Artiom Alhazov

Academy of Sciences of Moldova | ASM · Institute of Mathematics and Computer Science

It is known that the satisfiability problem (SAT) can be solved with a semi-uniform family of deterministic polarizationless P systems with active membranes with non–elementary membrane division. We present a double improvement of this result by showing that the satisfia-bility of a quantified Boolean formula (QSAT) can be solved by a uniform famil...

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 allo...

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 w...

P systems are parallel molecular computing models based on processing multisets of objects in cell-like membrane structures. Recently, Petr Sosík has shown that a semi-uniform family of P systems with active membranes and 2-division is able to solve the PSPACE-complete problem QBF-SAT in linear time; he has also conjectured that the membrane dissol...

The P systems (or membrane systems) are a class of distributed parallel computing devices of a biochemical type, where membrane division is the frequently investigated way for obtaining an exponential working space in a linear time, and on this basis solving hard problems, typically NP-complete problems, in polynomial (often, linear) time. In this...

Inspired by the programming game Core Wars, we propose in this work a framework and the organization of king of the hill-style tournaments between P systems. We call these tournaments Queens of the Hill and the individual contestants valkyries. The goal of each valkyrie is to dissolve as many membranes of as many other valkyries as possible, while...

Membranes are one of the key concepts in P systems and membrane computing, and a lot of research activities focus on their properties and possible extensions: membrane division, membrane dissolution, mobile membranes, etc. In this work, we explore the possibility of using membranes for thinking about the emergence of milieu separations at the origi...

Reaction systems are a model of computing aiming to formalize biochemistry by capturing the qualitative relations between the species, and explicitly discarding any accounts of multiplicity. From the point of view of the formal language theory, this situates them in the realm of set rewriting. In this work, we propose a series of extensions of reac...

A Boolean network is a discrete dynamical system operating on vectors of Boolean variables. The action of a Boolean network can be conveniently expressed as a system of Boolean update functions, computing the new values for each component of the Boolean vector as a function of the other components. Boolean networks are widely used in modelling biol...

P systems with active membranes are a variant of P systems where membranes can be created by division of existing membranes, thus creating an exponential amount of resources in a polynomial number of steps. Time and space complexity classes for active membrane systems have been introduced, to characterize classes of problems that can be solved by d...

Membrane computing and P systems are a paradigm of massively parallel natural computing introduced by Gheorghe P\u{a}un in 1999, inspired by the structure of the living cell and by its biochemical reactions. In spite of this explicit biological motivation, P systems have not been extensively used in modelling real-world systems. To confirm this int...

We consider tissue P systems working on vesicles of multisets with the very simple operations of insertion, deletion, and substitution of single objects. With the whole multiset being enclosed in a vesicle, sending it to a target cell can be indicated in those simple rules working on the multiset. As derivation modes we consider the sequential deri...

Catalytic P systems and purely catalytic P systems are among the first variants of membrane systems ever considered in this area. These variants of systems also feature some prominent computational complexity questions, and in particular the problem if only one catalyst in catalytic P systems and two catalysts in purely catalytic P systems are enou...

In this paper we consider prescribed sets of rules working on several objects either in parallel – in this case the rules have to take different objects – or else sequentially in any order – in this case several rules may take the same object to work on. We show that prescribed teams of size two, i.e., containing exactly two rules, are sufficient...

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 add...

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 in the whole system: is one catalyst enough to allow for generating all recursively enumerable sets of mu...

We extend and refine previous results within the general framework for regulated rewriting based on the applicability of rules in sequential grammars [3]. Besides the well-known control mechanisms as control graphs, matrices, permitting and forbidden rules, partial order on rules, and priority relations on rules we also consider the new variant of...

The first definition of space complexity for P systems was based on a hypothetical real implementation by means of biochemical materials, and thus it assumes that every single object or membrane requires some constant physical space. This is equivalent to using a unary encoding to represent multiplicities for each object and membrane. A different a...

P systems are a model of compartmentalized multiset rewriting inspired by the structure of living cells and the way they function. In this paper, we focus of a variant in P systems in which membranes have limited capacity, i.e., the number of objects they may hold is limited by a fixed bound. This feature corresponds to an important physical proper...

