The innovative model of partial array languages generated by basic puzzle partial array grammars is available in the literature. Here we define Partial array Token Petri Net Structure (PATPNS) to generate partial array languages. Further we introduce Partial Array Token Petri Net P System (PATPNPS) to generate partial array languages and compared with basic puzzle partial array grammars for generative power. PATPNS is also compared with local and recognizable partial array languages.
Siromoney et al. introduced a parallel/sequential generative model called Tabled Matrix Grammars (TMGs) by generalising phrase structure matrix grammars generating abstract families of languages (AFLs). James et al. introduced Parallel Contextual Array Insertion Deletion P Systems (PCAIDPSs) to generate two-dimensional array languages using insertion and deletion operations through parallel contextual mappings. In this paper, we compare the generative powers of PCAIDPSs and TMGs. We prove that the family of languages generated by PCAIDPS with two membranes properly includes the family of languages generated by Tabled Context-sensitive Matrix Grammars (TCSMGs).
Selection of relevant genes is the crucial task for sample classification in microarray data, where researchers try to identify the smallest possible set of genes that can still achieve good predictive performance. Due to the problem of higher risk of overfitting in wrapper methods and sensitivity of the best embedded way to filter out factor that leads to unstable model and significantly different gene subsets, in this paper, we propose a novel model for evaluating and improving techniques for selecting informative genes from microarray data. This model inspired by membrane computing and used the kernel P system (kP) as the variant of the P system to improve the performance of the intelligent algorithm, multi-objective binary particle swarm optimization (MObPSO). The proposed model consists of two main parts. First, kP-MObPSO, which resembles a wrapper type feature selection, and the second part that improves the results of the first part through an embedded feature selection and classification idea based on the kP system. Division, rewriting, and input/output rules are used to make interaction among the genes inside and between the particles. The proposed model applied to the colorectal and breast dataset contains 100 genes with six attributes. The embedded part of the model extracts the marker gene sets indicate more stability and reliability based on ROC measure as well as better error rate in comparison to the wrapper part of the model. In the paper, the lowest error rate by an embedded model is displayed as 0.1111 for breast cancer and 0.0769 for colorectal data.
We introduce and examine two variants of networks of reaction systems, called communicating reaction systems with direct communication, where the reaction systems send products or reactions to each other. We show that these types of networks of reaction systems can be obtained by simple mappings from single reaction systems. We also discuss some aspects of communication within these networks, and suggest open problems for future research.
We study the transition graphs, and thus, the possible computational paths of reaction systems which are reversible according to different notions of reversibility. We show that systems which are reversible in the sense of our earlier work produce very simple types of transition graphs. A somewhat more complicated, but still quite simple class of transition graphs is obtained if we consider so-called initialized reversible systems. Finally we introduce the notion of reversibility with lookbehind, and show that systems which are reversible in this sense produce the same transition graphs (and thus, the same computations) as the state transition diagrams of reversible finite transition systems.
Matrix grammars are one of the first approaches ever proposed in regulated rewriting, prescribing that rules have to be applied in a certain order. In traditional regulated rewriting, the most interesting case shows up when all rules are context-free. Typical descriptional complexity measures incorporate the number of nonterminals or the length, i.e., the number of rules per matrix. When viewing matrices as program fragments, it becomes natural to consider additional applicability conditions for such matrices. Here, we focus on forbidding sets, i.e., a matrix is applicable to a sentential form w only if none of the words in its forbidding set occurs as a subword in w. This gives rise to further natural descriptional complexity measures: How long could words in forbidding sets be? How many words could be in any forbidding set? How many matrices contain non-empty forbidding contexts? As context-free grammars with forbidding sets are known as generalized forbidding grammars, we call this variant of matrix grammars also generalized forbidding. In this paper, we attempt to answer the four questions above while studying the computational completeness of generalized forbidding matrix grammars. In the course of our studies, we also define several new normal forms for type-0 grammars that might be of independent interest.
Reaction system was introduced by Ehrenfeucht and Rozenberg [2] as a model of interactions in biochemical reactions while the seminal paper by Gh. Pǎun [5] introducing the bio-inspired model of P system launched the field of membrane computing. An investigation bridging these two models is done by Pǎun and Pérez-Jiménez [8]. Here we introduce a variant of transition P system having a finite base set S, called transition P system based on reactions (in short, (R)TPS) with the regions of the system having reactions (playing the role of evolution rules) as well as states (in the place of objects) that are subsets (that can be empty) of S. Long terminating state sequences and cycles have been generated in studies of reaction systems. Here we construct (R)TPS generating such sequences with some improvements in the lengths of the sequences.
