Sergiu Ivanov

• PhD
• Professor (Assistant) at University of Paris-Saclay

This paper offers a comprehensive retrospective on the development and results in the field of insertion-deletion systems over the past 15 years, building upon an earlier foundational overview from 2010. We review key theoretical developments, new extensions, and variations that have emerged, examining their impact on the computational power of ins...

tile assembly model (aTam) is a model of DNA self-assembly. Most of the studies focus on cooperative aTam where a form of synchronization between the tiles is possible. Simulating Turing machines is achievable in this context. Few results and constructions are known for the non-cooperative case (a variant of Wang tilings where assemblies do not nee...

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...

We discuss in this chapter several network modelling methods and their applicability to precision medicine. We review several network centrality methods (degree centrality, closeness centrality, eccentricity centrality, betweenness centrality, and eigenvector‐based prestige) and two systems controllability methods (minimum dominating sets and netwo...

We discuss in this chapter several network modeling methods and their applicability to precision medicine. We review several network centrality methods (degree centrality, closeness centrality, eccentricity centrality, betweenness centrality, and eigenvector-based prestige) and two systems controlability methods (minimum dominating sets and network...

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...

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...

In this paper we consider the model of single insertion-deletion systems that at each step insert or delete a single symbol in a context-free manner (i.e. at any position in the word). The corresponding operation is performed if the word contains a set of permitting (that have to be present in the word) and/or forbidding (that must not be present i...

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...

We discuss in this survey several network modeling methods and their applicability to precision medicine. We review several network centrality methods (degree centrality, closeness centrality, eccentricity centrality, betweenness centrality, and eigenvector-based prestige) and two systems controllability methods (minimum dominating sets and network...

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...

Network controllability is a major challenge in network medicine. The problem is to rewire the molecular network for reprogramming the cell fate. The reprogramming action is considered as a control usually performed once. However, in some cases, a therapy has to follow a time-scheduled drug administration protocol. Furthermore, some diseases are in...

Formal interaction networks are well suited for representing complex biological systems and have been used to model signalling pathways, gene regulatory networks, interaction within ecosystems, etc. In this paper, we introduce Sign Boolean Networks (SBNs), which are a uniform variant of Threshold Boolean Networks (TBFs). We continue the study of th...

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...

Controlling a dynamical system is the ability of changing its configuration arbitrarily through a suitable choice of inputs. It is a very well-studied concept in control theory, with wide-ranging applications in medicine, biology, social sciences and engineering. We introduce in this article the concept of controllability of reaction systems as the...

Formal interaction networks are well suited for representing complex biological systems and have been used to model signalling pathways, gene regulatory networks, interaction within ecosystems, etc. In this paper, we introduce Sign Boolean Networks (SBNs), which are a uniform variant of Threshold Boolean Networks (TBFs). We continue the study of th...

Formal interaction networks are well suited for representing complex biological systems and have been used to model signalling pathways, gene regulatory networks, interaction within ecosystems, etc. In this paper, we introduce Sign Boolean Networks (SBNs), which are a uniform variant of Threshold Boolean Networks (TBFs). We continue the study of th...

Controlling a dynamical system is the ability of changing its configuration arbitrarily through a suitable choice of inputs. It is a very well studied concept in control theory, with wide ranging applications in medicine, biology, social sciences, engineering. We introduce in this article the concept of controllability of reaction systems as the ab...

Discrete modelling frameworks of Biological networks can be divided in two distinct categories: Boolean and multivalued. Although multivalued networks are more expressive for qualifying the regulatory behaviours modelled by more than two values, the ability to automatically convert them to Boolean network with an equivalent behaviour breaks down th...

Discrete modelling frameworks of Biological networks can be divided in two distinct categories: Boolean and Multi-valued. Although Multi-valued networks are more expressive for qualifying the regulatory behaviours modelled by more than two values, the ability to automatically convert them to Boolean network with an equivalent behaviour breaks down...

A major challenge in precision medicine consists in finding the appropriate network rewiring to induce a particular reprogramming of the cell phenotype. The rewiring is caused by specific network action either inhibiting or over-expressing targeted molecules. In some cases, a therapy abides by a time-scheduled drug administration protocol. Furtherm...

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...

Various threshold Boolean networks (TBNs), a formalism used to model different types of biological networks (genes notably), can produce similar dynamics, i.e. share same behaviors. Among them, some are complex (according to Kolmogorov complexity), others not. By computing both structural and behavioral complexities, we show that most TBNs are stru...

Various threshold Boolean automata networks (TBAN), a formalism used to model different types of biological networks (genes notably), can show similar behaviours. Among them, some are complex (according to Kolmogorov complexity), others not. By computing both structural and behavioural complexities, we show that most TBANs are complex, even for sim...

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...

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...

Gene regulatory networks (GRN) are often modeled by Boolean networks to describe their structures and properties. Constraint logic programming (CPL) can be used to infer networks that satisfy constraints applied on their structure and their dynamics. Such approach yield complete satisfiable network sets that can be large. Having such complete sets...

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...

We introduce WEBRSIM, the first web-based simulator for reaction systems. The simulator has an easy-to-use interface where the input is a reaction system and four functionalities: the computation of the interactive process driven by a given context sequence, the behaviour graph of the reaction system, its conservation dependency graph, and all its...

Gene regulatory networks (GRN) are often modeled by Boolean networks to describe their structures and properties. Constraint logic programming (CPL) can be used to infer networks that satisfy constraints applied on their structure and their dynamics. Such approach yield complete satisfiable network sets that can be large. Having such complete sets...

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 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...

SymPy is an open source computer algebra system written in pure Python. It is built with a focus on extensibility and ease of use, through both interactive and programmatic applications. These characteristics have led SymPy to become a popular symbolic library for the scientific Python ecosystem. This paper presents the architecture of SymPy, a des...

