Related papers: Growing Random Strings in CA
We develop and analyze a simple cellular automaton (CA) model that reproduces the main properties of the evolution of soft X-ray coronal loops. We are motivated by the observation that these loops evolve in three distinguishable phases that…
The successive discrete structures generated by a sequential algorithm from random input constitute a Markov chain that may exhibit long term dependence on its first few input values. Using examples from random graph theory and search…
Discrete diffusion models are a class of generative models that produce samples from an approximated data distribution within a discrete state space. Often, there is a need to target specific regions of the data distribution. Current…
Internet communication systems involving cryptography and data hiding often require billions of random numbers. In addition to the speed of the algorithm, the quality of the pseudo-random number generator and the ease of its implementation…
We search for regularities in the sequences of numbers of preimages for elementary cellular automata. For 46 out of 88 "minimal" rules, we find recognizable patterns, usually in the form of second order recurrence equations with constant…
Cellular automata (CA) is an important modelling paradigm for complex systems. In the design of cellular automata, the most difficult task is to find the transformation rules that describe the temporal evolution or pattern of a modelled…
Wolfram has provided a qualitative classification of cellular automata(CA) rules according to which, there exits a class of CA rules (called Class 4) which exhibit complex pattern formation and long-lived dynamical activity (long…
Evolving one-dimensional cellular automata (CAs) with genetic algorithms has provided insight into how improved performance on a task requiring global coordination emerges when only local interactions are possible. Two approaches that can…
Cellular automata are discrete dynamical systems that consist of patterns of symbols on a grid, which change according to a locally determined transition rule. In this paper, we will consider cellular automata that arise from polynomial…
We present a family of one-dimensional cellular automata modeling the diffusion of an innovation in a population. Starting from simple deterministic rules, we construct models parameterized by the interaction range and exhibiting a…
Cellular automata are one-dimensional arrays of interconnected interacting finite automata. We investigate one of the weakest classes, the real-time one-way cellular automata, and impose an additional restriction on their inter-cell…
In this paper we have proposed a new test for pixel randomness using non-parametric method in statistics. In order to validate this new non-parametric test we have designed an encryption scheme based on 2D cellular automata. The strength of…
In this paper, we mainly study linear one-dimensional and two-dimensional elementary cellular automata that generate symmetrical spatio-temporal patterns. For spatio-temporal patterns of cellular automata from the single site seed, we…
The evolution of random undirected graphs by the clustering attachment (CA) both without node and edge deletion and with uniform node or edge deletion is investigated. Theoretical results are obtained for the CA without node and edge…
This paper designs an efficient two-class pattern classifier utilizing asynchronous cellular automata (ACAs). The two-state three-neighborhood one-dimensional ACAs that converge to fixed points from arbitrary seeds are used here for pattern…
Sequence theories are an extension of theories of strings with an infinite alphabet of letters, together with a corresponding alphabet theory (e.g. linear integer arithmetic). Sequences are natural abstractions of extendable arrays, which…
Long samples of text from neural language models can be of poor quality. Truncation sampling algorithms--like top-$p$ or top-$k$ -- address this by setting some words' probabilities to zero at each step. This work provides framing for the…
Cellular automata are discrete and computational models thatcan be shown as general models of complexity. They are used in varied applications to derive the generalized behavior of the presented model. In this paper we have took one such…
Lattice gas cellular automata (Lgca) are particular cellular automata that imitate the behavior of par- ticles moving on a lattice. We used a particular set of Lgca rules, called hpp, to mix bits in data blocks and obtain a symmetric…
An interesting thread in the research of Boolean functions for cryptography and coding theory is the study of secondary constructions: given a known function with a good cryptographic profile, the aim is to extend it to a (usually larger)…