Volume 34, Number 1 (2025)

---

Special Issue: Selected Papers from the Second Asian Symposium on Cellular Automata Technology, 2023 (ASCAT 2023)
Sukanta Das and Genaro J. Martinez

This special issue contains five papers on cellular automata and their applications, preliminary versions of which were presented at the Second Asian Symposium on Cellular Automata Technology, 2023 (ASCAT 2023). The symposium was officially organized by the departments of Information Technology and Computer Science and Technology of Indian Institute of Engineering Science and Technology, Shibpur (IIEST, Shibpur), India, March 2– 4, 2023, in hybrid mode. The ASCAT is marked as an annual event of Cellular Automata India, an open research group that was created to understand, apply and explore several directions about the nature, formalism and applications of cellular automata theory.
        In this symposium, 14 papers were selected for presentation. Based on the review reports of the papers, we invited the authors of eight papers to submit extended versions for possible inclusion in the planned special issue. ASCAT 2023 organized a PhD forum, whose participants were also invited to submit the unpublished work of their PhD research. All the PhD submissions were reviewed carefully, and finally five papers were chosen for this special issue. Out of these five papers, one is from the PhD forum and the rest are extended versions of the presented works. We thank all the authors for their effort. We are very greatly thankful to the reviewers who gave their time to review the papers and to select these five papers. We are sure that these papers contribute to the field of cellular automata and related subjects.

Keywords: ASCAT 2023; Second Asian Symposium on Cellular Automata Technology; cellular automata applications

Cite this publication as:
S. Das and G. J. Martínez, “Special Issue: Selected Papers from the Second Asian Symposium on Cellular Automata Technology, 2023 (ASCAT 2023),” Complex Systems, 34(1), 2025 p. i.
https://doi.org/10.25088/ComplexSystems.34.1.i

---

Nonuniform Temporally Stochastic Cellular Automata as Model of Contagious Disease Spread
Subrata Paul and Kamalika Bhattacharjee

In this paper, we introduce a new cellular automaton (CA) variant called the nonuniform temporally stochastic CA (NTSCA), where an NTSCA contains a sequence of temporally stochastic cellular automata (TSCAs). Different TSCAs are used for different time frames during the evolution of the model to simulate the propagation of contagious viruses. We also propose the idea of a distant neighbor to depict the spread of viruses that occurs when asymptotic carriers are transported large distances. The essence of this spread is embodied by a specific set of features. These features are included in the NTSCA by utilizing information propagation, information cooking and partial blocking of information. Based on these parameters, the required rules are identified and used in the applied TSCAs. The dynamical changes of TSCAs during evolution make the system chaotic and enable imitating the propagation of diseases. We successfully imitate the spread of two such contagious diseases borne by viruses, COVID-19 (in India) and SARS 2003 (in China) and compare the results with real-time data.

Keywords: nonuniform temporally stochastic cellular automata; NTSCAs; distant neighbor; information propagation; information cooking; partial blocking; epidemic; COVID-19; SARS 2003

Cite this publication as:
S. Paul and K. Bhattacharjee, “Nonuniform Temporally Stochastic Cellular Automata as Model of Contagious Disease Spread,” Complex Systems, 34(1), 2025 pp. 1–27.
https://doi.org/10.25088/ComplexSystems.34.1.1

---

Cellular Automaton–Based Sentiment Analysis for Bipolar Classification of Reviews
Elizabeth M. J., Parimal Pal Chaudhuri and Raju Hazari

One of the main goals of sentiment analysis is to analyze human perception to continuously adapt to each person’s demands. The information gathered is structured to understand the mood or emotional tone of the reviews and comments. In every aspect of society, there is always an opportunity for opinions and suggestions from the public. So, the quality of the services provided by various resources can considerably increase if we can determine whether those thoughts are positive, negative or neutral. In this paper, we employ cellular automata (CAs) to categorize the reviews as positive or negative. The fundamental advantage of the suggested technique is that there is less need to be concerned about the linguistic characteristics of human languages. The proposed method performs better by leveraging a variety of parameters that are extracted by analyzing cycle length (CL) graphs generated using CL signals produced by elementary CAs (ECAs) without employing any form of pre-trained language model. We evaluated the effectiveness of the proposed cellular automaton–based machine learning (CAML) classifier by assessing certain parameters such as recall, precision, F1 score and accuracy. Our method achieves a maximum accuracy of 92.44% for the sentiment tweet dataset. We compared the proposed technique with all existing machine learning models, as well as recent methodologies employed in the field. The suggested method performs well in predicting the positive and negative classes of sentiments using CAs.