SymPy is an open source computer algebra system written in pure Python. It is built with a focus on extensibility and ease of use, through both interactive and programmatic applications. These characteristics have led SymPy to become the standard symbolic library for the scientific Python ecosystem. This paper presents the architecture of SymPy, a...

SymPy is an open source computer algebra system written in pure Python. It is built with a focus on extensibility and ease of use, through both interactive and programmatic applications. These characteristics have led SymPy to become the standard symbolic library for the scientific Python ecosystem. This paper presents the architecture of SymPy, a...

SymPy is an open source computer algebra system written in pure Python. It is built with a focus on extensibility and ease of use, through both interactive and programmatic applications. These characteristics have led SymPy to become the standard symbolic library for the scientific Python ecosystem. This paper presents the architecture of SymPy, a...

SymPy is an open source computer algebra system written in pure Python. It is built with a focus on extensibility and ease of use, through both interactive and programmatic applications. These characteristics have led SymPy to become the standard symbolic library for the scientific Python ecosystem. This paper presents the architecture of SymPy, a...

Reaction systems are a new mathematical formalism inspired by the living cell and driven by only two basic mechanisms: facilitation and inhibition. As a modeling framework, they differ from the traditional approaches based on ODEs and CTMCs in two fundamental aspects: their qualitative character and the non-permanency of resources. In this article...

In this paper we investigate several variants of P automata having infinite runs on finite inputs. By imposing specific conditions on the infinite evolution of the systems, it is easy to find ways for going beyond Turing if we are watching the behavior of the systems on infinite runs. In a similar way, we can assign ω-languages as observer language...

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...

In this article, we consider leftist insertion-deletion systems, in which all rules have contexts on the same side, and may only insert or delete one symbol at a time. We start by introducing extended rules, in which the contexts may be specified as regular expressions, instead of fixed words. We then prove that leftist systems with such extended r...

In this paper we investigate several variants of P automata having infinite runs on finite inputs. By imposing specific conditions on the infinite evolution of the systems, it is easy to find ways for going beyond Turing if we are watching the behavior of the systems on infinite runs. As specific variants we introduce a new halting variant for P au...

In this paper we extend the definition of a multiset by allowing elements to have multiplicities from an arbitrary totally ordered Abelian group instead of only using natural numbers. We consider P systems with such generalized multisets and give well-founded notations for the applicability of rules and for different derivation modes. These new def...

Cette thèse adresse les problèmes d'universalité et de complétude computationelle pour plusieurs modèles de calcul inspirés par la biologie. Il s'agit principalement des systèmes d'insertion/effacement, réseaux de processeurs évolutionnaires, ainsi que des systèmes de réécriture de multi-ensembles. Les résultats décrits se classent dans deux catégo...

Reaction systems is a new mathematical formalism inspired by the biological cell, which focuses on an abstract set-based representation of chemical reactions via facilitation and inhibition. In this article we focus on the property of mass conservation for reaction systems. We show that conservation of sets gives rise to a relation between the spec...

Polymorphic P systems represent a variant of the bio-inspired computational model of P systems, in which the rules are not explicitly given in the description of the system, but are implicitly defined by the contents of certain membranes. In this paper we give a characterisation of the most basic class of such systems, in which only non-cooperative...

This paper investigates the universality problem for Petri nets with inhibitor arcs. Four descriptional complexity parameters are considered: the number of places, transitions, inhibitor arcs, and the maximal degree of a transition. Each of these parameters is aimed to be minimized, a special attention being given to the number of places. Four cons...

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...

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 investigate the problem of construction of small-size universal Petri nets with inhibitor arcs. We consider four descriptional complexity parameters: the number of places, transitions, inhibitor arcs, and the maximal degree of a transition, each of which we try to minimize. We give six constructions having the following values of parameters (lis...

We consider the (one-dimensional) array counterpart of contextual as well as insertion and deletion string grammars and consider the operations of array insertion and deletion in array grammars. First we show that the emptiness problem for P systems with (one-dimensional) insertion rules is undecidable. Then we show computational completeness of P...

In this article we consider insertion-deletion P systems inserting or deleting one symbol in one or two symbol(s) left context (more precisely of size (1,2,0;1,1,0) and (1,1,0;1,2,0)). We show that computational completeness can be achieved by using only 3 membranes in a tree-like structure. Hence we obtain a trade-off between the sizes of contexts...

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...

An important direction in the research of P systems is paving the way to modelling real-world biological structures. Clock-free P systems represent an attempt at bringing the P formalism closer to biological origins by eliminating global synchronization, the global clock. The goal of this paper is to provide a formalization of clock-free P systems...

While originally P systems were defined to contain multiset rewriting rules, it turned out that considering different types of rules may produce important results, such as increasing the computational power of the rules. This paper focuses on factoring out the concept of a membrane structure out of various P system models with the goal of providing...

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...

In this article we introduce the operations of insertion and deletion working in a random-context and semi-conditional manner. We show that the conditional use of rules strictly increase the computational power. In the case of semi-conditional insertion-deletion systems context-free insertion and deletion rules of one symbol are sufficient to get t...

Clock-free P systems are an almost completely asynchronous model of P systems in which each rule application lasts for a different time. This makes the processes in this model more similar to the chemical processes in the biological cell, but also poses similar design problems as in concurrent programming. In this paper an attempt is made to solve...

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...

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...

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.

The aim of this paper is to study the family of languages generated by the transitional membrane systems without cooperation and without additional ingredients. The fundamental nature of these basic systems makes it possible to also define the corresponding family of languages in terms of derivation trees of context-free grammars. We also compare t...