Claudio Zandron's research while affiliated with Università degli Studi di Milano-Bicocca and other places
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Publications (133)
A variant of membrane computing models called Spiking Neural P systems (SNP systems) closely mimics the structure and behavior of biological neurons. As third-generation neural networks, SNP systems have flexible architectures allowing the design of bio-inspired machine learning algorithms. This paper proposes Modular Spiking Neural P (MSNP) system...
Water-based computing emerged as a branch of membrane computing in which water tanks act as permeable membranes connected via pipes. Valves residing at the pipes control the flow of water in terms of processing rules. Resulting water tank systems provide a promising platform for exploration and for case studies of information processing by flow of...
In rewriting P systems, that is P systems using structured strings instead of atomic symbols, rules can be applied in parallel on all strings, but a single rule at a time can be applied on each string. Nonetheless, parallel application of rules also on each string has been considered in various works. This leads to possible application of rules wit...
Inferring the structure and operation of a computing model, given some observations of its behavior, is in general a desirable but daunting task. In this paper we try to solve a constrained version of this problem. We consider a P system Π with active membranes and using cooperative rewriting, communication, and division rules and a collection of p...
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...
Spiking neural P systems are parallel and distributed computation devices which are inspired by the neuro-physiological behavior of biological neurons. In this paper we will present, with a tutorial approach, the main underlying ideas and the most interesting variants that have been proposed in the literature. In particular, we will discuss the res...
Spiking neural membrane systems are models of computation inspired by the natural functioning of the brain using the concepts of neurons and synapses, and represent a way of building computational systems of a biological inspiration. A variant of such a model, allowing to create new neurons and synapses during the computation, has been considered i...
P-Systems are abstract machines inspired to the behaviour of cells which we can see like simple biological processing unit. Many types of P-System have been developed considering different aspects of the cells working principles, obtaining different computational models. In this paper we introduce Active P-Colonies (APC), a variant of the model P-C...
Among the computational ingredients that determine the computing power of polarizationless P systems with active membranes, the depth of the membrane hierarchy is one of the least explored. It is known that this model of P systems can solve -complete problems when no constraints are given on the depth of the membrane hierarchy, whereas the complexi...
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...
This book constitutes the refereed post-conference proceedings of the 20th International Conference on Membrane Computing, CMC 2020, held as a virtual event, in September 2020.
The 10 full papers presented were selected from 31 submissions. The papers deal with all aspects on membrane computing and related areas.
This book constitutes the proceedings of the 15th International Conference on Language and Automata Theory and Applications, LATA 2021, held in Milan, Italy, in March 2021.
The 26 full papers presented in this volume were carefully reviewed and selected from 52 submissions. They were organized in topical sections named: algebraic structures; automa...
Many variants of P systems with active membranes are able to solve traditionally intractable problems. Sometimes they also characterize well known complexity classes, depending upon the computational features they use. In this paper we continue the investigation of the importance of (minimal) cooperative rules to increase the computational power of...
It is known that the polarizationless P systems of the kind involved in the definition of the P conjecture are able to solve problems in the complexity class \(\textsf {P}\) by leveraging their uniformity condition. Here, we show that they are indeed able to simulate a deterministic Turing machine working in polynomial time with a weaker uniformity...
P systems with active membranes have been widely used to attack problems in \({\mathbf{NP}}\) or even in \({{\mathbf{PSPACE }}}\); in general, an exponential amount of space is generated in polynomial time by dividing existing membranes. Natural questions arise in this framework, concerning the power of P systems when different bounds are considere...
Uniform families of shallow P systems with active membranes and charges are known to characterize the complexity class \(\textsc {P}^{\#\textsf {P}}\), since this kind of P systems are able to “count” the number of objects sent out by the dividing membranes. Such a power is absent in monodirectional systems, where no send-in rules are allowed: in t...
In P systems with active membranes, the question of understanding the power of non-confluence within a polynomial time bound is still an open problem. It is known that, for shallow P systems, that is, with only one level of nesting, non-confluence allows them to solve conjecturally harder problems than confluent P systems, thus reaching \(\mathbf{P...
