Search

Membrane systems (with symbol objects) are distributed controlled multiset processing systems. Non-cooperative P systems with either promoters or inhibitors (of weight not restricted to one) are known to be computationally complete. In this paper we show that the power of the deterministic subclass of such systems is computationally complete in the sequential mode, but only subregular in the asynchronous mode and in the maximally parallel mode.

We consider the (d-dimensional) array counterpart of string insertion and deletion grammars and use the operations of array insertion and deletion in the framework of P systems where the applicability of the rules depends on the membrane region. In this paper, we especially focus on examples of two-dimensional array insertion and deletion P systems and show that we can already obtain computational completeness using such P systems with a membrane structure of tree height of at most two and only the targets here, in, and out.

Objects generated in P systems usually are assumed to survive as long as the computation goes on. In this paper, decaying objects are considered, i.e., objects only surviving a bounded number of computation steps. Variants of (tissue) P systems with decaying objects working in transition modes where the number of rules applied in each computation step is bounded, are shown to be very restricted in their generative power, i.e., if the results are collected in a specified output cell/membrane, then only finite sets of multisets can be generated, and if the results are specified by the objects sent out into the environment, we obtain the regular sets. Only if the decaying objects are regenerated within a certain period of computation steps, i.e., if we allow an unbounded number of rules to be applied, then computational completeness can be obtained, yet eventually more ingredients are needed for the rules than in the case of non-decaying objects, e.g., permitting and/or forbidden contexts. As special variants of P systems, catalytic P systems, P systems using cooperative rules, and spiking neural P systems are investigated.

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.

We study reversibility and determinism aspects of sequential multiset processing systems, and the strong versions of these properties. Syntactic criteria are established for both strong determinism and for strong reversibility. It also shown that without control all four classes -deterministic, strongly deterministic, reversible, strongly reversibleare not universal, while allowing priorities or inhibitors the first and the third class become universal. Moreover, strongly deterministic multiset rewriting systems with priorities are also universal.

In this paper, we consider spiking neural P systems without delay with specific restrictions on the types of neurons. Two neurons are considered to be of the same type if the rules, the number of spikes in the initial configuration and the number of outgoing synapses are identical. We show that computational completeness can be achieved in both the generating and the accepting case with only two types of neurons, where the number of neurons with unbounded rules is constant even minimal.

In addition to the maximally parallel transition mode used from the beginning in the area of membrane computing, many other transition modes for (tissue) P systems have been investigated since then. In this paper we consider (tissue) P systems with hybrid transition modes where each set of a covering of the whole set of rules may work in a different transition mode in a first level and all partitions of rules work together at a (second) level of the whole system on the current configuration in a maximally parallel way. With all partitions of noncooperative rules working in the maximally parallel mode, we obtain a characterization of Parikh sets of ET0L-languages, whereas with hybrid systems with the partitions either working in the maximally parallel and in the =1-mode or with all partitions working in the =1-mode we can simulate catalytic or purely catalytic P systems, respectively, thus obtaining computational completeness.

A variety of different transition modes for (tissue) P systems as well as several halting modes currently are used in the area of membrane computing. In this paper, the definitions of the most important transition modes and halting modes are explained based on networks of cells, a general model for tissue P systems. Moreover, some results for specific variants of (tissue) P systems working on multisets of objects are recalled.

We consider membrane systems using noncooperative rules, but considering computations without using halting conditions. As results of a computation we take the contents of a specified output membrane/cell in each transition step, no matter whether this computation will ever halt or not, eventually taking only results completely consisting of terminal objects only. The computational power of membrane systems using noncooperative rules turns out to be equivalent to that of Lindenmayer systems.

We consider a new variant of the halting condition in P systems, i.e., a computation in a P system is already called halting if not for all membranes a rule is applicable anymore at the same time, whereas usually a computation is called halting if no rule is applicable anymore in the whole system. This new variant of partial halting is especially investigated for several variants of P systems using membrane rules with permitting contexts and working in different derivation modes.

The paper introduces communication modes in tissue P systems that are based on the applicability of the rules to the objects present inside the cells. This notion of a communication mode is inspired by the concept of a derivation mode used in the area of grammar systems. Three different communication modes are identified depending on both the way the objects are moved from one cell to another one, altogether as a multiset or independently from each other, and on the moment when communication can take place, immediately after a terminal object is produced inside a cell, immediately after a cell has reached a terminal configuration or only when the system as a whole has reached a final configuration. The computational power of tissue P systems with different communication modes is compared with the power of the basic model of P systems and some classes of L systems.

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].

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.