Spiking neural P systems are a class of distributed parallel computing models, inspired by the way in which neurons process information and communicate with each other by means of spikes. In 2007, Freund and Verlan developed a formal framework for P systems to capture most of the essential features of P systems and to define their functioning in a...

Asynchronous tissue P systems with symport/antiport rules are a class of parallel computing models inspired by cell tissue working in a non-synchronized way, where the use of rules is not obligatory, that is, at a computation step, an enabled rule may or may not be applied. In this work, the notion of local synchronization is introduced at three le...

We introduce new possibilities to control the application of rules based on the preceding applications, which can be defined in a general way for (hierarchical) P systems and the main known derivation modes. Computational completeness can be obtained even with non-cooperative rules and using both activation and blocking of rules, especially for the...

We consider tissue P systems working in the sequential mode on vesicles of multisets with the very simple operations of insertion, deletion, and substitution of single objects. In a computation step, one rule is to be applied if possible, and then, in any case, the whole multiset being enclosed in a vesicle moves to one of the cells as indicated by...

Spiking neural P systems (SN P systems) are a class of parallel computing models, inspired by the way in which neurons process information and communicate to each other by means of spikes. In this work, we consider a variant of SN P systems, SN P systems with polarizations (PSN P systems), where the integrate-and-fire conditions are associated with...

In the majority of models of P systems, rules are applied at the ticks of a global clock and their products are introduced into the system for the following step. In timed P systems, different integer durations are statically assigned to rules; time-free P systems are P systems yielding the same languages independently of these durations. In clock-...

P systems are a model of distributed and compartmentalized multiset rewriting, complete with various signal transmission mechanisms. We introduce a novel kind of P systems in which rules are dynamically constructed in each step by non-deterministic pairing of left-hand and right-hand sides. We define three variants of right-hand side randomization...

We consider extended spiking neural P systems with the additional possibility of so-called “white hole rules”, which send the complete contents of a neuron to other neurons, and we prove that this extension of the original model can easily simulate register machines. Based on this proof, we then define red–green variants of these extended spiking n...

A k-counter machine (CM(k)) is an automaton with k counters as an auxiliary memory. It is known that CM(k) are universal for \(k\ge 2\). As shown by Morita reversible CM(2) are universal. Based on results from Korec we construct four small universal reversible counter machines highlighting different trade-offs: (10, 109, 129), (11, 227, 270), (9, 9...

We introduce several variants of input-driven tissue P automata – we also will call them chocolate automata – where the rules to be applied only depend on the input symbol. Both strings and multisets are considered as input objects; the strings are either read from an input tape or defined by the sequence of symbols taken in, and the multisets are...

The objective of this work is to present concrete membrane systems generating non-semilinear sets that are small in the following sense: Attention is paid to such parameters of descriptional complexity as the alphabet size, the number of rules, the total number of inhibitors used, and the maximal rule size. A total of 54 systems is described, depen...

We consider tissue P systems working on vesicles of multisets with the very simple operations of insertion, deletion, and substitution of single objects. With the whole multiset being enclosed in a vesicle, sending it to a target cell can be indicated in those simple rules working on the multiset. As derivation modes we consider the sequential mode...

We show multiple ways of how to simulate R systems by non-cooperative P systems with atomic control by promoters and/or inhibitors, or with matter/antimatter annihilation rules, with a slowdown by a constant factor only. The descriptional complexity of the simulating P systems is also linear with respect to that of the simulated R system. All const...

We further investigate the computing power of the recently introduced P systems with \(\mathbb Z\)-multisets (also known as hybrid sets) as generative devices. These systems apply catalytic rules in the maximally parallel way, even consuming absent non-catalysts, thus effectively generating vectors of arbitrary (not just non-negative) integers. The...

In P systems working in the set derivation mode, even in the maximally parallel derivation mode, rules are only applied in at most one copy in each derivation step. We also consider the set mode in the cases of taking those sets of rules with the maximal number of applicable rules or with affecting the maximal number of objects. For many variants o...

