We propose an extension to multisets of the model of reaction systems, classically based on sets. In the proposed model, four main variations are present with respect to the classical model: (1) reactions (here called m-reactions) have multisets rather than sets in their reactant, inhibitor, and product components; (2) states are multisets of entities, rather than sets; (3) based on the numerosity of the entities in the state, several instances of non-conflicting m-reactions can be simultaneously applied, forming a block; and (4) entities not consumed in the application of a block remain in the state, to which the cumulatively produced multiset of entities is added. Threshold phenomena (reaching a critical mass enabling new m-reactions or saturating the state with entities inhibiting m-reactions to be enabled) can therefore be observed, so that some context-independent behaviours can be observed, which are not possible in the classical case. The paper explores some formal consequences of the proposed model and illustrates its relevance by presenting a model of the dynamics of the heat shock response cellular regulatory mechanism.
We develop a process-algebraic framework for multiset reaction systems (MRSs), in which both reactions and system states are represented as multisets rather than sets. This representation enables quantitative reasoning about resources and naturally supports nondeterministic behaviour: unlike standard reaction systems, unconsumed resources persist into the next state, and several maximally enabled multisets of reactions may coexist at the same state. We equip the framework with a compositional operational semantics defined by structural operational semantics (SOS) rules, introduce a process representation for MRSs and the notion of maximal interactive processes, and prove that the induced labelled transition system faithfully corresponds to the rewriting dynamics of MRSs (Theorem 1). Building on this foundation, we extend the framework to distributed multiset reaction systems (DMRSs), in which processes are located at nodes of a network and communicate asynchronously by sending products to neighbouring locations. A distinguishing feature of the model is that reactions may dynamically modify the network topology through controlled division mechanisms, thereby integrating locality, asynchronous communication, and structural evolution within a single operational semantics. Finally, we investigate the computational power of DMRSs by studying their ability to solve the NP-complete Subset Sum problem. We present two constructions: a semi-uniform one, in which a dedicated DMRS is built for each problem instance, and a uniform one, in which a single DMRS handles all instances of a fixed size while the instance parameters are supplied as contextual resources. In both cases the system solves Subset Sum in at most 2n+3 computation steps, where n is the number of input integers, by exploiting nondeterminism and large-scale parallelism: division generates all 2^n candidate subsets in parallel, and resource-based cancellation detects valid solutions. These results demonstrate that DMRSs constitute a powerful and flexible formal framework for distributed, resource-driven computation.
Automated recognition of bird species from audio is critical for biodiversity monitoring, yet it remains difficult in practice because field recordings often contain multiple birds vocalizing at the same time, strong environmental noise, and limited labeled data. Most existing systems either assume single-species recordings, require clean inputs, or depend on manually engineered preprocessing, such as source separation. This work introduces a novel two-stage fine-tuning framework that adapts a large self-supervised speech model (HuBERT) to the highly non-speech, polyphonic, multi-label setting of wild bird soundscapes. The proposed approach departs from conventional direct fine-tuning by using a two-stage curriculum. In Stage 1, HuBERT is fine-tuned on clean single-species recordings to learn discriminative, species-specific acoustic representations without interference. In Stage 2, the model is then transferred and further fine-tuned on synthetically constructed overlapping vocalizations, enabling it to generalize to real noisy soundscapes where multiple species co-occur. This two-stage adaptation strategy bridges the acoustic gap between human speech pretraining and avian bioacoustics, and allows robust multi-label prediction directly on overlapping audio without requiring explicit source separation. Extensive experiments on ten bird species show that the proposed two-stage HuBERT achieves an F1-score of 0.94 on overlapping recordings, outperforming (i) HuBERT variants trained only on clean or overlapping audio, and (ii) state-of-the-art CNN, RNN, graph-based, and transformer baselines reported in prior studies. These results demonstrate that two-stage self-supervised adaptation is an effective and scalable direction for real-time, multi-species bird monitoring in complex natural environments.
We propose an extension to the framework of reaction systems such that the environment not only plays the role of contributing entities to the successor state, but also influences the actual generation of products. In particular, we consider that an environment can assign valences to entities, be they used as reactants or inhibitors in a reaction, as well as select the entities which can appear in the successor state as product of a reaction. This provides a framework for immersing reaction system specifications into different contexts. We also derive a notion of polarised reaction systems, where entities can appear only as reactants or inhibitors in any given reaction. We compare the expressive power of the models, also showing some equivalences between them, and test them on three case studies derived from physiology, ecology, and chemistry.