We first give a historical overview of the most important results obtained in the area of P systems and tissue P systems with symport/antiport rules, especially with respect to the development of computational completeness results improving descriptional complexity parameters. We consider the number of membranes (cells in tissue P systems), the weight of the rules, and the number of objects. Then we establish our newest results: P systems with only one membrane, symport rules of weight three, and with only seven additional objects remaining in the skin membrane at the end of a halting computation are computationally complete; P systems with minimal cooperation, i.e., P systems with symport/antiport rules of size one and P systems with symport rules of weight two, are computationally complete with only two membranes with only three and six, respectively, superfluous objects remaining in the output membrane at the end of a halting computation.

Among the many events that occur in the life of biological organisms there are multitudes of specific chemical transformations that provide the cell with usable energy and molecules needed to form its structure and coordinate its activities. These biochemical reactions, as well as all other cellular processes, are governed by basic principles of chemistry and physics. A significant factor that determines whether or not reactions could take place is the entropy (it measures the randomness of the system). This measure depends on various factors. In an abstract framework, all these factors, which describe the way molecules interact, can be expressed by means of a computable multi-valued function that, depending on the current state of the system, establishes the possible ways of the evolution of the system. Inspired by these facts, we introduce and study several bio-mimetic computational rewriting systems that use discrete components (i.e., finite alphabets, finite set(s) of rewriting rules, etc.) and perform their computational steps in a non-deterministic manner and in a degree of rewriting parallelism that depends on the current state of the system, both specified by a given multi-valued function. Furthermore, we describe systems which produce the same output independently of the values taken by the considered functions.

In the area of P systems, applying the rules in a maximally parallel way is one of the most common features of many models introduced so far. Whereas the idea of membranes as well as many operations and rules used in membrane systems have a concrete biological background, the universal clock assumed to control the parallel application of rules is unrealistic, but on the other hand relevant for many interesting theoretical results, especially when proving computational completeness and solving computationally hard problems. Based on a quite general definition of tissue P systems, we investigate several models of P systems and compare their computational power in the classic case (i.e., applying the rules in the maximally parallel mode) and in the case of applying the rules in an asynchronous way (i.e., an arbitrary number of rules may be applied in one derivation step) or in the sequential mode (i.e., exactly one rule is applied in one derivation step). Moreover, we also recall some results for (tissue) P systems working in an asynchronous or sequential mode already in the original definition. Finally, we also raise several questions for future research in this subarea of (tissue) P systems working in the asynchronous mode and (tissue) P systems working in the sequential mode.

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.

We present an algorithm for deterministically deciding SAT in linear time by P systems with active membranes using only two polarizations and rules of types (a), (c), and (e). Moreover, various restrictions on the general form of the rules are considered: global, non-renaming, independent of the polarization, preserving it, changing it, producing two membranes with different polarizations, having exactly one or two objects in (each membrane of) the right-hand side, thus improving results from [1]. Several problems related to different combinations of these restrictions are formulated, too.

Taking advantage of the weak determinism inherent to the simulation of deterministic register machines by catalytic P systems, we present an efficient implementation of such P systems.

We consider P systems with active membranes, but without polarizations, yet with using membrane division and membrane generation, but as the result of a halting computation we do not take the terminal string generated in a designated output membrane, instead we consider the resulting tree representing the membrane structure of the final configuration as its result. We show that each recursively enumerable tree language can be obtained in that way generated by P systems with active membranes working on strings.

We introduce a new variant of splicing P systems, where the rules are directly assigned to the membranes and not to the regions as this is usually observed in the area of membrane systems. The strings involved in the splicing operation are either taken from inside or from outside the membrane and the strings resulting from the splicing operation also may go inside or outside the membrane. Instead of the splicing operation, also the operations of cutting and recombination are used as rules assigned to membranes. For the application of rules leading from one configuration of the system to the succeeding configuration we consider a sequential model and do not use the model of maximal parallelism. We will show that for such sequential P systems using splicing rules or cutting/recombination rules assigned to the skin membrane we already obtain universal computational power with only one membrane.

Based on a quite general definition of P systems where the rules are applied in a sequential way (and not in the maximally parallel way as it usually happens in most models of P systems considered so far in the literature), we investigate the generative power of various models of such P systems working in the sequential mode on arrays and strings, respectively. P systems working in the sequential mode on arrays/strings without priority relations for the rules reveal the same computational power as the corresponding matrix grammars without appearance checking working on arrays/strings. For obtaining the computational power of matrix grammars with appearance checking, priority relations for the rules (as one of many other possible additional features) are needed.

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.

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.

