, NP-complete problems can be efficiently solved. In this paper we show that the allowed length of communication rules plays a relevant role from the efficiency point of view of the systems.

The Computational Complexity of Tissue P Systems with Evolutional Symport/Antiport Rules

“…In [31], it was shown that the class of decision problems solvable in polynomial time by means of families of tissue P systems with cell division and symport rules with length 1 is equal to class P. Bearing in mind that systems from TSEC(1, ) are noncooperative ones, the dependency graph technique used in the cited paper can be used to obtain the result, in a similar way. TSEC(3, 2).…”

“…It was shown that in the framework of tissue P systems with cell division, only tractable problems can be efficiently solved by using communication rules with length at most one [31] (the length of such a rule is the total number of objects involved in it), but a uniform polynomial time solution to the HAM-CYCLE problem by a family of such P systems using communication rules with length at most two has been given [30]. On the other hand, in the framework of tissue P systems with cell separation, by using communication rules with length at most two, only tractable problems can be efficiently solved, but the SAT problem can be solved by this kind of P systems using communication rules with length at most three [26].…”

Membrane fission versus cell division: When membrane proliferation is not enough

“…The dependency graph technique consists on the construction of a directed graph (dependency graph) G associated with a P system verifying the following: there exists an accepting computation of if and only if there exists a path between two distinguished nodes in the dependency graph associated with it (see [5] and [6] for more details). This property is verified by recognizer P systems with symport/antiport rules where all its communication rules are of length 1.…”

A polynomial alternative to unbounded environment for tissue P systems with cell division

“…Proof Let us recall that PMC TDC(1) = P (see [3] for details). Then, P ⊆ PMC TDC(1) ⊆ PMC TDC(1) = P.…”

“…On the one hand, it is well known that P = PMC TDC(1) [3]. On the other hand, in [15], a uniform and polynomial time solution of the HAM-CYCLE problem by a family of tissue P systems from TDC(2).…”