A hybrid network of evolutionary processors (HNEP) is a graph where each node is associated with a special rewriting system called an evolutionary processor, an input filter, and an output filter. Each evolutionary processor is given a finite set of one type of point mutations (insertion, deletion or a substitution of a symbol) which can be applied...

We consider d-dimensional contextual array grammars and investigate their computational power when using various control mechanisms – matrices, regular control languages, and tissue P systems, which work like regular control languages, but may end up with a final check for the non-applicability of some rules. For d≥2, d-dimensional contextual array...

This paper is an overview of authors' results in solving word formation problem for Romanian. Generalized formal models for inflexion and affixation are discussed. Two different approaches of their application are presented: a classical one based on specific grammars, and a bio-molecular one using membrane systems.

This is an introductory paper of fresh started research that concerns the development of new HPC parallelization strategies based on intrinsically parallel unconventional computation paradigms. The main goal of this research is to use theses developed parallelization technologies for overcoming modern HPC energy consumption issues. Development of n...

We continue the line of research of deterministic parallel non-cooperative multiset rewriting with control. We here generalize control, i.e., rule applicability context conditions, from promoters and inhibitors, which are checking presence or absence of certain objects up to some bound, to regular and even stronger predicates, focusing on predicate...

The aim of this paper is to study the computational power of P systems with one active membrane without polarizations. For P systems with active membranes, it is known that computational completeness can be obtained with either of the following combinations of features: (i) two polarizations, (ii) membrane creation and dissolution, (iii) four membr...

We present a number of tiny P systems generating or accepting nonsemilinear sets of (vectors of) natural numbers with very small numbers of rules, even for 1, 2, 3, 4, and 5 rules, depending on the particular model and the additional features used in these systems. Among the models we consider are P systems with target agreement and target selectio...

Computational completeness is known for P systems with two catalysts and purely catalytic P systems with three catalysts as well as for P systems with one bi-stable catalyst. We complete this picture by showing computational completeness for purely catalytic P systems with one bi-stable catalyst and one catalyst. Moreover, we present some concrete...

In this paper, we consider recognizer P systems with antimatter and the influence of the matter/antimatter annihilation rules having weak priority over all the other rules or not. We first provide a uniform family of P systems with active membranes which solves the strongly NP-complete problem SAT, the Satisfiability Problem, without polarizations...

In this paper we overview several universal universality constructions for different type of devices based on (circular) string rewriting, multiset rewriting and splicing operations. We consider systems that have relatively small description and that are or can be effectively used for subsequent constructions of (small) universal devices.

The concept of a matter object being annihilated when meeting its corresponding anti-matter object is investigated in the context of membrane systems, i.e., of (distributed) multiset rewriting systems applying rules in the maximally parallel way. Computational completeness can be obtained with using only non-cooperative rules besides these matter/a...

We introduce the new concept of toxic objects, objects that must not stay idle as otherwise the computation is abandoned without yielding a result. P systems of many kinds using toxic objects allow for smaller descriptional complexity, especially for smaller numbers of rules, as trap rules can be avoided. Besides presenting a number of tiny P syste...

The concept of a matter object being annihilated when meeting its corresponding anti-matter object is investigated in the context of P systems. Computational completeness can be obtained with using only non-cooperative rules besides these matter/anti-matter annihilation rules if these annihilation rules have priority over the other rules. Without t...

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. Since recently, it is known that the power of the deterministic subclass of such systems is subregular. We present ne...

This work presents a hybrid model of high performance computations, representing the P system framework with additional quantum functionalities. This model is supposed to take advantages of both biomolecular and quantum paradigms and to overcome some of their inherent limitations. We extend a recently proposed formal model of interface between a me...

We consider purely catalytic P systems with two catalysts together with promoters and inhibitors on the rules. We show that computational completeness can be achieved in a deterministic way by using atomic promoters or sets of atomic inhibitors. By using atomic inhibitors computational completeness is achieved only with a non-deterministic construc...

A hybrid network of evolutionary processors (HNEP) is a graph where each node is associated with a special rewriting system called an evolutionary processor, an input filter, and an output filter. Each evolutionary processor is given a finite set of one type of point mutations (insertion, deletion or a substitution of a symbol) which can be applied...

