Marion Oswald

Computationally universal P systems without priorities: two catalysts are sufficient

The original model of P systems with symbol objects introduced by Paun was shown to be computationally universal, provided that catalysts and priorities of rules are used. By reduction via register machines Sosik and Freund proved that the priorities may be omitted from the model without loss of computational power. Freund, Oswald, and Sosik considered several variants of P systems with catalysts (but without priorities) and investigated the number of catalysts needed for these specific variants to be computationally universal. It was shown that for the classic model of P systems with the minimal number of two membranes the number of catalysts can be reduced from six to five; using the idea of final states the number of catalysts could even be reduced to four. In this paper we are able to reduce the number of catalysts again: two catalysts are already sufficient. For extended P systems we even need only one membrane and two catalysts. For the (purely) catalytic systems considered by Ibarra only three catalysts are already enough.

P Systems with Activated/Prohibited Membrane Channels

We investigate a variant of purely communicating P systems, where multisets of activators can open channels for certain objects to pass through membranes in one direction; however, the permeability of a channel can be controlled by multisets of prohibitors, too.We will show that for such systems with only one membrane and using only singleton activator and prohibitor sets, we already obtain universal computational power. When using systems with activating multisets for membrane channels only, we obtain a similar result. By showing a close correspondence to P systems with symport/antiport as introduced in [13] we can optimize some results given there.

Tissue p systems with antiport rules and small numbers of symbols and cells

We consider tissue P systems with antiport rules and investigate their computational power when using only a (very) small number of symbols and cells. Even when using only one symbol, any recursively enumerable set of natural numbers can be generated with at most seven cells. On the other hand, with only one cell we can only generate regular sets when using one channel with the environment, whereas one cell with two channels between the cell and the environment obtains computational completeness with at most five symbols. Between these extreme cases of one symbol and one cell, respectively, there seems to be a trade-off between the number of cells and the number of symbols, e.g., for the case of tissue P systems with two channels between a cell and the environment we show that computational completeness can be obtained with two cells and three symbols as well as with three cells and two symbols, respectively.

P colonies working in the maximally parallel and in the sequential mode

We consider P colonies as introduced in Kelemen et al. (2005) and investigate their computational power when working in the maximally parallel and in the sequential mode. It turns out that there is a trade-off between maximal parallelism and checking programs: Using checking programs (i.e., priorities on the communication rules in the programs of the agents), P colonies working in the sequential mode with height at most 5 are computationally complete, whereas when working in the maximally parallel mode, P colonies (again with height 5) already obtain the same computational power without using checking programs. Moreover, when allowing an arbitrary number of programs for each agent, we can prove that P colonies with only one agent (thus these P colonies are working in the sequential mode) are already computationally complete. Finally, P colonies with an arbitrary number of agents working in the sequential mode as well as even P colonies with only one agent using an arbitrary number of non-checking programs characterize the family of languages generated by matrix grammars without appearance checking.

Extended spiking neural p systems

We consider extended variants of spiking neural P systems and show how these extensions of the original model allow for easy proofs of the computational completeness of extended spiking neural P systems and for the characterization of semilinear sets and regular languages by finite extended spiking neural P systems (defined by having only finite checking sets in the rules assigned to the cells) with only a bounded number of neurons.

A general framework for regulated rewriting based on the applicability of rules

We introduce a general model for various mechanisms of regulated rewriting based on the applicability of rules, especially we consider graph-controlled, programmed, matrix, random context, and ordered grammars as well as some basic variants of grammar systems. Most of the general relations between graph-controlled grammars, matrix grammars, random-context grammars, and ordered grammars established in this paper are independent from the objects and the kind of rules and only based on the notion of applicability of rules within the different regulating mechanisms and their specific structure in allowing sequences of rules to be applied. For example, graph-controlled grammars are always at least as powerful as programmed and matrix grammars. For the simulation of random context and ordered grammars by matrix and graph-controlled grammars, some specific requirements have to be fulfilled by the types of rules.

Sequential p systems with unit rules and energy assigned to membranes

We introduce a new variant of membrane systems where the rules are directly assigned to membranes (and not to the regions as this is usually observed in the area of membrane systems) and, moreover, every membrane carries an energy value that can be changed during a computation by objects passing through the membrane. For the application of rules leading from one configuration of the system to the succeeding configuration we consider a sequential derivation mode and do not use the mode of maximal parallelism. The result of a successful computation is considered to be the distribution of energy values carried by the membranes. We show that for such systems using a kind of priority relation on the rules we already obtain universal computational power. When omitting the priority relation, we obtain a characterization of the family of Parikh sets generated by context-free matrix grammars (with λ -rules).

ω -P Automata with Communication Rules

We introduce ω -P automata based on the model of P systems with membrane channels (see [8]) using only communication rules. We show that ω -P automata with only two membranes can simulate the computational power of usual (non-deterministic) ω -Turing machines. A very restricted variant of ω -P automata allows for the simulation of ω -finite automata in only one membrane.

CELL/SYMBOL COMPLEXITY OF TISSUE P SYSTEMS WITH SYMPORT/ANTIPORT RULES

We consider tissue P systems with symport/antiport rules and investigate their computational power when using only a (very) small number of symbols and cells. Even when using only one symbol, we need at most six (seven when allowing only one channel between a cell and the environment) cells to generate any recursively enumerable set of natural numbers. On the other hand, with only one cell we can only generate regular sets when using one channel with the environment, whereas one cell with two channels between the cell and the environment obtains computational completeness with five symbols. Between these extreme cases of one symbol and one cell, respectively, there seems to be a trade-off between the number of cells and the number of symbols. For example, for the case of tissue P systems with two channels between a cell and the environment we show that computational completeness can be obtained with two cells and three symbols as well as with three cells and two symbols, respectively. Moreover, we also show that some variants of tissue P systems characterize the families of finite or regular sets of natural numbers.

Symbol/Membrane complexity of p systems with symport/antiport rules

We consider P systems with symport/antiport rules and small numbers of symbols and membranes and present several results for P systems with symport/antiport rules simulating register machines with the number of registers depending on the number s of symbols and the number m of membranes. For instance, any recursively enumerable set of natural numbers can be generated (accepted) by systems with s ≥ 2 symbols and m ≥ 1 membranes such that m + s ≥ 6. In particular, the result of the original paper [17] proving universality for three symbols and four membranes is improved (e.g., three symbols and three membranes are sufficient). The general results that P systems with symport/antiport rules with s symbols and m membranes are able to simulate register machines with max{m(s-2),(m-1)(s-1)} registers also allows us to give upper bounds for the numbers s and m needed to generate/accept any recursively enumerable set of k-dimensional vectors of non-negative integers or to compute any partial recursive function f : ℕα →ℕβ. Finally, we also study the computational power of P systems with symport/antiport rules and only one symbol: with one membrane, we can exactly generate the family of finite sets of non-negative integers; with one symbol and two membranes, we can generate at least all semilinear sets. The most interesting open question is whether P systems with symport/antiport rules and only one symbol can gain computational completeness (even with an arbitrary number of membranes) as it was shown for tissue P systems in [1].