We consider a variant of test tube systems communicating by applying splicing rules, yet without allowing operations in the tubes themselves. These test tube systems communicating by applying splicing rules of some restricted type are shown to be equivalent to a variant of splicing test tube systems using a corresponding restricted type of splicing rules. Both variants of test tube systems using splicing rules are proved to be equivalent to membrane systems with splicing rules assigned to membranes, too. In all the systems considered in this paper, for the application of rules leading from one configuration to the succeeding configuration we use a sequential model, where only one splicing rule is applied in one step; moreover, all these systems have universal computational power.

Symport and antiport are biological ways for transporting molecules through membranes in a "collaborating" manner; in the case of symport several molecules pass in the same direction, in the case of antiport two or more molecules pass in opposite directions. In this paper we first survey the results on the computing power of membrane systems (P systems) using only symport/antiport rules and then improve some of the results known so far. A recent variant of P systems with purely communicating rules introduced in [24] with the name of communicating P systems is revisited and optimal (with respect to the number of membranes) universality results for that particular variant are obtained, too.

As already considered in [13], we investigate P systems where each evolution rule "produces" or "consumes" some quantity of energy, in amounts which are expressed as integer numbers. Yet in contrast to P systems with energy accounting as considered in [13], for energy-controlled P systems we demand that in each evolution step and in each membrane the total energy consumed by the application of a multiset of evolution rules has to be the maximum possible within a specific non-negative range. Only equipped with this control feature, energy-controlled P systems are very powerful. In the case of multisets of symbol objects we find that energy-controlled P systems with even only one membrane and an energy range of {0, 1} for the total energy involved in an evolution step characterize the recursively enumerable sets of vectors of natural numbers (without using catalysts or priorities or membrane dissolving features). In the case of string objects similar results can be obtained. Energy-controlled P systems with even only one membrane and the minimal energy range of {0} for the total energy involved in an evolution step at least generate any set of vectors of natural numbers that can be generated by matrix grammars without appearance checking.

We investigate the three classes of accepting P systems considered so far, namely the P automata of Csuhaj-Varju, Vaszil [3], their variant introduced by Madhu, Krithivasan [10], and the related machinery of Freund, Oswald [5]. All three variants of automata-like P systems are based on symport/antiport rules. For slight variants of the first two classes we prove that any recursively enumerable language can be recognized by systems with only two membranes (this considerably improves the result from [3], where systems with seven membranes were proved to be universal). We also introduce the initial mode of accepting strings (the strings are introduced into the system, symbol by symbol, at the beginning of a computation), and we briefly investigate this mode for the three classes of automata, especially for languages over a one-letter alphabet. Some open problems are formulated, too.

The “classical” model of P systems was introduced by Gheorghe PĂun in 1998; this model with symbol objects was shown to be computationally universal in [8], provided that catalysts and priorities of rules are used. We now show by reduction via register machines that the priorities may be omitted from the model without loss of computational power. As a consequence, several universality results for P systems in [10] are improved.

We investigate the computational power of generalized P-systems of specific types in comparison with the computational power of certain control mechanisms for string rewriting grammars.An important restriction dwells in using sets of operators instead of multisets within sequential P-systems; this restriction is shown to be substantial, i.e., sequential P-systems of specific type using multisets are more powerful than the corresponding sequential P-systems using only sets.

We improve the results elaborated in [6] on the number of non-terminal symbols needed in matrix grammars, programmed grammars, and graph-controlled grammars with appearance checking for generating arbitrary recursively enumerable languages. Of special interest is the result that the number of non-terminal symbols used in the appearance checking mode can be restricted to two. In the case of graph controlled (and programmed grammars) with appearance checking also the number of non-terminal symbols can be reduced to three (and four, respectively); in the case of matrix grammars with appearance checking we either need four non-terminal symbols with three of them being used in the appearance checking mode or else again we only need two nonterminal symbols being used in the appearance checking mode, but in that case we cannot bound the total number of non-terminal symbols.

Recently P-systems were introduced by Gheorghe Paun as a new model for computations based on membrane structures. The basic variants of P-systems shown to have universal computational power only took account of the multiplicities of atomic objects, some other variants considered rewriting rules on strings. Using the membranes as a kind of filter for specific objects when transferring them into an inner compartment or out into the surrounding compartment turned out to be a very powerful mechanism in combination with suitable rules to be applied within the membranes in the model of generalized P-systems, GP-systems for short. GP-systems were shown to allow for the simulation of graph controlled grammars of arbitrary type based on productions working on single objects; moreover, various variants of GP-systems using splicing or cutting and recombination of strings were shown to have universal computational power, too. In this paper, we consider GP-systems with homogeneous membrane structures, GhP-systems for short, using splicing or cutting and recombination of string objects with specific markers at the ends of the strings that can be interpreted as electrical charges. The sum of these electrical charges determines the permeability of the membranes to the string objects, and we allow only objects with the absolute value of the difference of electrical charges being equal to 1 to pass a membrane in both directions. We show that such GhP-systems have universal computational power; for GhP-systems using splicing and a bounded number of markers the obtained results are optimal with respect to the underlying membrane structure. Moreover, a very restricted variant of such GhP-systems characterizes the (strictly) minimal linear languages.