This work presents a hybrid model of high perfomance computations. The model is based on membrane system (P system) where some membranes may contain quantum device that is triggered by the data entering the membrane. This model is supposed to take advantages of both biomolecular and quantum paradigms and to overcome some of their inherent limitatio...

In this paper, we examine P systems with a linear membrane structure, i.e., P systems in which only one membrane is elementary and the output of which is read out as the sequence of membrane labels in the halting configuration or vectors/numbers represented by this sequence. We investigate the computational power of such systems, depending on the n...

It is well known that the polynomial complexity class of recognizer P systems with active membranes without polarizations, without dissolution and with division for elementary and non-elementary membranes is exactly the complexity class P (see [9], Theorem 2). In this paper, we prove that if such a P systems model is endowed with antimatter and ann...

We take a recently introduced model of obligatory hybrid networks of evolutionary processors (OHNEPs), and consider the case of a complete underlying graph and the nodes having only one operation per node. A HNEP is a distributed parallel string processing system, where each node may be equipped with some elementary operations (one-symbol insertion...

One of the concepts that lie at the basis of membrane computing is the multiset rewriting rule. On the other hand, the paradigm of rules is profusely used in computer science for representing and dealing with knowledge. Therefore, establishing a “bridge” between these domains is important, for instance, by designing P systems reproducing the modus...

This paper describes membrane computational models parsing affixed Romanian words with prefixes, suffixes, terminations, alterations in the root, and continues previous works on word derivation mod-eling. An algorithm for Romanian affixes extraction is given, and several models of P systems are proposed.

This paper describes membrane computational models parsing affixed Romanian words with prefixes, suffixes, terminations, and alterations in the root. An algorithm for Romanian affixes extraction is given, and several models of P systems are proposed.

We investigate the computational power of energy-based P systems, a model of membrane systems, where a fixed amount of energy is associated with each object and the rules transform single objects by adding or removing energy from them. We answer the recently proposed open questions about the power of such systems without priorities associated with...

Membrane systems with symbol objects are formal models of distributed parallel multiset processing. Symport rules move multiple objects to a neighbouring region. It is known that for P systems with symport rules of weight at most 3 and a single membrane, seven superfluous symbols are enough for computational completeness, and one is necessary. We p...

Networks of evolutionary processors (NEPs) are distributed word rewriting systems typically viewed as language generators. Each node contains a set of words, a set of operations (typically insertion, deletion or rewriting of one symbol with another one), an input filter and an output filter. The purpose of this paper is to overview existing models...

We prove that arbitrary single-tape Turing machines can be simulated by uniform families of P systems with active membranes with a cubic slowdown and quadratic space overhead. This result is the culmination of a series of previous partial results, finally establishing the equivalence (up to a polynomial) of many space complexity classes defined in...

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...

In this article we introduce the regulating mechanism of control languages for the application of rules assigned to the membranes of a sequential P system and the variant of time-varying sets of rules available at different transition steps. Computational completeness can only be achieved when allowing the system to have no rules applicable for a b...

In this paper we consider universal systems based on splicing. As in previous works, we take the number of rules as the parameter for the descriptional complexity. We present three results: universal double splicing extended H system with 5 rules, universal splicing test tube system with 8 rules and a universal splicing P system with 5 rules.

Alan Turing began a new area in science; he discovered that there are universal computers, which in principal are very simple. Up to now this is the basis of a modern computing theory and practice. In the paper one considers Turing computability in the frame of P (membrane) systems and other distributive systems. An overview of the recent results a...

In this paper we study a notion of self-stabilization, inspired from biology and engineering. Multiple variants of formalization of this notion are considered, and we discuss how such properties affect the computational power of multiset rewriting systems.

In this paper we define a general class of P systems covering some biological operations with membranes, including evolution, communication, 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 o...

We study reversibility and determinism aspects and the strong versions of these properties of sequential multiset processing systems and of maximally parallel systems, from the computability point of view. In the sequential case, syntactic criteria are established for both strong determinism and strong reversibility. In the parallel case, a criteri...

