arXiv subjects

Kamalika Bhattacharjee

Publications and source records attributed to Kamalika Bhattacharjee.

10 recordsLinked to original sources

arXiv2026

Cellular Automata based Resource Efficient Maximally Equidistributed Pseudo-Random Number Generators

An equidistribution is a theoretical quality criteria that measures the uniformity of a linear pseudo-random number generator (PRNG). In this work, we first show that all existing linear cellular automaton (CA) based pseudo-random number generators (PRNGs) are weak in the equidistribution characteristic. Then we propose a list of light-weight combined CA-based PRNGs with time spacing ($2 \leq s \leq 10$) using linear maximal length cellular automata of degree $31 \leq k \leq 128$ (close to computer word size). We show that these PRNGs achieve maximal period as well as satisfy the maximal equidistribution property. Finally, we show that these combined maximal length CA-based PRNGs pass almost all the empirical testbeds, with speed and performance comparable to the Mersenne Twister.

cs.CR↗

arXiv2026

Algebraic Characterization of Reversible First Degree Cellular Automata over $\mathbb{Z}_d$

There exists algorithms to detect reversibility of cellular automaton (CA) for both finite and infinite lattices taking quadratic time. But, can we identify a $d$-state CA rule in constant time that is always reversible for every lattice size $n\in \mathbb{N}$? To address this issue, this paper explores the reversibility properties of a subset of one-dimensional, $3$-neighborhood, $d$-state finite cellular automata (CAs), known as the first degree cellular automata (FDCAs) for any number of cells $(n\in \mathbb{N})$ under the null boundary condition. {In a first degree cellular automaton (FDCA), the local rule is defined using eight parameters. To ensure that the global transition function of $d$-state FDCA is reversible for any number of cells $(n\in \mathbb{N})$, it is necessary and sufficient to verify only three algebraic conditions among the parameter values. Based on these conditions, for any given $d$, one can synthesize all reversible FDCAs rules. Similarly, given a FDCA rule, one can check these conditions to decide its reversibility in constant time.

cs.FL↗

arXiv2025

A Search for Good Pseudo-random Number Generators : Survey and Empirical Studies

This paper targets to search so-called \emph{good} generators by doing a brief survey over the generators developed in the history of pseudo-random number generators (PRNGs), verify their claims and rank them based on strong empirical tests in same platforms. To do this, the genre of PRNGs developed so far are explored and classified into three groups -- linear congruential generator based, linear feedback shift register based and cellular automata based. From each group, the well-known widely used generators which claimed themselves to be `\emph{good}' are chosen. Overall $30$ PRNGs are selected in this way on which two types of empirical testing are done -- blind statistical tests with Diehard battery of tests, battery \emph{rabbit} of TestU01 library and NIST statistical test-suite as well as graphical tests (lattice test and space-time diagram test). Finally, the selected PRNGs are divided into $24$ groups and are ranked according to their overall performance in all empirical tests.

cs.CR↗

arXiv2024

Hierarchical Clustering using Reversible Binary Cellular Automata for High-Dimensional Data

This work proposes a hierarchical clustering algorithm for high-dimensional datasets using the cyclic space of reversible finite cellular automata. In cellular automaton (CA) based clustering, if two objects belong to the same cycle, they are closely related and considered as part of the same cluster. However, if a high-dimensional dataset is clustered using the cycles of one CA, closely related objects may belong to different cycles. This paper identifies the relationship between objects in two different cycles based on the median of all elements in each cycle so that they can be grouped in the next stage. Further, to minimize the number of intermediate clusters which in turn reduces the computational cost, a rule selection strategy is taken to find the best rules based on information propagation and cycle structure. After encoding the dataset using frequency-based encoding such that the consecutive data elements maintain a minimum hamming distance in encoded form, our proposed clustering algorithm iterates over three stages to finally cluster the data elements into the desired number of clusters given by user. This algorithm can be applied to various fields, including healthcare, sports, chemical research, agriculture, etc. When verified over standard benchmark datasets with various performance metrics, our algorithm is at par with the existing algorithms with quadratic time complexity.

cs.FL↗

arXiv2024

Gödel Number based Clustering Algorithm with Decimal First Degree Cellular Automata

