This special issue is dedicated to Giancarlo Mauri on the occasion of his 70th birthday.Giancarlo is a well-known prolific

This special issue celebrates the 85th birthday of Andrzej Ehrenfeucht, an iconic scientist. He has contributed many seminal results and opened new research directions in mathematical logic, theoretical computer science, and natural computing. His research is characterized by originality and elegance -he is famous for discovering unique approaches to and elegant structures within problems he works on.

Spiking Neural [Formula: see text] Systems are Neural System models characterized by the fact that each neuron mimics a biological cell and the communication between neurons is based on spikes. In the Spiking Neural [Formula: see text] systems investigated so far, the application of evolution rules depends on the contents of a neuron (checked by means of a regular expression). In these [Formula: see text] systems, a specified number of spikes are consumed and a specified number of spikes are produced, and then sent to each of the neurons linked by a synapse to the evolving neuron. [Formula: see text]In the present work, a novel communication strategy among neurons of Spiking Neural [Formula: see text] Systems is proposed. In the resulting models, called Spiking Neural [Formula: see text] Systems with Communication on Request, the spikes are requested from neighboring neurons, depending on the contents of the neuron (still checked by means of a regular expression). Unlike the traditional Spiking Neural [Formula: see text] systems, no spikes are consumed or created: the spikes are only moved along synapses and replicated (when two or more neurons request the contents of the same neuron). [Formula: see text]The Spiking Neural [Formula: see text] Systems with Communication on Request are proved to be computationally universal, that is, equivalent with Turing machines as long as two types of spikes are used. Following this work, further research questions are listed to be open problems.

A control strategy on the computations in a one-catalyst P system is provided: the rules are assumed “colored” and in each step only rules of the same “color” are used. Such control leads to Turing universality for one-catalyst P systems with one membrane. Turing universality is also reached for purely catalytic P systems with two catalysts, and for purely catalytic P systems with only one catalyst and cooperating rules working in the so-called terminal mode.

International audience

The questions whether catalytic P systems with only one catalyst and purely catalytic P systems with only two catalysts can already be computationally complete in the generative case, still are open problems. For accepting P systems or P automata, th

This volume contains a selection of papers presented at the 9th edition of the international conference Bio-Inspired Computing: Theories and Applications, BIC

on the occasion of his 65th birthday.

We introduce and briefly investigate P systems with controlled computations. First, P systems with label restricted transitions are considered (in each step, all rules used have either the same label, or, possibly, the empty label, λ), then P systems with the computations controlled by languages (as in context-free controlled grammars). The relationships between the families of sets of numbers computed by the various classes of controlled P systems are investigated, also comparing them with length sets of languages in Chomsky and Lindenmayer hierarchies (characterizations of the length sets of ET0L and of recursively enumerable languages are obtained in this framework). A series of open problems and research topics are formulated.

This paper continues an investigation into bridging two research areas concerned with natural computing: membrane computing and reaction systems. More specifically, the paper considers a transfer of two assumptions/axioms of reaction systems, non-permanency and the threshold assumption, into the framework of membrane computing. It is proved that: (1) spiking neural P systems with non-permanency of spikes assumption characterize the semilinear sets of numbers, and (2) symport/antiport P systems with threshold assumption (translated as ω multiplicity of objects) can solve SAT in polynomial time. Also, several open research problems are stated.

We bring together two topics recently introduced in membrane computing, the much investigated spiking neural P systems (in short, SN P systems), inspired from the way the neurons communicate through spikes, and the dP systems (distributed P systems, with components which “read” strings from the environment and then cooperate in accepting their concatenation). The goal is to introduce SN dP systems, and to this aim we first introduce SN P systems with the possibility to input, at their request, spikes from the environment; this is done by so-called request rules. A preliminary investigation of the obtained SN dP systems (they can also be called automata) is carried out. As expected, request rules are useful, while the distribution in terms of dP systems can handle languages which cannot be generated by usual SN P systems. We always work with extended SN P systems; the non-extended case, as well as several other natural questions remain open.