In this paper we introduce a new hybrid system for the automated recognition of hand-written characters - we combine the most promising approaches of the last decade, i.e., neural networks and structural/ syntactical analysis methods. The given patterns represent handwritten capital letters and digits stored in arrays. The first part of the hybrid system consists of the implementation of a neural network and yields a rapid and reliable pre-selection of the most probable characters the given pattern may represent. Depending on the quality and the special characteristics of the given pattern a flexible set of characters is communicated to the second part of the hybrid system, the structural analysis module. The final decision is based on the evaluation of the presence of features, being characteristic for a specific character, in the underlying pattern. Basically, the structural analysis module consists of graph controlled array grammar systems using prescribed teams of productions. We describe the main parts of the implemented hybrid system and demonstrate the power of our approach.

We consider a variant of P-systems, a new model for computations using membrane structures and recently introduced by Gheorghe Paun. Using the membranes as a kind of filter for specific objects when transferring them into an inner compartment turns out to be a very powerful mechanism in combination with suitable rules to be applied within the membranes. The model of generalized P-systems, GP-systems for short, considered in this paper allows for the simulation of graph controlled grammars of arbitrary type based on productions working on single objects; for example, the general results we establish in this paper can immediately be applied to the graph controlled versions of context-free string grammars, n-dimensional #-context-free array grammars, and elementary graph grammars.

We introduce the, concept of k-head finite two-dimensional array automata and show how this model of two-dimensional array automata can be applied in the field of syntactic: character recognition. Moreover, we discuss some of the problems arising; with implementing the theoretical concept to obtain an efficient tool for the syntactic analysis of handwritten (uppercase characters.

We consider (n-dimensional) array grammars in the accepting mode with various control mechanisms and compare these families of array grammars with the corresponding families obtained by array grammars in the generating mode.

The aim of this paper is to elaborate the power of cooperation in generating and analysing (handwritten) characters by array grammars. We present various non-context-free sets of arrays that can be generated in a simple way by cooperating distributed array grammar systems with prescribed teams working in different modes and show the power of the mechanism of cooperation for picture description and analysis as well as the efficiency of these models where several sets of productions work in parallel on the given sentential form.

We prove that grammar systems with (prescribed or free) teams (of constant size at least two or arbitrary size) working as long as they can do, characterize the family of languages generated by (context-free) matrix grammars with appearance checking; in this way, the results in [Paun, Rozenberg 1994] are completed and improved.

A new mechanism for generating graph languages is introduced which is based on the controlled rewriting of graphs using only six elementary types of graph productions, namely the addition, the deletion and the renaming of a node or an edge. Although these elementary graph productions are acting strictly locally and no embedding transformations are needed, in the unrestricted and monotone case, elementary programmed graph grammars have the same generative power as expression graph grammars. As a graph with attributes assigned to its nodes and edges is an even more useful tool for the description of certain data structures than a directed graph, attributed elementary programmed graph grammars turn out to be adequate graph rewriting systems applicable in many areas of computer science.

The notion of n-dimensional attributed parallel array grammars is introduced for describing neural networks. Because of the underlying grid structure, Kohonen’s model of feature maps is especially well suited for being represented by n-dimensional attributed parallel array grammars. Using our formal description model we prove that Kohonen’s global algorithm can be replaced by a local one.

Brane calculi are a family of biologically inspired process calculi proposed in [3] for modeling the interactions of dynamically nested membranes. In [3] two basic calculi are proposed. Mate/Bud/Drip (MBD) is one of such basic calculi, and its primitives are inspired by membrane fusion and fission. In this paper we investigate the expressiveness of MBD w.r.t. its ability to act as a computational device. In particular, we compare the expressiveness of two different semantics for MBD: the standard interleaving semantics – where a single interaction is executed at each computational step – and the maximal parallelism semantics – according to which a computational step is composed of a maximal set of independent interactions. For the interleaving semantics, we show a nondeterministic encoding of Register Machines in MBD, that preserves the existence of a terminating computation, but that could introduce additional divergent (i.e., infinite) computations. For the maximal parallelism semantics, we provide a deterministic encoding of Register Machines, which preserves both the existence of a terminating computation and the existence of a divergent computation. The impossibilty of providing a deterministic encoding under the interleaving semantics is a consequence of the decidability of the existence of a divergent computation proved in [1].