In P systems with active membranes, the question of understanding the power of non-confluence within a polynomial time bound is still an open problem. It is known that, for shallow P systems, that is, with only one level of nesting, non-confluence allows them to solve conjecturally harder problems than confluent P systems, thus reaching PSPACE. Her...
Among Open image in new window -complete problems, QSAT, or quantified SAT, is one of the most used to show that the class of problems solvable in polynomial time by families of a given variant of P systems includes the whole Open image in new window . However, most solutions require a membrane nesting depth that is linear with respect to the numbe...
It is well known that the kind of P systems involved in the definition of the P conjecture is able to solve problems in the complexity class $\mathbf{P}$ by leveraging the uniformity condition. Here we show that these systems are indeed able to simulate deterministic Turing machines working in polynomial time with a weaker uniformity condition and...
This book constitutes revised selected papers from the 19th International Conference on Membrane Computing (CMC19), CMC 2018, which was held in Dresden, Germany, in September 2018.
The 15 papers presented in this volume were carefully reviewed and selected from 20 submissions. The contributions aim to abstract computing ideas and models from the s...
P systems with active membranes are a variant of P systems where membranes play an active role during the computation, for example by dividing existing membranes in order to create new ones. In this way, an exponential number of membranes can be obtained in polynomial time, and then used in parallel to attack computationally hard problems. Many int...
The literature on membrane computing describes several variants of P systems whose complexity classes C are “closed under exponentiation” that is, they satisfy the inclusion [Figure presented], where [Figure presented] is the class of problems solved by polynomial-time Turing machines with oracles for problems in C. This closure automatically impli...
We present some high-level open problems in the complexity theory of membrane systems, related to the actual computing power of confluence vs determinism, semi-uniformity vs uniformity, deep vs shallow membrane structures, membrane division vs internal evolution of membranes. For each of these problems we present some reasonable approaches that are...
Traditionally, P systems allow their membranes or cells to grow exponentially (or even more) in volume with respect to the size of the multiset of objects they contain in the initial configuration. This behaviour is, in general, biologically unrealistic, since large cells tend to divide in order to maintain a suitably large surface-area-to-volume r...
We analyse the computational efficiency of tissue P systems, a biologically-inspired computing device modelling the communication between cells. In particular, we focus on tissue P systems with fission rules (cell division and/or cell separation), where the number of cells can increase exponentially during the computation. We prove that the complex...
We give a characterisation of the class of problems solved in polynomial time by uniform and semi-uniform families of P systems with active membranes, using matter/antimatter annihilation rules and elementary membrane division. Like several other variants of P systems with elementary division, this class is exactly , that is, the problems solvable...
We show that recogniser P systems with active membranes can be augmented with a priority over their set of rules and any number of membrane charges without loss of generality, as they can be simulated by standard P systems with active membranes, in particular using only two charges. Furthermore, we show that more general accepting conditions, such...
We prove that non-confluent (i.e., strongly nondeterministic) P systems with active membranes working in polynomial time are able to simulate polynomial-space nondeterministic Turing machines, and thus to solve all \({\mathbf{PSPACE }}\) problems. Unlike the confluent case, this result holds for shallow P systems. In particular, depth 1 (i.e., only...
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...
This book contains revised selected papers from the 17th International Conference on Membrane Computing, CMC 2017, held in Milan, Italy, in July 2016.
The 19 full papers presented in this volume were carefully reviewed and selected from 28 submissions. They deal with membrane computing (P systems theory), an area of copmputer science aiming to abs...
We investigate the influence that the flow of information in membrane systems has on their computational complexity. In particular, we analyse the behaviour of P systems with active membranes where communication only happens from a membrane towards its parent, and never in the opposite direction. We prove that these “monodirectional P systems” are,...
It has been recently proved that polynomial-time tissue P systems with cell division are only able to solve decision problems in the complexity class P when their cell structure is embedded into the Euclidean space Rd, for d ∈ N. In this paper we show that if the space has an appropriate shape and is polynomial-time navigable (but not embeddable in...
