Hybrid Transition Modes in (Tissue) P Systems

2006

2005

The original model of P systems with symbol objects introduced by Pȃun was shown to be computationally universal, provided that catalysts and priorities of rules are used. By reduction via register machines Sosík and Freund proved that the priorities may be omitted from the model without loss of computational power. Freund, Oswald, and Sosík 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.

Journal of Membrane Computing, 2021

Catalytic P systems are among the first variants of membrane systems ever considered in this area. This variant of systems also features some prominent computational complexity questions, and in particular the problem of using only one catalyst: is one catalyst enough to allow for generating all recursively enumerable sets of multisets? Several additional ingredients have been shown to be sufficient for obtaining even computational completeness with only one catalyst. Last year we could show that the derivation mode max objects , where we only take those multisets of rules which affect the maximal number of objects in the underlying configuration one catalyst is sufficient for obtaining computational completeness without any other ingredients. In this paper we follow this way of research and show that one catalyst is also sufficient for obtaining computational completeness when using specific variants of derivation modes based on non-extendable multisets of rules: we only take those non-extendable multisets whose application yields the maximal number of generated objects or else those non-extendable multisets whose application yields the maximal difference in the number of objects between the newly generated configuration and the current configuration. A similar computational completeness result can even be obtained when omitting the condition of non-extendability of the applied multisets when taking the maximal difference of objects or the maximal number of generated objects. Moreover, we reconsider simple P system with energy control-both symbol and rule energy-controlled P systems equipped with these new variants of derivation modes yield computational completeness.

FUDMA JOURNAL OF SCIENCES

Quasi-general models of membrane computing have been designed by means of rules which represent the processes taking place in a biological cell without explicitly specifying the specialties of the rules, viz: their mixture, chemical or physical characteristics as is obtainable in a biological cell. In this paper, an attempt to model a variant of membrane computing called specialization P system is made. It is capable of simulating biological activities at cellular level, and as the name implies, in a specialized manner. It is shown that with only one membrane and three rules, a deterministic cooperative specialization P system under catalysis is able to characterize the family of recursively enumerable languages.

Triangle

In this paper we define a general class of P systems covering some biological operations with membranes, including evolution, communication, and modifying the membrane structure, and we describe and formally specify some of these operations: membrane merging, membrane separation, membrane release. We also investigate a particular combination of types of rules that can be used in solving the SAT problem in linear time.

Electronic Proceedings in Theoretical Computer Science

Whether P systems with only one catalyst can already be computationally complete, is still an open problem. Here we establish computational completeness by using specific variants of additional control mechanisms. At each step using only multiset rewriting rules from one set of a finite number of sets of multiset rewriting rules allows for obtaining computational completeness with one catalyst and only one membrane. If the targets are used for choosing the multiset of rules to be applied, for getting computational completeness with only one catalyst more than one membrane is needed. If the available sets of rules change periodically with time, computational completeness can be obtained with one catalyst in one membrane. Moreover, we also improve existing computational completeness results for P systems with mobile catalysts and for P systems with membrane creation.

Machines, Computations, and Universality, 2004

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

Theoretical Computer Science, 2004

We look at 1-region membrane computing systems which only use rules of the form Ca → Cv, where C is a catalyst, a is a noncatalyst, and v is a (possibly null) string of noncatalysts. There are no rules of the form a → v. Thus, we can think of these systems as "purely" catalytic. We consider two types: (1) when the initial conÿguration contains only one catalyst, and (2) when the initial conÿguration contains multiple catalysts. We show that systems of the ÿrst type are equivalent to communication-free Petri nets, which are also equivalent to commutative context-free grammars. They deÿne precisely the semilinear sets. This partially answers an open question (in: WMC-CdeA'02, Computationally universal P systems without priorities: two catalysts are su cient, available at http://psystems. disco.unimib.it, 2003). Systems of the second type deÿne exactly the recursively enumerable sets of tuples (i.e., Turing machine computable). We also study an extended model where the rules are of the form q : (p; Ca → Cv) (where q and p are states), i.e., the application of the rules is guided by a ÿnite-state control. For this generalized model, type (1) as well as type (2) with some restriction correspond to vector addition systems. Finally, we brie y investigate the closure properties of catalytic systems.

2015

We study variants of P systems that are working in the sequential mode. Usually, they are not computationally complete, but there are possible extensions that can increase the computation power. Extensions that implement a notion of zero-checking are often computationally complete. P systems with an ability to create new membranes are a rare exception as they are known to be computationally complete even in the sequential mode without using a dedicated zero-check operation. Using sets instead of multisets was inspired by Reaction systems and we show how to use this relaxation in the context of active membranes. We challenge the original definition of a membrane creation because possible multiplicity of labels of child membranes are in conflict with no multiplicity of objects in Reaction systems. We propose more suitable notions of membrane creation and prove computational completeness by simulating a register machine.

International Journal Information Technologies and Knowledge Issn 1313 048x 2008 01 Vol 2 N 1, 2008

Transition P-systems are based on biological membranes and try to emulate cell behavior and its evolution due to the presence of chemical elements. These systems perform computation through transition between two consecutive configurations, which consist in a m-tuple of multisets present at any moment in the existing m regions of the system. Transition between two configurations is performed by using evolution rules also present in each region. Among main Transition P-systems characteristics are massive parallelism and non determinism. This work is part of a very large project and tries to determine the design of a hardware circuit that can improve remarkably the process involved in the evolution of a membrane. Process in biological cells has two different levels of parallelism: the first one, obviously, is the evolution of each cell inside the whole set, and the second one is the application of the rules inside one membrane. This paper presents an evolution of the work done previously and includes an improvement that uses massive parallelism to do transition between two states. To achieve this, the initial set of rules is transformed into a new set that consists in all their possible combinations, and each of them is treated like a new rule (participant antecedents are added to generate a new multiset), converting an unique rule application in a way of parallelism in the means that several rules are applied at the same time. In this paper, we present a circuit that is able to process this kind of rules and to decode the result, taking advantage of all the potential that hardware has to implement P Systems versus previously proposed sequential solutions.