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In this article, we consider for the first time the operations of insertion and deletion working in a matrix controlled manner. We show that, similarly as in the case of context-free productions, the computational power is strictly increased when using a matrix control: 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 using only binary matrices.

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

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 computationally complete; however, a direct translation leads to quite a big 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) 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.

a b s t r a c tGeneralized communicating P systems are purely communicating tissue-like membrane systems with communication rules which allow the movement of only pairs of objects. In this paper, we study the power of these systems in the case of eight restricted variants of communication rules. We show that seven of these restrictions lead to computational completeness, while using the remaining one the systems are able to compute only finite singletons of non-negative integers. The obtained results complete the investigations of the computational power of generalized communicating P systems and provide further examples for simple architectures with simple functioning rules which are as powerful as Turing machines.