We prove that polynomial-time tissue P systems with cell division or cell separation can be simulated efficiently by Turing machines with oracles for counting problems. This shows that the corresponding complexity classes are included in \(\mathbf{P }^{\varvec{\#}\mathbf{P }}\), thus improving, under standard complexity theory assumptions, the prev...
Membrane systems, also called P systems, are an interesting class of parallel and distributed models of computation inspired
by cell biology. They have been thoroughly investigated in the literature, both from the theoretical standpoint—analysing
their computing power and efficiency—and as tools to model natural phenomena. In this article, we focus...
The computational power of membrane systems, in their different variants, can be studied by defining classes of problems that can be solved within given bounds on computation time or space, and comparing them with usual computational complexity classes related to the Turing Machine model. Here we will consider in particular membrane systems with ac...
This book constitutes revised selected papers from the International Conference on Membrane Computing, CMC 2015, held in Valencia, Spain, in August 2015.
The 22 full papers presented in this volume were carefully reviewed and selected from 34 submissions. The volume also contains 3 invited talks in full-paper length.
Polynomial-time P systems with active membranes characterise PSPACE by exploiting membranes nested to a polynomial depth, which may be subject to membrane division rules. When only elementary (leaf) membrane division rules are allowed, the computing power decreases to P-PP = P-#P, the class of problems solvable in polynomial time by deterministic T...
The decision problems solved in polynomial time by P systems with elementary active membranes are known to include the class \(\mathbf{P}^{\# \mathbf{P}}\). This consists of all the problems solved by polynomial-time deterministic Turing machines with polynomial-time counting oracles. In this paper we prove the reverse inclusion by simulating P sys...
P systems with active membranes are a variant of P systems where the membranes can be created during the computation by division of existing ones. Using this feature, one can create an exponential number of membranes in a polynomial time, and use them in parallel to solve computationally hard problems, such as problems in \(\mathbf{NP }\) or even i...
P systems are a computational model inspired by the functioning of the cell and based upon the notion of cellular membrane. We show how different features of P systems with active membranes, a variant of the basic model where membranes can be multiplied by division, can be used to approach various problems in computation theory.
P systems with active membranes have the ability of solving computationally hard problems. In this paper, the authors prove that uniform families of P systems with active membranes operating in polynomial time can solve the whole class of PP decision problems, without using nonelementary membrane division or dissolution rules. This result also hold...
We prove that all-parallel enzymatic numerical P systems whose production functions can be expressed as a combination of sums, differences, products and integer divisions characterise PSPACE when working in polynomial time. We also show that, when only sums and differences are available, exactly the problems in P can be solved in polynomial time. T...
We show that a constant amount of space is sufficient to simulate a polynomial-space bounded Turing machine by P systems with active membranes. We thus obtain a new characterisation of PSPACE, which raises interesting questions about the definition of space complexity for P systems. We then propose an alternative definition, where the size of the a...
For many models of P systems and tissue P systems, the main behavior of a specific system can be simulated by a corresponding system with only one membrane or cell, respectively; this effective construction is called flattening. In this paper we describe the main procedure of flattening for specific variants of static (tissue) P systems as well as...
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...
We improve previously known universality results on enzymatic numerical P systems (EN P systems, for short) working in all-parallel and one-parallel modes. By using a flattening technique, we first show that any EN P system working in one of these modes can be simulated by an equivalent one-membrane EN P system working in the same mode. Then we sho...
We introduce a weak uniformity condition for families of P systems, DLOGTIME uniformity, inspired by Boolean circuit complexity. We then prove that DLOGTIME-uniform families of P systems with active membranes working in logarithmic space (not counting their input) can simulate logarithmic-space deterministic Turing machines.
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...
We prove that recognizer P systems with active membranes using polynomial space characterize the complexity class PSPACE. This result holds for both confluent and nonconfluent systems, and independently of the use of membrane division rules.
We show how existing P systems with active membranes can be used as modules inside a larger P system; this allows us to simulate subroutines or oracles. As an application of this construction, which is (in principle) quite general, we provide a new, improved lower bound to the complexity class PMC
\(_{\mathcal{AM}(-{\rm d},-{\rm n})}\) of problems...