A Petri Net is a mathematical model used to generate string languages, which is useful in data analysis, pattern matchings, simulations etc. Array Token Petri Nets were introduced to generate two-dimensional and three-dimensional picture languages. In this paper, we introduce Triangular Array Token Petri Net (TATPN) to generate certain interesting patterns of triangular picture languages using Elementary Evolution Rules (EER) and Parallel Evolution Rules (PER). We also introduce Triangular Array Token Petri Net P System and compared it with TATPN and TTPPS for generative power.
We set up the notion of evolutionary P systems as P systems with description of rules, or genomes, and translation, evaluation, selection, and modification operators on genomes. The system has a possibility of evolving a desired function. We propose a tissue evolutionary P system which evolves a context-free grammar generating a given target language, i.e., an evolutionary P system for grammatical inference. Experiments show that the proposed systems can evolve some context-free grammars generating the language \(\{a^nb^n\,|\,n > 0\}\) and the Dyck language over \(\{a,b\}\).
The 2D P colonies (see [ 2 ]) were introduced as a theoretical model of the multi-agent system for observing the behavior of the community of very simple agents living in the shared environment. Each agent is equipped with a set of programs consisting of a small number of simple rules. These programs allow the agent to act and move in the environment. The 2D P colonies showed to be suitable for the simulations of various (not only) multi-agent systems, and natural phenomena, like the flash floods. The gray wolf algorithm (see [ 9 ]) is the optimization-based algorithm inspired by social dynamics found in packs of gray wolves and by their ability to create hierarchies, in which every member has a clearly defined role, dynamically. The wolves’ primary goal is to find and hunt down prey, which in our case equals finding the optimal solution to the given problem. The gray wolf algorithm displays positive results thanks to the principles of randomness and communication between wolves. In this paper, we follow our previous research on the numerical 2D P colony with the blackboard (see [ 12 , 13 ]). We present the results of the computer simulation of numerical 2D P colonies and we compare these results with original gray wolf algorithm.
SN P systems with multiple channels are a new variant of spiking neural P systems (SN P systems, in short), which introduce channel labels into spiking rules. The computational power of SN P systems with multiple channels in computing Turing computable function is investigated, and two small SN P systems with multiple channels are constructed in this work. We obtain two universal systems with 57 neurons using standard spiking rules and 39 neurons using extended spiking rules, respectively.
In order to validate P system models and to assist on their formal verification, simulators are indispensable. Moreover, having efficient simulation tools is crucial, and for this purpose, parallel platforms should be employed. So far, several parallel simulators for P systems have been developed, specifically targeting GPUs (Graphics Processing Units). Although being a hot topic within Membrane Computing, mapping P system parallelism on GPUs is still not a mature area. In the past, we have successfully accelerated the simulation of two specific families of P systems solving SAT with GPUs, and learned in the process some semantics ingredients that fit well on these parallel devices. We are extending this exploration by designing an specific simulator of a P system model for the FACTORIZATION problem. In this paper, we analyse the two main approaches for simulators, and depict some design decisions required for this case study.
P systems are distributed and parallel computing models. In this paper, we proposed an improved Quicksort algorithm, called ECTPP-Quicksort, which is based on evolution-communication tissue-like P systems with promoters. ECTPP-Quicksort, taking advantage of the parallel nature, allows objects to be sorted to evolve according to instructions or rules simultaneously. In this way, the time complexity of Quicksort is improved greatly to $$O(log_2n)$$ compared to $$O(nlog_2n)$$ of the conventional Quicksort algorithm. We designed the rules, objects, membrane structures and some other characteristics of ECTPP-Quicksort P system in detail. It is meaningful to the development of membrane computing.
Morphogenetic systems (M systems) have been recently introduced as a computational model aiming at a deeper understanding of morphogenetic phenomena such as growth, self-reproduction, homeostasis and self-healing of evolving systems. M systems hybridize principles common in membrane computing and abstract self-assembly. The model unfolds in a 3D (or generally, dD) space, growing structures that are self-assembled from generalized tiles using shape and location sensitive local rules. The environment provides mutually reacting atomic particles that contribute to growth control. Initial studies of M systems demonstrated their computational universality and efficiency, as well as their robustness to injuries through their self-healing capabilities. Here, we make a systematic comparison of their generativity power with Lindenmayer systems, the best known model of pattern and shape assembly.