We study distributed agreement in microbial distributed systems under stochastic population dynamics and competitive interactions. Motivated by recent applications in synthetic biology, we examine how the presence and absence of direct competition among microbial species influences their ability to reach majority consensus. In this problem, two species are designated as input species, and the goal is to guarantee that eventually only the input species which had the highest initial count prevails. We show that direct competition dynamics reach majority consensus with high probability even when the initial gap between the species is small, i.e., Ω (√(nlog n)) , where n is the initial population size. In contrast, we show that absence of direct competition is not robust: solving majority consensus with constant probability requires a large initial gap of Ω (n) . To corroborate our analytical results, we use simulations to show that these consensus dynamics occur within practical biological time scales.
To model distributed and concurrent systems, cellular automata (CA) researchers have introduced the notion of fully asynchronous cellular automata (ACA) with atomicity property where the automata system does not allow the simultaneous update of two neighbouring cells. Moreover, this fully ACA also breaks the traditional notion of global clock in cellular automata. In this article, we introduce the notion of skew-asynchronous CA that questions the presence of atomicity property. That is, in the proposed skewed system, we allow simultaneous update of two-neighbouring cells. In fact, in the skewed system, we randomly choose one cell during each step of evolution and update the cell and its right neighbour. According to the initial experimental results, some convergent fully asynchronous elementary CA (ECA) systems show non-convergent (i.e., divergent) dynamics under skewed update. Moreover, some reversible ECA systems under fully asynchronous update show convergent dynamics under skewed update. This study also displays the brutal change in system dynamics for changing updating schemes (i.e., fully to skewed, or vice-versa) where the lattice size (say, n) plays a critical role, specifically, n ∈ 2ℕ , n ∈ 3ℕ and n ∈ 4ℕ . This study also reports the theory behind the convergent skewed systems after considering homogeneous fixed points all 0 and all 1. For the non-convergent skewed systems, we report the communication class properties of reversible ECA 58-HGEDCB and semi-reversible ECA 26-HGECB as a case study. Lastly, we introduce the notion of correlated skew-asynchronous updating scheme to understand the microscopic details of the skewed systems which show important continuous (second-order) phase transition dynamics for many ECA rules.
Cellular Automata (CA) classification enables the identification of appropriate rules for modeling a scenario. This paper examines the use of Communicability Sequence Entropy (CSE) in network representations of Elementary Cellular Automata (ECA) rules to identify more quantifiable similarities within the Wolfram Classification. Previous studies analyzed network representations of ECA rules using different centrality measures. Using information-theoretic measures for these network representations benefits from three domains: Network Science, Cellular Automata, and Information Theory, offering an alternative viewpoint on CA classification. This study uses network and information-theoretic measures to quantify ECA rule behavior by analyzing perturbation propagation and rule similarity. It finds cohesive groups in Classes 1, 3, and 4, but Class 2 remains inconsistent.
Finite discrete-time dynamical systems (FDDS) model phenomena that evolve deterministically in discrete time. It is possible to define sum and product operations on these systems (disjoint union and direct product, respectively), giving a commutative semiring. This algebraic structure led to several works employing polynomial equations to model hypotheses on phenomena modelled using FDDS. To solve these equations, algorithms for performing division and computing k-th roots are needed. In this paper, we propose two polynomial algorithms for these tasks, under the condition that the result is a connected FDDS. These algorithms exploit the notion of unroll of a FDDS, an alternative representation based on a forest of infinite trees constructed by computing the transition function of the system backwards. This ultimately leads to an efficient solution to equations of the type AX^k=B for connected X and some generalisations. These results are some of the important final steps for solving more general polynomial equations on FDDS.
Chemical reaction networks (CRNs) are a powerful framework for programming the dynamics of molecular concentrations over time. While digital chemical reaction circuits are well established, with the ability to construct essentially any small Boolean logic circuit, there is currently no general method for translating analog electronic circuits consisting of reversible resistor, inductor, and capacitor (RLC) components into CRNs. In this work, we present a systematic approach to translate RLC circuits into CRN motifs that preserve key dynamics, where chemical concentration is the analog for voltage, flux is the analog for current, and reaction rate constants are the analogs of resistance. The resulting analog CRN circuits lay a foundation for embedding analog computation within chemical and biological environments.