We prove that uniform families of P systems with active membranes operating in polynomial time can solve the whole class of PP decision problems, without using nonelementary membrane division or dissolution rules. This result also holds for families having a stricter uniformity condition than the usual one. 1
We consider recognizer P systems having three polarizations associated to the membranes, and we show that they are able to
solve the PSPACE-complete problem Quantified 3SAT when working in polynomial space and exponential time. The solution is uniform (all the instances of a fixed size are solved
by the same P system) and uses only communication ru...
We prove that a uniform family of P systems with active membranes, where division rules only operate on elementary membranes
and dissolution rules are avoided, can be used to solve the following PP-complete decision problem in polynomial time: given a Boolean formula of m variables in 3CNF, do at least Ö{2m}\sqrt{2^m} among the 2
m
possible truth a...
We prove that uniform and semi-uniform families of P systems with active membranes using only communication and nonelementary
division rules are not computationally universal. However, they are powerful enough to solve exactly the problems solvable
by Turing machines operating in time and space that are ”tetrational” (i.e., bounded by a stack of ex...
Within the framework of membrane systems, distributed parallel computing models inspired by the functioning of the living
cell, various computational complexity classes have been defined, which can be compared against the computational complexity
classes defined for Turing machines. Here some issues and results concerning computational complexity...
We describe a solution to the SAT problem via non-confluent P systems with active membranes, without using membrane division rules. Furthermore, we provide an algorithm for simulating such devices on a nondeterministic Turing machine with a polynomial slowdown. Together, these results prove that the complexity class of problems solvable non-conflue...
We show that a deterministic single-tape Turing machine, operating in polynomial space with respect to the input length, can
be efficiently simulated (both in terms of time and space) by a semi-uniform family of Psystems with active membranes and
three polarizations, using only communication rules. Then, basing upon this simulation, we prove that a...
We identify a family of decision problems that are hard for some complexity classes defined in terms of P systems with active membranes working in polynomial time. Furthermore, we prove the completeness of these problems in the case where the systems are equipped with a form of priority that linearly orders their rules. Finally, we highlight some p...
We investigate polarizationless P systems with active membranes working in maximally parallel manner, which do not make use
of evolution or communication rules, in order to find which features are sufficient to efficiently solve computationally hard
problems. We show that such systems are able to solve the PSPACE-complete problem Quantified 3-sat,...
We consider the structure of the intestinal epithelial tissue and of cell–cell junctions as the biological model inspiring a new class of P systems. First we define the concept of cell polarity, a formal property derived from epithelial cells, which present morphologically and functionally distinct regions of the plasma membrane. Then we show two p...
We continue the investigations concerning the possibility of using spiking neural P systems as a framework for solving computationally
hard problems, addressing two problems which were already recently considered in this respect: SubsetSum{\tt Subset}\,{\tt Sum} and SAT.{\tt SAT}. For both of them we provide uniform constructions of standard spikin...
We define space complexity classes in the framework of membrane com-puting, giving some initial results about their mutual relations and their connection with time complexity classes, and identifying some potentially interesting problems which require further research.
Energy plays an important role in many theoretical computational models. In this paper we review some results we have obtained in the last few years concerning the computational power of two variants of P systems that manipulate energy while performing their computations: energy-based and UREM P systems. In the former, a fixed amount of energy is a...
We introduce Genetic Systems, a formalism inspired by genetic regulatory networks and suitable for modeling the interactions between the genes and the proteins, acting as regulatory products.The generation of new objects, representing proteins, is driven by genetic gates: a new object is produced when all the activator objects are available in the...
In this paper we study some computational properties of spiking neural P systems. In particular, we show that by using nondeterminism in a slightly extended version of spiking neural P systems it is possible to solve in constant time both the numerical NP{complete problem Subset Sum and the strongly NP{complete problem 3-SAT. Then, we show how to s...