A reversible logic element is a primitive from which reversible computing systems can be constructed. A rotary element is a typical one with 1-bit memory (hence it has 2 states) and with 4 input/output symbols. It is known that we can construct any reversible Turing machine by using only rotary elements very simply. In this sense it is a universal...

We show that exponential-space P systems with active membranes charac-terize the complexity class EXPSPACE. This result is proved by simulating Turing machines working in exponential space via uniform families of P systems with restricted elementary active membranes; the simulation is efficient, in the sense that the time and space required are at...

One of the concepts that lie at the basis of membrane computing is the multiset rewriting rule. On the other hand, the paradigm of rules is profusely used in computer science for representing and dealing with knowledge. Therefore, establishing a “bridge” between these domains is important, for instance, by designing P systems reproducing the modus...

We consider the problem of construction of small universal devices based on splicing. Our descriptional complexity measure will be the number of rules present in the system. We present two universal time-varying distributed H systems: of degree 2 with 15 rules and of degree 1 with 17 rules, and also three universal splicing test tube systems with 3...

The goal of this survey is to overview some important properties of membrane systems that are referred to as “promising” or dynamic. It is sometimes quite desirable to achieve them, although they are mostly undecidable. We summarize how some of these properties affect the computational power or the descriptional complexity of membrane systems. A nu...

This paper focuses on P systems with one-symbol insertion and deletion without contexts. The main aim of this paper is to consider the operations applied at the ends of the string, and prove the computational completeness in case of priority of deletion over insertion. This result presents interest since the strings are controlled by a tree structu...

In this paper we consider complete obligatory hybrid networks of evolutionary processors (OHNEPs) with insertion and deletion operations (without substitution). Such networks are not computationally complete and we modify the notion of obligatory operation introduced in [1] in order to reach universality. We use very simple evolutionary processors...

On the one hand, one of the concepts which lies at the basis of membrane computing is the multiset rewriting rule. On the other hand, the paradigm of rules is profusely used in computer science for representing and dealing with knowledge. Therefore, it makes much scene to establish a ”bridge ” between these domains, for instance, by designing P sys...

In this paper, we consider insertion–deletion P systems with priority of deletion over insertion. We show that such systems with one-symbol context-free insertion and deletion rules are able to generate Parikh sets of all recursively enumerable languages (PsRE). If a one-symbol one-sided context is added to the insertion or deletion rules, then all...

It is known that insertion-deletion (P) systems with two symbols context-free insertion and deletion rules are not computationally complete. It is thus interesting to consider conditions that would allow such systems to reach computational completeness. In this paper we consider insertion-deletion P systems with insertion and deletion operations ap...

Membrane computing is a formal framework of distributed parallel computing. In this paper we introduce a variant of the multiset rewriting model where the rules of every region are defined by the contents of interior regions, rather than being explicitly specified in the description of the system. This idea is inspired by the von Neumann’s concept...

In this article we present a universal splicing P system with 6 rules. Thus we improve the previous result that used 8 rules and lower the possible value for the boundary between the universality and non-universality for such systems.

One of the concepts that lie at the basis of membrane computing is the multiset rewriting rule. On the other hand, the paradigm of rules is profusely used in computer science for representing and dealing with knowledge. Therefore, establishing a “bridge” between these domains is important, for instance, by designing P systems reproducing the modus...

The focus of this paper is the family of languages generated by transitional non-cooperative P systems without further ingredients. This family can also be defined by so-called time yields of derivation trees of context-free grammars. In this paper we prove that such languages can be parsed in polynomial time, where the degree of polynomial may dep...

We describe the investigations on natural computing in the Institute of Mathematics and Computer Science of the Academy of Sciences of Moldova during last fifteen years. Most of these investigations are inspired by results and ideas belonging to Corresponding Member of the Romanian Academy Gheorghe Paun.

It is known that the satisfiability problem ({\tt SAT}) can be efficiently solved by a uniform family of P systems with active membranes with two polarizations working in a maximally parallel way. We study P systems with active membranes without non-elementary membrane division, working in minimally parallel way. The main question we address is wha...