Keywords: elementary cellular automata; ECA; machine learning; sentiment analysis; rule-based approach; text classification

Cite this publication as:
Elizabeth M J,  P. P. Chaudhuri and R. Hazari, “Cellular Automaton–Based Sentiment Analysis for Bipolar Classification
of Reviews,” Complex Systems, 34(1), 2025 pp. 29–57.
https://doi.org/10.25088/ComplexSystems.34.1.29

---

Isomorphic Classification of First Degree Cellular Automata
Vicky Vikrant, Kamalika Bhattacharjee and Sukanya Mukherjee

This paper explores the concept of isomorphism in cellular automata (CAs), focusing on identifying and understanding isomorphic relationships between distinct CAs. A cellular automaton (CA) is said to be isomorphic to another CA if the configuration transition diagrams of the two CAs are identical. To illustrate how isomorphism entails the preservation of structural properties while allowing for variations in state representations, we exhaustively explore the isomorphic reversible rules in the first degree CAs (FDCAs), that is, the simple three-neighborhood CAs represented by eight parameters. The experimental study includes reversible FDCAs for states two to 10 with cell lengths of four to seven under the null boundary condition and states two to seven with cell lengths of four to seven under the periodic boundary condition. Given a CA, we also provide two synthesis methods for identifying the set of CAs that are isomorphic to it. The first method operates by permuting the states of a group of CA cell locations, whereas the second method involves exchanging cells at various points. We demonstrate that, depending on the range of exchanged cell positions, the isomorphic CAs produced in this way may have a bigger neighborhood than the input CA. Finally, we provide an exhaustive classification of the elementary CAs (ECAs) using the first synthesis method and compare it with existing results.

Keywords: first degree cellular automaton; FDCA; parameters; reversibility; cycle structure; classification; synthesis schemes

Cite this publication as:
V. Vikrant, K. Bhattacharjee and S. Mukherjee, “Isomorphic Classification of First Degree Cellular Automata,” Complex Systems, 34(1), 2025 pp. 59–90.
https://doi.org/10.25088/ComplexSystems.34.1.59

---

Exploring Nonuniform Structure of NSRTDs for Characterizing MACA Rules in the Null-Boundary Condition
Suvadip Hazra, Som Banerjee, Mamata Dalui and Bidesh Chakraborty

The cellular automaton (CA), a discrete model, is gaining popularity in simulations and scientific exploration across various domains, including cryptography, error-correcting codes, VLSI design and test pattern generation. This paper examines a two-state three-neighborhood nonuniform finite CA with a specified number of fixed points. We utilize a graph-based tool known as the next state rule minterm transition diagram (NSRTD) to analyze the spatiotemporal behavior of these cellular automata (CAs) across all lengths. We devise methods for synthesizing nonuniform single length cycle multi-attractor CAs (MACAs), a specialized class of irreversible CA with a predefined number of fixed points for any arbitrary length. Despite the method’s exponential worst-case time complexity, it offers the advantage of selecting rules for each CA cell from a set of candidate rules, ensuring the desired number of fixed points.

Keywords: cellular automata; length cycle multi-attractor cellular automata; MACA; next state rule minterm transition diagram; NSRTD; fixed-point attractor

Cite this publication as:
S. Hazra, S. Banerjee, M. Dalui and B. Chakraborty, “Exploring Nonuniform Structure of NSRTDs for Characterizing MACA Rules in the Null-Boundary Condition,” Complex Systems, 34(1), 2025 pp. 91–127.
https://doi.org/10.25088/ComplexSystems.34.1.91

---

Nonlinearity in Large-Cycle Cellular Automata
Sukanya Mukherjee and Sumit Adak

The class of maximal-length cellular automata (CAs) has gained significant attention over the last few years due to the fact that it can generate cycles with the longest possible lengths. For every l of the form $l=2^n-1$ where n∈N, a cycle of length l can be generated by a cellular automaton (CA) of size $\lfloor {\log }_{2}l\rfloor +1$; this maximal-length CA is in fact the optimal (minimum-sized) CA to generate a cycle of length l. However, maximal-length CAs are, in general, linear and have some drawbacks. Moreover, it is nontrivial to address this problem for any l∈N, that is, removing the constraint that l is of the form $2^n-1$. In this paper we therefore employ nonlinearity in the rules and aim to generate the near-optimal CA for any given cycle length l, meaning that the generated CAs will be of size $n=\left(\lfloor {\log }_{2}l\rfloor +1\right)+d$, where the displacement d is as small as possible. We use a generic operator to concatenate a collection of component CAs of sizes $n_1,n_2,\dots ,n_k$ by employing an evolutionary strategy. Here, $n=n_1+n_2+\cdots +n_k$ and $l\ge \mathrm{lcm}\left({\ell }_1,{\ell }_2,\dots ,{\ell }_k\right)$, where ${\ell }_i$ (1≤i≤k) is the maximum cycle length of a CA of size $n_i$. An influencing factor in the design of component CAs is to achieve the near-optimal CA for a given cycle length. Here we consider nonlinear reversible large-cycle CAs as component CAs. We also measure the effectiveness of nonlinearity in large-cycle generation.

Keywords: cellular automata; CAs; reversible CAs; large-cycle CA; nonlinearity; neighborhood dependent; evolution

Cite this publication as:
S. Mukherjee and S. Adak, “Nonlinearity in Large-Cycle Cellular Automata,” Complex Systems, 34(1), 2025 pp. 129–160.
https://doi.org/10.25088/ComplexSystems.34.1.129