Given a computational model M{\cal M}, and a “reasonable” encoding function C: M ® {0,1}*{\cal C}: {\cal M} \to \{0,1\}^\ast that encodes any computation device M of M{\cal M} as a finite bit string, we define the description size of M (under the encoding C{\cal C}) as the length of C(M){\cal C}(M). The description size of the entire class M{\cal M...
Membrane systems were introduced by Gh. Paun in 1998 as a class of distributed parallel computing devices of biochemical type, inspired from the functioning of living cells. Since then, they have been the subject of various studies, aimed at investigating and point out many aspects related to their computational power and efficiency. More recently,...
Membrane systems (also called P systems) and Brane calculi have been recently introduced as formal models inspired by the structure and the functioning of living cells, but having in mind different goals. The aim of Membrane systems was the formal investigation of the computational nature and power of various features of the cell, while Brane calcu...
Recognizer P systems with active membranes have proven to be very efficient computing devices, being able to solve NP-complete decision problems in a polynomial time. However such solutions usually exploit many powerful features, such as electrical charges (polarizations) associated to membranes, evolution rules, communication rules, and strong or...
Genetic Systems are a formalism inspired by genetic regulatory networks, suitable for modeling the interactions between genes
and proteins, acting as regulatory products. The evolution is driven by genetic gates: a new object (representing a protein)
is produced when all activator objects are available in the system, and no inhibitor object is pres...
We introduce Genetic Systems, a formalism inspired by genetic regulatory networks and suitable for modeling the interactions
between the genes and the proteins, acting as regulatory products.
The generation of new objects, representing proteins, is driven by genetic gates: a new object is produced when all the activator
objects are available in th...
Starting from an extended nondeterministic spiking neural P system that solves the Subset Sum problem in a constant number of steps, recently proposed in a previous paper, we investigate how difierent properties of spiking neural P systems afiect the capability to solve numerical NP{complete problems. In particular, we show that by using maximal pa...
We study a Păun’s conjecture concerning the unsolvability of NP–complete problems by polarizationless P systems with active membranes in the usual framework, without cooperation, without
priorities, without changing labels, using evolution, communication, dissolution and division rules, and working in maximal
parallel manner. We also analyse a vers...
P systems have been used many times to face with computationally difficult problems, such as NP-complete decision problems and NP-hard optimization problems. We focus our attention on another computationally intractable problem: factorization. In particular, we first propose a simple method to encode binary numbers using multisets. Then, we describ...
Genetic Systems are a formalism inspired by genetic regulatory networks, suitable for modeling the interactions between genes
and proteins, acting as regulatory products. The evolution is driven by genetic gates: a new object (representing a protein)
is produced when all activator objects are available in the system, and no inhibitor object is pres...
Nadia Busi obtained a Master in Computer Science in 1993, at the University of Bologna. In 1997 she obtained a PhD in Theoretical Computer Science at the University of Siena; her thesis entitled “Petri Nets with Inhibitor and Read Arcs: Semantics, Analysis and Application to Process Calculi” won the annual prize of the Italian Chapter of EATCS for...
We present a model for self-assembly of graphs based on multisets and the formalism of membrane systems. The model deals with aggregates of cells which are defined as undirected graphs where a multiset over a fixed alphabet is assigned to each vertex. The evolution of these aggregates is determined by an application of multiset-based aggregation ru...
In recent years, the modeling and analysis techniques developed in the area of formal languages and of concurrent process calculi have been successfully applied to the field of systems biology. In this setting, brane calculi and membrane systems are two of the most prominent approaches for the modeling of the behaviour of biological membranes. Memb...
We introduce energy-based P systems as a parallel and distributed model of computation in which the amount of energy manipulated and/or consumed during computations is taken into account. Basing upon the seminal paper of Fredkin and Toffoli on conservative logic, we first show how energy-based P systems can be used to simulate the Fredkin gate, a r...
We introduce a new variant of membrane systems where the rules are directly assigned to membranes and, moreover, every membrane carries an energy value that can be changed during a computation by objects passing through the membrane. The result of a successful computation is considered to be the distribution of energy values carried b y the membran...
