Andrei Paun

The power of communication: P systems with symport/antiport

In the attempt to have a framework where the computation is done by communication only, we consider the biological phenomenon of trans-membrane transport of couples of chemicals (one say symport when two chemicals pass together through a membrane, in the same direction, and antiport when two chemicals pass simultaneously through a membrane, in opposite directions). Surprisingly enough, membrane systems without changing (evolving) the used objects and with the communication based on rules of this type are computationally complete, and this result is achieved even for pairs of communicated objects (as encountered in biology). Five membranes are used; the number of membranes is reduced to two if more than two chemicals may collaborate when passing through membranes.

On P Systems with Active Membranes

The paper deals with the vivid area of computing with membranes (P systems). We improve here two recent results about the socalled P systems with active membranes. First, we show that the Hamiltonian Path Problem can be solved in polynomial time by P systems with active membranes where the membranes are only divided into two new membranes (a result of this type was obtained by Krishna and Rama, [4], but making use of the possibility of dividing a membrane in an arbitrary number of new membranes). We also show that HPP can be solved in polynomial time also by a variant of P systems, with the possibility of dividing non-elementary membranes under the influence of objects present in them. Then, we show that membrane division (and even membrane dissolving) is not necessary in order to show that such systems are computationally complete.

An O(n2) Algorithm for Constructing Minimal Cover Automata for Finite Languages

Cover automata were introduced in [1] as an efficient representation of finite languages. In [1], an algorithm was given to transform a DFA that accepts a finite language to a minimal deterministic finite cover automaton (DFCA) with the time complexity O(n4), where n is the number of states of the given DFA. In this paper, we introduce a new efficient transformation algorithm with the time complexity O(n2), which is a significant improvement from the previous algorithm.

State and Transition Complexity of Watson-Crick Finite Automata

We consider the number of states and the number of transitions in Watson-Crick finite (non-deterministic) automata as descriptional complexity measures. The succinctness of recognizing regular languages by Watson-Crick (arbitrary or 1-limited) automata in comparison with non-deterministic finite automata is investigated, as well as decidability and computability questions. Major differences are found between finite automata and Watson-Crick finite automata from both these points of view.

On P Systems with Global Rules

Abstract We contribute to the vivid area of membrane computing (P systems) by considering the case when the same evolution rules are valid in all regions of a system. Such a P system is called with global rules . We consider the case of string-objects, with the evolution rules based on splicing and by rewriting. Universality results are proved for both types of systems. For splicing we also try to minimize the diameter of the used rules, while for rewriting systems we improve a result from the literature, proving that two membranes suffice for simulating Turing machines.

The number of similarity relations and the number of minimal deterministic finite cover automata

Finite Deterministic Cover Automata (DFCA) can be obtained from Deterministic Finite Automata (DFA) using the similarity relation. Since the similarity relation is not an equivalence relation, the minimal DFCA for a finite language is usually not unique. We count the number of minimal DFCA that can be obtained from a given minimal DFA with n states by merging the similar states in the given DFA. We compute an upper bound for this number and prove that in the worst case (for a non-unary alphabet) it is ⌈4<i>n</i>-9+√8<i>n</i>+1/8⌉!/(2⌈4<i>n</i>-9+√8<i>n</i>+1/8⌉ - <i>n</i> + 1)! We prove that this upper bound is reached, i.e. for any given positive integer <i>n</i> we find a minimal DFA with <i>n</i> states, which has the number of minimal DFCA obtained by merging similar states equal to this maximum.

OPTIMAL RESULTS FOR THE COMPUTATIONAL COMPLETENESS OF GEMMATING (TISSUE) P SYSTEMS

Gemmating P systems were introduced as a theoretical model based on the biological idea of the gemmation of mobile membranes. In the general model of extended gemmating P systems, strings are modif...