Related papers: Generating Hard Problems of Cellular Automata
Cryptographic schemes using one-dimensional, three-neighbor cellular automata as a primitive have been put forth since at least 1985. Early results showed good statistical pseudorandomness, and the simplicity of their construction made them…
Cellular automata are a discrete dynamical system which models massively parallel computation. Much attention is devoted to computations with small time complexity for which the parallelism may provide further possibilities. In this paper,…
A transition from asymmetric to symmetric patterns in time-dependent extended systems is described. It is found that one dimensional cellular automata, started from fully random initial conditions, can be forced to evolve into complex…
Digital twin (DT) technology has a high potential to satisfy different requirements of the ever-expanding new applications. Nonetheless, the DT placement in wireless digital twin networks (WDTNs) poses a significant challenge due to the…
We consider the parity problem in one-dimensional, binary, circular cellular automata: if the initial configuration contains an odd number of 1s, the lattice should converge to all 1s; otherwise, it should converge to all 0s. It is easy to…
We study the dynamics of (synchronous) one-dimensional cellular automata with cyclical boundary conditions that evolve according to the majority rule with radius $ r $. We introduce a notion that we term cell stability with which we express…
This paper considers the discrete convexity of a cross-layer on-off transmission control problem in wireless communications. In this system, a scheduler decides whether or not to transmit in order to optimize the long-term quality of…
The Collatz, or 3x+1, Conjecture claims that for every positive integer n, there exists some k such that T^k(n)=1, where T is the Collatz map. We present three cellular automata (CA) that transform the global problem of mimicking the…
In this thesis, we focus on some of the NP-hard problems in control theory. Thanks to the converse Lyapunov theory, these problems can often be modeled as optimization over polynomials. To avoid the problem of intractability, we establish a…
We study the complexity of the Distributed Constraint Satisfaction Problem (DCSP) on a synchronous, anonymous network from a theoretical standpoint. In this setting, variables and constraints are controlled by agents which communicate with…
This paper studies joint spectrum allocation and user association in large heterogeneous cellular networks. The objective is to maximize some network utility function based on given traffic statistics collected over a slow timescale,…
The paper deals with finite-state Markov decision processes (MDPs) with integer weights assigned to each state-action pair. New algorithms are presented to classify end components according to their limiting behavior with respect to the…
Balliu et al. (DISC 2020) classified the hardness of solving binary labeling problems with distributed graph algorithms; in these problems the task is to select a subset of edges in a $2$-colored tree in which white nodes of degree $d$ and…
Let $G=(V,E)$ be a simple graph with $|V|=n$ nodes and $|E|=m$ links, a subset $K \subseteq V$ of \emph{terminals}, a vector $p=(p_1,\ldots,p_m) \in [0,1]^m$ and a positive integer $d$, called \emph{diameter}. We assume nodes are perfect…
A general mathematical method is presented for the systematic construction of coupled map lattices (CMLs) out of deterministic cellular automata (CAs). The entire CA rule space is addressed by means of a universal map for CAs that we have…
This brief paper: (1) Discusses strategies to generate random test cases that can be used to extensively test any Linear Distance Program (LDP) software. (2) Gives three numerical examples of input cases generated by this strategy that…
The Skolem problem and the related Positivity problem for linear recurrence sequences are outstanding number-theoretic problems whose decidability has been open for many decades. In this paper, the inherent mathematical difficulty of a…
One key challenge in Artificial Life is designing systems that display an emergence of complex behaviors. Many such systems depend on a high-dimensional parameter space, only a small subset of which displays interesting dynamics. Focusing…
We study discrete dynamical systems through the topological concepts of limit set, which consists of all points that can be reached arbitrarily late, and asymptotic set, which consists of all adhering values of orbits. In particular, we…
Fast shipping and efficient routing are key problems of modern logistics. Building on previous studies that address package delivery from a source node to a destination within a graph using multiple agents (such as vehicles, drones, and…