We introduce Genetic P systems, a class of P systems with evolution rules inspired by the functioning of the genes.
The creation of new objects – representing proteins – is driven by genetic gates: a new object is produced when all the activator objects are present, and no inhibitor object is available. Activator objects are not consumed by the app...
We compare various computational complexity classes defined within the framework of membrane systems, a distributed parallel computing device which is inspired from the functioning of the cell,
with usual computational complexity classes for Turing machines. In particular, we focus our attention on the comparison among complexity classes for membra...
Current P systems which solve NP–complete numerical problems represent the instances of the problems in unary notation. However, in classical complexity theory, based upon Turing machines, switching from binary to unary encoded instances generally corresponds to simplify the problem. In this paper we show that, when working with P systems, we can a...
Dynamical probabilistic P systems are discrete, stochastic, and parallel devices, where the probability values associated with the rules change during the evolution of the system. These systems are proposed as a novel approach to the analysis and simulation of the behavior of complex systems. We introduce all necessary definitions of these systems...
In [3] P systems with gemmation of mobile membranes were examined. It was shown that (extended) systems with eight membranes are as powerful as the Turing machines. Moreover, it was proved that extended gemmating P systems with only pre-dynamical rules are still computationally complete: in this case nine membranes are needed to obtain this computa...
Citations
... Inspired by the presence of biocatalysts in biological reactions, a variation of TPs with promoters has been proposed to recruit promoters for solving image processing problems [15]. A novel kind of TP, monodirectional tissue-like P systems [16] and simply called MTPs, which is based on the biological fact that objects only move in one direction, has been constructed to enhance computing power in solving NP-complete problems [17][18][19]. ...
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... In theoretical studies, many kinds of TPs based on various biological motivations have been constructed and developed to expand the types of MC [9,10]. The analysis of these extended systems on computing power and computational efficiency is an essential point in theoretical works [11,12]. TPs with evolutional symport/antiport are presented to rewrite and modify objects in the communication process [13,14]. ...
... Evolutionary algorithms simulate natural selection and can find the most effective solutions to complicated problems [31], [32]. In the case of communication networks, evolutionary computing can be employed to optimize resource allocation, routing, and scheduling [33]. ...
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... Such systems have also been considered to study computational complexity aspects for a variant where membranes can be created by division [44], resembling the process of cell mitosis. These studies concern both time complexity aspects [30-34, 41, 49, 51] as well as space complexity [1,2,4,47,48,50,55,58]. A recent survey on this subject can be found in [53]. ...
![[object Object]](https://i1.rgstatic.net/ii/profile.image/279758526009346-1443711038330_Q64/Artiom-Alhazov.jpg)
... Definitions of SN P systems, their syntax and semantics, are only mentioned in brief below to be able to focus more on three main notions in the present section. Excellent introductions to and definitions of SN P systems include the seminal work in [55], the dedicated chapter in the handbook in [89], with open access tutorials in [61] and [80]. ...
... Various implementations of this computing system have been employed in a range of practical applications. [16][17][18] For example, time series forecasting, 19 sequence recommendation, 20 image processing, 21 etc. ...
... Membrane Computing, since its beginnings [1], has covered a wide spectrum of applications, from computability theory [2] and computational complexity theory [3] to pandemics [4] and engineering [5]. The model is inspired in the structure and behavior of living cells and the chemical reactions occurring within them. ...
... neural P systems, cell P systems, tissue P systems, etc., [29,15,12]. P systems have generated new perspectives on the P vs NP problem, being used to efficiently solve hard problems [27,3,7,28]. There are also multiple applications of P systems in various fields like formal verification, artificial intelligence, or cryptography [30]. ...
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... • the proceedings of the Conference on Membrane Computing (CMC), e.g. [10], ...
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... A strong investigation effort has been done on the model, and it is still in progress, considering different aspects. Recent works appeared considering questions related to computing properties [22,25], computing efficiency [1,16,17], relations with other formal models like, e.g., Petri nets [4], Morphogenetic systems [34], or Markov chains [32], and application to real problems [3,7,30,35,38]. ...
