Sergey Verlan

A formal framework for static (tissue) P systems

The formalism of P systems is known for many years, yet just recently new derivation modes and halting conditions have been proposed. For developing comparable results, a formal description of their functioning, in particular, of the derivation step is necessary. We introduce a formal general framework for static membrane systems that aims to capture most of the essential features of (tissue) P systems and to define their functioning in a formal way.

Context-free insertion-deletion systems

We consider a class of insertion-deletion systems which have not been investigated so far, those without any context controlling the insertion-deletion operations. Rather unexpectedly, we found that context-free insertion-deletion systems characterize the recursively enumerable languages. Moreover, this assertion is valid for systems with only one axiom, and also using inserted and deleted strings of a small length. As direct consequences of the main result we found that set-conditional insertion-deletion systems with two axioms generate any recursively enumerable language (this solves an open problem), as well as that membrane systems with one membrane having context-free insertion-deleletion rules without conditional use of them generate all recursively enumerable languages (this improves an earlier result). Some open problems are also formulated.

On the rule complexity of universal tissue p systems

In the last time several attempts to decrease different complexity parameters (number of membranes, size of rules, number of objects etc.) of universal P systems were done. In this article we consider another parameter which was not investigated yet: the number of rules. We show that 8 rules suffice to recognise any recursively enumerable language if splicing tissue P systems are considered.

Insertion-deletion systems with one-sided contexts

It was shown in (Verlan, 2005) that complexity measures for insertion-deletion systems need a revision and new complexity measures taking into account the sizes of both left and right context were proposed. In this article we investigate insertion-deletion systems having a context only on one side of insertion or deletion rules. We show that a minimal deletion (of one symbol) in one-symbol one-sided context is sufficient for the computational completeness if a cooperation of 4 symbols is used for insertion rules and not sufficient if an insertion of one symbol in onesymbol left and right context is used. We also prove the computational completeness for the case of the minimal context-free deletion (of two symbols) and insertion of two symbols in one-symbol one-sided context.

Generalized communicating P systems

This paper considers a generalization of various communication models based on the P system paradigm where two objects synchronously move across components. More precisely, the model uses blocks of four cells such that pairs of objects from two input cells travel together to target output cells. It is shown that the model introduced, based on interactions between blocks, is complete, being able to generate all recursively enumerable sets of natural numbers. It is also proven that completeness is achievable by using a minimal interaction between blocks, i.e. every pair of cells is the input or output for at most one block. It is also shown that the concepts introduced in this paper to define the model may be simulated by more particular communication primitives, including symport, antiport and uniport rules. This enables us to automatically translate a system using interaction rules in any of minimal symport, minimal antiport or conditional uniport P systems.

On small universal antiport P systems

It is known that P systems with antiport rules simulate register machines, i.e., they are computationally complete. Hence, due to the existence of universal register machines, there exist computationally complete subclasses of antiport P systems with bounded size, i.e., systems where each size parameter is limited by some constant. However, so far there has been no estimation of these numbers given in the literature. In this article, three universal antiport P systems of bounded size are demonstrated, different from each other in their size parameters. We present universal antiport P systems with 73, 43, and 30 rules where the maximum of the weight of the rules is 4, 5, and 6, respectively.

Time-Varying Distributed H Systems with Parallel Computations: the Problem is Solved

In this article we show that time-varying distributed H systems (TVDH systems) with one component are able to model any type-0 grammar. Thus we completely answered to the question of constructing TVDH systems of smallest degree which generate any RE language using the parallel nature of molecular computations based on splicing operations. Another interesting point is that the proof is based on a simulation of a TVDH system of degree two and not of type-0 grammars as it is usually done in similar proofs.

Matrix insertion-deletion systems

We investigate in this article the operations of insertion and deletion working in a matrix-controlled manner. We show that this allows to us strictly increase the computational power: in the case of systems that are not computationally complete (with total size equal to 4), the computational completeness can be obtained by introducing the matrix control and using only binary matrices.

P systems with minimal insertion and deletion

In this paper, we consider insertion-deletion P systems with priority of deletion over insertion. We show that such systems with one-symbol context-free insertion and deletion rules are able to generate Parikh sets of all recursively enumerable languages (PsRE). If a one-symbol one-sided context is added to the insertion or deletion rules, 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 the family of matrix languages (MAT).

Minimization strategies for maximally parallel multiset rewriting systems

Maximally parallel multiset rewriting systems (MPMRS) give a convenient way to express relations between unstructured objects. The functioning of various computational devices may be expressed in terms of MPMRS (e.g., register machines and many variants of P systems). In particular, this means that MPMRS are Turing universal; however, a direct translation leads to quite a large number of rules. Like for other classes of computationally complete devices, there is a challenge to find a universal system having the smallest number of rules. In this article we present different rule minimization strategies for MPMRS based on encodings and structural transformations. We apply these strategies to the translation of a small universal register machine (Korec (1996) [9]) and we show that there exists a universal MPMRS with 23 rules. Since MPMRS are identical to a restricted variant of P systems with antiport rules, the results we obtained improve previously known results on the number of rules for those systems.