A variant of spiking neural P systems with positive or negative weights on synapses is introduced, where the rules of a neuron fire when the potential of that neuron equals a given value. The involved values-weights, firing thresholds, potential consumed by each rule-can be real (computable) numbers, rational numbers, integers, and natural numbers. The power of the obtained systems is investigated. For instance, it is proved that integers (very restricted: 1, -1 for weights, 1 and 2 for firing thresholds, and as parameters in the rules) suffice for computing all Turing computable sets of numbers in both the generative and the accepting modes. When only natural numbers are used, a characterization of the family of semilinear sets of numbers is obtained. It is shown that spiking neural P systems with weights can efficiently solve computationally hard problems in a nondeterministic way. Some open problems and suggestions for further research are formulated.

This is intended to be a quick introduction to membrane computing, a branch of natural computing inspired in the structure and functioning of living cells and in their organization in tissues. The corresponding models, called P systems, are parallel distributed computing devices, handling multisets of abstract objects in a compartmentalized architecture defined by cell-like or tissue-like membrane arrangements.

This paper addresses the problem of removing the polarization of membranes from P systems with active membranes - and this is achieved by allowing the change of membrane labels by means of communication rules or by membrane dividing rules. As consequences of these results, we obtain the universality of P systems with active membranes which are allowed to change the labels of membranes, but do not use polarizations. Universality results are easily obtained also by direct proofs. By direct constructions, we also prove that SAT can be solved in linear time by systems without polarizations and with label changing possibilities. If non-elementary membranes can be divided, then SAT can be solved in linear time without using polarizations and label changing. Several open problems are also formulated.

We consider a combination of P systems with objects described by symbols with P systems with objects described by strings. Namely, we work with multisets of strings and consider as the result of a computation the number of strings in a given output membrane. The strings (also called worms) are processed by replication, splitting, mutation, and recombination; no priority among rules and no other ingredient is used. In these circumstances, it is proved that: (1) P systems of this type can generate all recursively enumerable sets of numbers; and moreover, (2) the Hamiltonian Path Problem in a directed graph can be solved in quadratic time, while the SAT problem can be solved in linear time. The interest of the latter result comes from the fact that it is the first time that a polynomial solution to an NP-complete problem has been obtained in the P system framework without making use of the (non-realistic) operation of membrane division.

A membrane computing system (also called P system) consists of computing cells which are organized hierarchically by the inclusion relation: cells may include cells, which again may include cells, etc. Each cell is enclosed by its membrane. Each cell is an independent computing agent with its own computing program, which produces objects. The interaction between cells consists of the exchange of objects through membranes. The output of a computation is a partially ordered set of objects which leave the system through its external membrane. The fundamental properties of computations in such P systems with external output are investigated. These include the computing power, normal forms, and basic decision problems.

We continue the study of pictorial languages as formalized in Ref. 1 (based on the operations of shifting and superposing elementary pictures). If the pixels are superposed without composing their colors, then we produce only recursive languages. When the colors of the superposed pixels can be composed, then any array grammar can be simulated (hence, all recursively enumerable languages can be obtained). Bidimensional pictorial frameworks with a nonrecursive membership problem are obtained in the restricted case when (1) we do not allow the superposition of nontransparent pixels, excepting the fact that (2) for each color there is a complementary color, which, superposed on the original one, leads to a transparent pixel.

This paper introduces the formal framework of grammar systems to handle a practical and important property of decentralized rule-based knowledge systems. The property is called robustness. In our framework, a rule-based system is robust when some rules can be removed from it and yet its critical functionality remains unchanged. As a theoretical framework for study robustness of decentralized rule-based systems we use grammar systems. We prove within that framework that the question whether a knowledge system is robust or not is undecidable. In contrast, we prove with the same framework that whether or not a component is ever enabled, or whether or not a component working in a special—so called maximal—mode blocks the further functioningof a systems when enabled, are decidable. Some open problems are also formulated.

