The Power of Symport-3 with Few Extra Symbols

Membrane systems (with symbol objects) are formal models of distributed parallel multiset processing. Symport rules move multiple objects to a neighboring region. It is known that P systems with symport rules of weight at most 3 and a single membrane are computationally complete with 7 superfluous symbols. It is also known that without any superfluous symbols such systems only generate finite sets. We improve the lower bounds on the generative power of P systems with few superfluous objects as follows. 0: empty set and all singletons; k: all sets with at most k elements and all sets of numbers k+regular with up to k states, 1 k 5; 6: all regular sets of non-negative integers. All results except the last one are also valid for different modes, e.g., sequential one, also for higher values of k

Minimal Cooperation in Symport/Antiport P Systems with One Membrane

In this paper we consider symport/antiport P systems with one membrane and rules having at most two objects. Although it has been proved that only finite number sets can be generated by both OP1(sym2) (one-membrane systems with symport rules of weight at most 2) and OP1(sym1; anti1) (one-membrane systems with symport/antiport rules of weight 1), the exact characterization is still an open question. We give some lower bounds, consider a few extensions, and state some open questions

P Systems with Minimal Left and Right Insertion and Deletion

Summary. In this article we investigate the operations of insertion and deletion performed at the ends of a string. We show that using these operations in a P systems framework (which corresponds to using specific variants of graph control), computational completeness can even be achieved with the operations of left and right insertion and deletion of only one symbol.

P Systems with Minimal Insertion and Deletion

In this paper we consider insertion-deletion P systems with priority of deletion over the insertion.We show that such systems with one symbol context-free insertion and deletion rules are able to generate PsRE. If one-symbol one-sided context is added to insertion or deletion rules but no priority is considered, then all recursively enumerable languages can be generated. The same result holds if a deletion of two symbols is permitted. We also show that the priority relation is very important and in its absence the corresponding class of P systems is strictly included in MAT

Dictionary Search and Update by P Systems with String-Objects and Active Membranes

Membrane computing is a formal framework of distributed parallel computing. In this paper we implement working with the prefix tree by P systems with strings and active membranes

The Membrane Systems Language Class

The aim of this paper is to introduce the class of languages generated by the transitional model of membrane systems without cooperation and without additional ingredients. The fundamental nature of these basic systems makes it possible to also define the corresponding class of languages it in terms of derivation trees of context-free grammars. We also compare this class to the well-known language classes and discuss its properties

New Choice for Small Universal Devices: Symport/Antiport P Systems

Symport/antiport P systems provide a very simple machinery inspired by corresponding operations in the living cell. It turns out that systems of small descriptional complexity are needed to achieve the universality by these systems. This makes them a good candidate for small universal devices replacing register machines for different simulations, especially when a simulating parallel machinery is involved. This article contains survey of these systems and presents different trade-offs between parameters

Solving Problems in Various Domains by Hybrid Models of High Performance Computations

This work presents a hybrid model of high performance computations. The model is based on membrane system (P~system) where some membranes may contain quantum device that is triggered by the data entering the membrane. This model is supposed to take advantages of both biomolecular and quantum paradigms and to overcome some of their inherent limitations. The proposed approach is demonstrated through two selected problems: SAT, and image retrieving

Graph-Controlled Insertion-Deletion Systems

In this article, we consider the operations of insertion and deletion working in a graph-controlled manner. We show that like in the case of context-free productions, the computational power is strictly increased when using a control graph: computational completeness can be obtained by systems with insertion or deletion rules involving at most two symbols in a contextual or in a context-free manner and with the control graph having only four nodes.Comment: In Proceedings DCFS 2010, arXiv:1008.127

Abstracts of Dr. Theses

The classical Turing model and modern biomolecular models of computer and computations, based on splicing are discussed