相关论文: Abstract Geometrical Computation 11: Slanted Firin…

Signal machines form an abstract and idealised model of collision computing. Based on dimensionless signals moving on the real line, they model particle/signal dynamics in Cellular Automata. Each particle, or signal, moves at constant speed…

We construct a time-optimal quasi-solution of the firing mob synchronisation problem over finite, connected, and undirected multigraphs whose maximum degrees are uniformly bounded by a constant. It is only a quasi-solution because its…

A signal machine is an abstract geometrical model for computation, proposed as an extension to the one-dimensional cellular automata, in which discrete time and space of cellular automata is replaced with continuous time and space in signal…

The firing squad synchronization problem (FSSP) on cellular automata has been studied extensively for more than forty years, and a rich variety of synchronization algorithms have been proposed for not only one-dimensional arrays but…

Geometrical Computation as a new model of computation is the counterpart of Cellular Automata that has Turing computing ability. In this paper we provide an algorithm to simulate Alternating Turing Machine in the context of Signal Machine…

An Abstract Graph Machine(AGM) is an abstract model for distributed memory parallel stabilizing graph algorithms. A stabilizing algorithm starts from a particular initial state and goes through series of different state changes until it…

Complex systems in a wide variety of areas such as biological modeling, image processing, and language recognition can be modeled using networks of very simple machines called finite automata. Connecting subsystems modeled using finite…

A symmetry of a dynamical system is a map that transforms one trajectory to another trajectory. We introduce a new type of abstraction for hybrid automata based on symmetries. The abstraction combines different modes in a concrete automaton…

In this work, we investigate the computational aspects of asynchronous cellular automata (ACAs), a modification of cellular automata in which cells update independently, following an asynchronous schedule. We introduce flip automata…

We aim to generate fine-grained 3D geometry from large-scale sparse LiDAR scans, abundantly captured by autonomous vehicles (AV). Contrary to prior work on AV scene completion, we aim to extrapolate fine geometry from unlabeled and beyond…

We propose a novel generalized cellular automaton(GCA) model for discrete-time pulse-coupled oscillators and study the emergence of synchrony. Given a finite simple graph and an integer $n\ge 3$, each vertex is an identical oscillator of…

Number-conserving cellular automata are discrete dynamical systems that simulate interacting particles like e.g. grains of sand. In an earlier paper, I had already derived a uniform construction for all transition rules of one-dimensional…

We present different classes of solutions to the Firing Squad Synchronization Problem on networks of different shapes. The nodes are finite state processors that work at unison discrete steps. The networks considered are the line, the ring…

The searching for the stable patterns in the evolution of cellular automata is implemented using stochastic synchronization between the present structures of the system and its precedent configurations. For most of the known evolution rules…

This study introduces Skewed Fully Asynchronous Cellular Automata (SACA), a novel update scheme in cellular automata that updates the states of only two consecutive and adjacent cells, such as ci and ci+1, simultaneously at each time step.…

Prior work on Automatically Scalable Computation (ASC) suggests that it is possible to parallelize sequential computation by building a model of whole-program execution, using that model to predict future computations, and then…

We propose an efficient symbolic control synthesis algorithm for equivariant continuous-time dynamical systems to satisfy reach-avoid specifications. The algorithm exploits dynamical symmetries to construct lean abstractions to avoid…

With distributed computing and mobile applications, synchronizing diverging replicas of data structures is a more and more common problem. We use algebraic methods to reason about filesystem operations, and introduce a simplified definition…

Decentralized and asynchronous communications are two popular techniques to speedup communication complexity of distributed machine learning, by respectively removing the dependency over a central orchestrator and the need for…

We say that a Cellular Automata (CA) is coalescing when its execution on two distinct (random) initial configurations in the same asynchronous mode (the same cells are updated in each configuration at each time step) makes both…