A key aspect of large scale mining is an accurate identification of rocks and ores. This study focuses on classifying various rock types, including igneous (basalt, granite), sedimentary (coal, limestone, sandstone, shale), and metamorphic (marble, quartzite), along with ores such as iron (hematite, magnetite, limonite, siderite), copper (chalcopyrite), aluminum (bauxite), and lead (galena). Data are collected from various locations in India. The classification process involves two steps: grain boundary detection using cellular automata (CAs) and classification using convolutional neural networks (CNN). A proposed cellular automaton (CA) based algorithm enhances grain visibility and generates refined images that serve as input to the CNN models. Two CNN models, referred to as Model-I and Model-II, are proposed for rock and ore classification, respectively. To enhance feature extraction and improve classification accuracy, a self-attention module is incorporated before the fully connected layer in Model-II. Comparative analysis shows Model-I achieves high accuracy for rock classification (97.8
Number system conversion is a fundamental and critical operation in computer science and information processing. This work proposes optimized P systems for number system conversion based on membrane computing, aiming to enhance conversion efficiency. Using cell-like P systems, decimal values are encoded as object multisets, and two novel mechanisms are introduced. For decimal to base-n conversion, an alternating computation mechanism across a double-layer membrane structure is designed, enabling parallel extraction of quotient and remainder by dynamically switching rule activation between membranes. For base-n to decimal conversion, a hierarchical progression mechanism across nested membranes is developed, which accumulates weighted values through carry propagation enabled by membranes. The proposed systems were validated through case studies on three representative bases (binary, octal, and hexadecimal), and simulations using UPSimulator confirmed their correctness and expected behavior. Comparing with the results reported in the literature, the proposed P systems reduce the required time steps and effectively eliminate the coefficient factor. This work demonstrates that routine arithmetic operations can benefit from membrane computing parallelism, offering a reusable design pattern for numerical P systems.
We investigate number conservation in non-uniform one-dimensional binary cellular automata with a neighborhood of size four. In this setting, cells may follow distinct local rules, leading to a wide range of dynamic behaviors. It is known that one way to synthesize such cellular automata on a finite grid of a given length is to use concatenation of smaller blocks, which are themselves number-conserving. By introducing new mathematical tools, we were able to find and describe in detail the dynamics of all such blocks of length less than five.
Reaction systems are rooted in processes inspired by the functioning of the living cell. The key idea behind the resulting formal model is that such processes are determined by the interactions of biochemical reactions. Moreover, such interactions are based on the fundamental mechanisms of facilitation and inhibition. Since their inception, reaction systems have developed into an extensively investigated model of computation with unique characteristics and a wide range of potential applications. The semantical model of reaction systems is based on the concept of system states consisting of sets of entities, and state transformations enacted by sets of reactions. Another important behavioural property is the non-permanency of the entities, and so data persistence has to be consciously implemented. Issues like this need to be taken into account in all simulations of reaction systems by means of other existing models and tools, such as Petri nets. In this paper, we provide four different Petri net encodings of basic reaction systems operating without interacting with external environment. We start from a naive encoding that is based on the behaviour of a reaction system ℛ only, transforming the transition system of ℛ into a Petri net in the form of a marked graph. Such a solution introduces exponentially many places and transitions. In the subsequent encodings, we cope with this exponentiality ending up with a solution that is polynomial in the size of the original reaction system. We then show how this polynomial encoding can be adapted to provide a polynomial encoding for reaction systems operating with contexts provided by context automata. The encoding method proposed in this paper is modular and can provide a basis for compositional construction of reaction systems.
This work explores a new cellular automaton model, where two rules, say f and g are applied with some probability to each cell temporarily. Rule f acts as default rule of the model, whereas rule g is treated as a noise rule and applied with probability τ . This class of cellular automata is called Temporally Stochastic Cellular Automata (TSCAs). The dynamical behaviour of these automata is studied to identify the list of convergent TSCAs. This work identifies the similarities between TSCAs and Markov chains, and shows that the dynamics of the TSCAs are Markovian. We utilise absorbing Markov chain as a tool to study the convergence of TSCAs. Finally, we study the theoretical aspects behind the convergence of TSCAs to validate the experimental outcomes of dynamical studies.