In this paper, a decimal first degree cellular automata (FDCA) based clustering algorithm is proposed where clusters are created based on reachability. Cyclic spaces are created and configurations which are in the same cycle are treated as the same cluster. Here, real-life data objects are encoded into decimal strings using Gödel number based encoding. The benefits of the scheme is, it reduces the encoded string length while maintaining the features properties. Candidate CA rules are identified based on some theoretical criteria such as self-replication and information flow. An iterative algorithm is developed to generate the desired number of clusters over three stages. The results of the clustering are evaluated based on benchmark clustering metrics such as Silhouette score, Davis Bouldin, Calinski Harabasz and Dunn Index. In comparison with the existing state-of-the-art clustering algorithms, our proposed algorithm gives better performance.

cs.FL↗

arXiv2022

Affinity Classification Problem by Stochastic Cellular Automata

This work introduces a new problem, named as, affinity classification problem which is a generalization of the density classification problem. To solve this problem, we introduce temporally stochastic cellular automata where two rules are stochastically applied in each step on all cells of the automata. Our model is defined on 2-dimensional grid having affection capability. We show that this model can be used in several applications like modeling self-healing systems.

cs.FL↗

arXiv2019

Cellular Automata: Reversibility, Semi-reversibility and Randomness

In this dissertation, we study two of the global properties of 1-dimensional cellular automata (CAs) under periodic boundary condition, namely, reversibility and randomness. To address reversibility of finite CAs, we develop a mathematical tool, named reachability tree, which can efficiently characterize those CAs. A decision algorithm is proposed using minimized reachability tree which takes a CA rule and size n as input and verifies whether the CA is reversible for that n. To decide reversibility of a finite CA, we need to know both the rule and the CA size. However, for infinite CAs, reversibility is decided based on the local rule only. Therefore, apparently, these two cases seem to be divergent. This dissertation targets to construct a bridge between these two cases. To do so, reversibility of CAs is redefined and the notion of semi-reversible CAs is introduced. Hence, we propose a new classification of finite CAs -(1) reversible CAs, (2) semi-reversible CAs and (3) strictly irreversible CAs. Finally, relation between reversibility of finite and infinite CAs is established. This dissertation also explores CAs as source of randomness and build pseudo-random number generators (PRNGs) based on CAs. We identify a list of properties for a CA to be a good source of randomness. Two heuristic algorithms are proposed to synthesize candidate (decimal) CAs which have great potentiality as PRNGs. Two schemes tare developed o use these CAs as window-based PRNGs - (1) as decimal number generators and as (2) binary number generators. We empirically observe that in comparison to the best PRNG SFMT19937-64, average performance of our proposed PRNGs are slightly better. Hence, our decimal CAs based PRNGs are one of the best PRNGs today.

cs.FL↗

arXiv2019

On Finite $1$-Dimensional Cellular Automata: Reversibility and Semi-reversibility

Reversibility of a one-dimensional finite cellular automaton (CA) is dependent on lattice size. A finite CA can be reversible for a set of lattice sizes. On the other hand, reversibility of an infinite CA, which is decided by exploring the rule only, is different in its kind from that of finite CA. Can we, however, link the reversibility of finite CA to that of infinite CA? In order to address this issue, we introduce a new notion, named semi-reversibility. We classify the CAs into three types with respect to reversibility property -- reversible, semi-reversible and strictly irreversible. A tool, reachability tree, has been used to decide the reversibility class of any CA. Finally, relation among the existing cases of reversibility is established.

cs.FL↗

arXiv2018

Reversibility of d-State Finite Cellular Automata

This paper investigates reversibility properties of 1-dimensional 3-neighborhood d-state finite cellular automata (CAs) of length n under periodic boundary condition. A tool named reachability tree has been developed from de Bruijn graph which represents all possible reachable configurations of an n-cell CA. This tool has been used to test reversibility of CAs. We have identified a large set of reversible CAs using this tool by following some greedy strategies.

cs.FL↗

arXiv2018

A Survey of Cellular Automata: Types, Dynamics, Non-uniformity and Applications

Cellular automata (CAs) are dynamical systems which exhibit complex global behavior from simple local interaction and computation. Since the inception of cellular automaton (CA) by von Neumann in 1950s, it has attracted the attention of several researchers over various backgrounds and fields for modelling different physical, natural as well as real-life phenomena. Classically, CAs are uniform. However, non-uniformity has also been introduced in update pattern, lattice structure, neighborhood dependency and local rule. In this survey, we tour to the various types of CAs introduced till date, the different characterization tools, the global behaviors of CAs, like universality, reversibility, dynamics etc. Special attention is given to non-uniformity in CAs and especially to non-uniform elementary CAs, which have been very useful in solving several real-life problems.

cs.FL↗