Vertebrates come with a skeleton of bones whose inner structure combines two contradicting properties in a fascinating way: On the one hand, bones are stable and robust against mechanical stress, and on the other hand they are lightweight to minimise the energy necessary for motion of the organism. By means of a biological process called ossification, the inner structure of bones becomes permanently optimised during organism’s lifetime which implies a high adaptability to varying environmental and behavioural needs. An appropriate computational model of ossification provides a promising bionics tool with widespread applicability for instance in architecture for construction of technical structures. To this end, we introduce the framework of osteogenetic P systems able to generate and to manage the spatial inner structure of bones in a dynamical manner during ossification. Starting from an initial porous network of interwoven filaments surrounded by vesicles, a variety of osteoblasts and osteoclasts is placed alongside the filaments throughout the whole network. External forces, freely configurable in their intensity and effective direction, affect the outer nodes of the network inducing a spatial distribution of mechanical stress in its inner filamentary structure. Now, the osteoblasts move towards heavily loaded positions and strengthen the corresponding filaments while osteoclasts eliminate filamentary material wherever dispensible. Over time, the inner network structure adapts to its demands by strong filaments along the main force lines. Complementing our framework of osteogenetic P systems, we demonstrate its practicability using two case studies: The first one describes generation of a dice-shaped cage resistant against weights on top. The second study addresses construction of an arched bridge with two opposite bearings.
The N-Queens Puzzle is an intriguing mathematical riddle that provokes many interesting but hard questions albeit having an astonishingly simple problem statement. One of these questions asks for the number of non-attacking placements of N queens onto a generalized N× N chessboard. While estimates and bounds can certainly be given, the exact solution counts, so far, have not lent themselves to a reasonable closed-form solution but rather to showcasing the arts of computer programming - and of digital design - in a tedious systematic exploration of the vast solution space. Already, Donald Knuth has made it a classic example illustrating the technique of backtracking. The largest problem sizes with known solution counts are N = 26 and N = 27. Both of them were first obtained by distributed computations relying on nodes featuring solver engines built within field-programmable hardware. This presentation will briefly introduce the capabilities and opportunities of programmable hardware highlighting its great fit for exploring the N-Queens Puzzle. It will illustrate how the computations were partitioned and how symmetries were used to prune the search spaces before even starting. Finally, the distributed architectures running the actual computations over several months each will be detailed.
Among -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 . However, most solutions require a membrane nesting depth that is linear with respect to the number of variables of the QSAT instance under consideration. While a system of a certain depth is needed, since depth 1 systems only allows to solve problems in , it was until now unclear if a linear depth was, in fact, necessary. Here we use P systems with active membranes with charges, and we provide a construction that proves that QSAT can be solved with a sublinear nesting depth of order n/log n , where n is the number of variables in the quantified formula given as input.
Belousov-Zhabotinsky (BZ) reactions exhibit spiking oscillations over time and in space. Treated as an in-vitro model system for chemical transmission of information via frequency encoding, they came into the focus of systems biology. Conducted in a Petri dish, monitoring of BZ reactions induces comprehensive video material and image sequences that need to be analysed in order to understand the reaction scheme and its parameters including side effects in detail. Aimed by the objective to relieve the biologist from this dreary task, we present a method to automate the identification and localisation of BZ oscillatory spots in a Petri dish by means of optic flow. As defined by Horn and Schunck, optic flow is the distribution of apparent movement velocities of brightness patterns in an image sequence. We extend the standard algorithm and adjust its parameters to make it applicable for automated analysis of BZ reactions in terms of membrane computing as molecular information processing units in space. Our approach introduces methods to cope with perturbations like different kinds of noise typically occurring by undesired alterations within brightness patterns caused by environmental influences and interference of different oscillatory spots. Current work in progress addresses estimation of propagation velocities for expanding concentric rings of each spot.
Computational complexity theory allows one to investigate the amount of resources (usually, time and/or space) which are needed to solve a given computational problem. Indeed, since the appearance of P systems several computational complexity techniques have been applied to study their computational power and efficiency. In this paper, starting from some results which have been obtained in the last few years by the group of Membrane Computing at the University of Milan-Bicocca (also known as the “Milano Team”), sometimes in collaboration with colleagues from the Membrane Computing community, I will make some observations on what is the relevance (in my opinion) of time and space complexity theory for P systems. Speaking about the results, I will focus in particular on the ideas lying behind them, without delving into technical details. I will also comment on the importance of these results for applications, such as modelling complex systems and implementing decentralized applications. I will finally conclude with some (somewhat provocative) connections with other Computer Science subjects, related with Cryptography, Computer and Network Security, and Decentralized Applications.