The P systems were recently introduced as distributed parallel computing models of a biochemical type. Multisets of objects are placed in a hierarchical structure of membranes and they evolve according to given rules, which are applied in a synchronous manner: at each step, all objects which can evolve, from all membranes, must evolve. We consider here the case when this restriction is removed. As expected, unsynchronized systems (even using catalysts) are weaker than the synchronized ones, providing that no priority relation among rules is considered. The power of P systems is not diminished when a priority is used and, moreover, the catalysts can change their states, among two possible states for each catalyst.

In the last years the operation of splicing which models a special type of recombination of genomes has been intensively studied, e.g. the effect of application of splicings to language families of classical formal language theory has been investigated. In this paper we present analogous results with respect to the operations inversion, translocation and duplication which are also descriptions of mutations of genomes.

A formal framework for studying systems made up of a community of agents and their environment is proposed. The suggested model, technically based on the theory of formal grammars and called an eco-grammar system, captures some common features of ecological, economic, social, and collective robotic systems. The article contains an informal presentation as well as the formal definition of the model, presents some properties of variants of eco-grammar systems, and discusses the emergence of important lifelike features such as birth and death. Emphasis is put on results with relevance for artificial life. Some recent developments are also briefly reported.

This paper is an up-to-dated survey of results about the power of controlled extended H systems of various types. Such systems are finite generative devices based on the splicing operation, which, in turn, is a model of the DNA recombination. When no control is imposed on the splicing operation, we get a characterization of regular languages. When a control is considered, we obtain characterizations of recursively enumerable languages. We briefly discuss here H systems with control mechanisms similar to those in regulated rewriting area in formal language theory. We do not present proofs, but only definitions, results, and bibliographical information. Looking for characterizations of families in Chomsky hierarchy other than those of regular and of recursively enumerable languages, we closely investigate the H systems with permitting context conditions. We disprove a conjecture of Chakaravarthy and Krithivasan: such systems of radius one and using only one-sided context conditions can generate all context-free languages (the conjecture was that a characterization of linear languages is obtained). Some open problems are also mentioned.

We investigate here the possibility of approximating a language starting from a partial knowledge of its strings. This is understood as the possibility to read only a bounded part of a string: a prefix or a subword. In this way, indiscernibility rela

In a parallel communicating grammar system, several grammars work together, synchronously, on their own sentential forms, and communicate on request. No restriction is imposed usually about the communicated strings. We consider here two types of rest

Continuing the work begun in [14], we consider contextual grammars (as introduced in [6] with linguistic motivation) with parallel derivations, in which the whole current string participates to a derivation step in the sense that it is splitted into substrings to which contexts are adjoined in a parallel manner. The generative power of such grammars is investigated, when the parallelism is total or partial, and when the selection of contexts is limited to strings in sets of a given type (finite, regular etc.) Then we consider the languages consisting of strings which cannot be further derived (we call them blocking languages). Some open problems are also formulated.

The paper looks for necessary conditions for a language to be generated by a cooperating distributed grammar system with modes = k and ≥ k of derivation. It is proved that the length set of such languages contains infinite arithmetical progressions. Some consequences of this result are derived, concerning the power of these grammars and the closure properties of the corresponding families. Then, one proves that these systems can generate non-semi-linear languages. (Both these questions were formulated as open problems in the field literature.)

The aim of this paper is to elaborate the power of cooperation in generating pictures by array grammars. As it is expected, the generative capacity of cooperating array grammar systems (with a fixed number, with a number greater than a given threshold, or with the maximal number of derivation steps in each component when it is enabled) is strictly greater than that of context-free array grammars. Yet the same result is also obtained in the case of systems with regular components, which contradicts the corresponding result for string grammar systems. In fact, some more results for array grammar systems are obtained which either contradict the results for the corresponding string grammar systems or are not even known for these string grammar systems. Various non-context-free sets of arrays which can be generated in a simple way by cooperating array grammar systems are presented and show the power of the mechanism of cooperation for picture descritpion.

We consider grammar systems in which several components are active at the same moment (a team of components is working). The power of such mechanisms is investigated and it is found that in many cases the team feature increases the generative capacity of grammar systems. In the so-called t-mode of derivation (a team works as much as it can) it is found that the team size does not induce an infinite hierarchy of languages. However, the family obtained in this case is a full abstract family of languages properly including ETOL.