The abstract Tile Assembly Model (aTAM) provides an excellent foundation for the mathematical study of DNA-tile-based self-assembling systems, especially those wherein logic is embedded within the designs of the tiles so that they follow prescribed algorithms. While such algorithmic self-assembling systems are theoretically powerful, being computationally universal and capable of building complex shapes using information-theoretically optimal numbers of tiles, physical DNA-based implementations of these systems still encounter formidable error rates and undesired nucleation that hinder this theoretical potential. Slat-based self-assembly is a recent development wherein DNA forms long slats that combine together in 2 layers, rather than square tiles in a plane. In this approach, the length of the slats is key; while tiles typically only bind to 2 neighboring tiles at a time, slats may bind to dozens of other slats. This increased coordination between slats means that several mismatched slats must coincidentally meet in just the right way for errors to persist, unlike tiles where only a few are required. Consequently, while still a novel technology, large slat-based DNA constructions have been successfully implemented in the lab with resilience to many tile-based construction problems. These improved error characteristics come at a cost however, as slat-based systems are often more difficult to design and simulate than tile-based ones. Moreover, it has not been clear whether slats, with their larger sizes and different geometries, have the same theoretical capabilities as tiles. In this paper, we show that slats are capable of doing anything that tiles can, at least at scale. We demonstrate that any aTAM system may be converted to and simulated by an effectively equivalent system of slats. Furthermore, we show that these simulating slat systems can be made more efficiently, using shorter slats and a smaller scale factor, if the simulated tile system avoids certain uncommon growth patterns. Specifically, we consider 5 classes of aTAM systems with increasing complexity, from zig-zag systems which grow in a rigid pattern to the full class of all aTAM systems, and show how they may be converted to equivalent slat systems. We show that the simplest class may be simulated by slats at only a 2c × 2c scale, where c is the freely chosen coordination number of the slats, and further show that the full class of aTAM systems can be simulated at only a 5c × 5c scale. These results prove that slats have the full theoretical power of aTAM tiles while also providing constructions that are compact enough for potential DNA-based implementations of slat systems that are both capable of powerful algorithmic self-assembly and possessing of the strong error resilience of slats. This paper is an extended version of a version that appeared in the proceedings of the 30th International Conference on DNA Computing and Molecular Programming (DNA 30).
This paper introduces a cellular automata-based machine learning approach designed to solve sentiment analysis and toxicity classification tasks in code-mixed data. The complex behaviour of cellular automata plays a major role in generating signals that effectively capture the context and unique features of comments where multiple languages or dialects coexist. Cellular automata evolve by updating each cell based on the surrounding context, which allows patterns related to sentiment or toxicity to emerge naturally. Unlike traditional models that require deep language understanding or grammar rules, CA can capture structural patterns and emotional cues purely based on word positions and interactions. These signals are then used to compute the weights of the words used in the text. These weights serve as inputs for deep learning models to accurately predict text labels. Our approach achieves a 90
Controllability, one of the fundamental concepts in control theory, consists in guiding a system from an initial state to a desired one within a limited (and possibly minimum) time interval. When the objective is limited to a specific sub-region of the system's domain, the concept is referred to as regional controllability. We examine this notion in the context of Boolean one-dimensional cellular automata of finite length. Depending on the local evolution rule, we investigate whether it is possible to control the evolution of the system by imposing particular values on the boundary conditions. This approach is related to key dynamical properties of CA, specifically chain transitivity and chain mixing. We show that the control problem can be formulated as a Boolean satisfiability (SAT) problem and can thus be addressed using SAT solvers. We also show how finding shortest paths in the configuration graph allows to determine controllability properties. From our observations we can state that only peripherally-linear rules are fully controllable, while for other rules, the reachability ratio, that is, the fraction of controllable pairs of initial and final configurations, is vanishing when the system size grows.
Non-uniform cellular automata (NUCA) are an extension of cellular automata with multiple local rules in different cells. We show that if the distribution of local rules is uniformly recurrent, or recurrent in the one-dimensional case, the Garden of Eden theorem holds. We also show that for any one-dimensional non-recurrent distribution, there is a substitution of local rules that defines a NUCA which does not satisfy the Garden of Eden theorem. Finally, we show that a one-dimensional rule distribution asymptotic to recurrent distribution defines a surjunctive NUCA.
Functional digraphs are unlabelled finite digraphs where each vertex has exactly one out-neighbor. They are isomorphic classes of finite discrete-time dynamical systems. Endowed with the direct sum and product, functional digraphs form a semiring with an interesting multiplicative structure. For instance, we do not know if the following division problem can be solved in polynomial time: given two functional digraphs A and B, does A divide B? That A divides B means that there exists a functional digraph X such that AX is isomorphic to B, and many such X can exist. We can thus ask for the number of solutions X. In this paper, we focus on the case where B is a sum of cycles (a disjoint union of cycles, corresponding to the limit behavior of finite discrete-time dynamical systems). There is then a naïve sub-exponential algorithm to compute the non-isomorphic solutions X, and our main result is an improvement of this algorithm which has the property to be polynomial when A is fixed. It uses a divide-and-conquer technique that should be useful for further developments on the division problem.
