scholarly journals ASYNCHRONOUS AUTOMATA NETWORKS CAN EMULATE ANY SYNCHRONOUS AUTOMATA NETWORK

2004 ◽  
Vol 14 (05n06) ◽  
pp. 719-739 ◽  
Author(s):  
CHRYSTOPHER L. NEHANIV
Keyword(s):  
Cellular Automaton ◽  
Local Time ◽  
Input Sequence ◽  
Clock Signal ◽  
Global State ◽  
Time Step ◽  
Open Problems ◽  
Locally Finite ◽  
Asynchronous Automata ◽  
Automata Network

We show that any locally finite automata network [Formula: see text] with global synchronous updates can be emulated by another one [Formula: see text], whose structure derives from that of [Formula: see text] by a simple construction, but whose updates are made asynchronously at its various component automata (e.g. possibly randomly or sequentially, with or without possible simultaneous updates at different nodes). By "emulation", we refer to the existence of a spatial-temporal covering 'local time', allowing one to project the behavior of [Formula: see text] continuously onto that of [Formula: see text]. We also show the existence of a spatial-temporal section of the asynchronous automata network's behavior which completely determines the synchronous global state of [Formula: see text] at every time step.We give the construction of the asynchronous automata network, establish its freedom from deadlocks, and construct local time functions and spatial-temporal sections relating any posssible behavior of [Formula: see text] to the single corresponding behavior of [Formula: see text] on a given input sequence starting from a given initial global state.This establishes that the behavior of any locally finite synchronous automata network actually can be emulated without the restriction of synchronous update, freeing us from the need of a global clock signal. Local information is sufficient to guarantee that the synchronous behavior of [Formula: see text] is completely determined by any asynchronous behavior of [Formula: see text] starting from a corresponding global state and given the same input sequence as [Formula: see text]. Moreover, the relative passage of corresponding local time at any two nodes in [Formula: see text] is bounded in a simple way by approximately one-third of the distance between them.As corollaries, any synchronous generalized cellular automaton or synchronous cellular automaton can be emulated by an asynchronous one of the same type.Implementation aspects of these asynchronous automata are also discussed, and open problems and research directions are indicated.

scholarly journals A 2-DIMENSIONAL CELLULAR AUTOMATON FOR AGENTS MOVING FROM ORIGINS TO DESTINATIONS

2005 ◽  
Vol 16 (12) ◽  
pp. 1849-1860 ◽  
Author(s):  
NAJEM MOUSSA
Keyword(s):  
Cellular Automaton ◽  
Cluster Size ◽  
Bimodal Distribution ◽  
Minimal Distance ◽  
Time Step ◽  
Neighbor Site ◽  
Model Dynamics ◽  
Long Time ◽  
Freely Moving ◽  
Small Clusters

We develop a two-dimensional cellular automaton (CA) as a simple model for agents moving from origins to destinations. Each agent moves towards an empty neighbor site corresponding to the minimal distance to its destination. The stochasticity or noise (p) is introduced in the model dynamics, through the uncertainty in estimating the distance from the destination. The friction parameter "μ" is also introduced to control the probability that movement of all involved agents to the same site (conflict) is denied at each time step. This model displays two states; namely the freely moving and the jamming state. If μ is large and p is low, the system is in the jamming state even if the density is low. However, if μ is large and p is high, a freely moving state takes place whenever the density is low. The cluster size and the travel time distributions in the two states are studied in detail. We find that only very small clusters are present in the freely moving state, while the jamming state displays a bimodal distribution. At low densities, agents can take a very long time to reach their destinations if μ is large and p is low (jamming state); but long travel times are suppressed if p becomes large (freely moving state).

scholarly journals Local time stepping with the discontinuous Galerkin method for wave propagation in 3D heterogeneous media

Geophysics ◽  
2013 ◽  
Vol 78 (3) ◽  
pp. T67-T77 ◽  
Author(s):  
Sara Minisini ◽  
Elena Zhebel ◽  
Alexey Kononov ◽  
Wim A. Mulder
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Discontinuous Galerkin ◽  
Local Time ◽  
Heterogeneous Media ◽  
Small Scale ◽  
Time Step ◽  
Element Discretization ◽  
Time Stepping ◽  
Local Time Stepping

Modeling and imaging techniques for geophysics are extremely demanding in terms of computational resources. Seismic data attempt to resolve smaller scales and deeper targets in increasingly more complex geologic settings. Finite elements enable accurate simulation of time-dependent wave propagation in heterogeneous media. They are more costly than finite-difference methods, but this is compensated by their superior accuracy if the finite-element mesh follows the sharp impedance contrasts and by their improved efficiency if the element size scales with wavelength, hence with the local wave velocity. However, 3D complex geologic settings often contain details on a very small scale compared to the dominant wavelength, requiring the mesh to contain elements that are smaller than dictated by the wavelength. Also, limitations of the mesh generation software may produce regions where the elements are much smaller than desired. In both cases, this leads to a reduction of the time step required to solve the wave propagation and significantly increases the computational cost. Local time stepping (LTS) can improve the computational efficiency and speed up the simulation. We evaluated a local formulation of an LTS scheme with second-order accuracy for the discontinuous Galerkin finite-element discretization of the wave equation. We tested the benefits of the scheme by considering a geologic model for a North-Sea-type example.

Pseudorandom Number Generators Based on Asynchronous Cellular Automata and Cellular Automata With Inhomogeneous Cells

2017 ◽  
pp. 127-138
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Local State ◽  
Active Cell ◽  
State Function ◽  
Local Function ◽  
Time Step ◽  
Random Number Generators ◽  
Asynchronous Cellular Automata ◽  
A Cell

The sixth chapter deals with the construction of pseudo-random number generators based on a combination of two cellular automata, which were considered in the previous chapters. The generator is constructed based on two cellular automata. The first cellular automaton controls the location of the active cell on the second cellular automaton, which realizes the local state function for each cell. The active cell on the second cellular automaton is the main cell and from its output bits of the bit sequence are formed at the output of the generator. As the first cellular automaton, an asynchronous cellular automaton is used in this chapter, and a synchronous cellular automaton is used as the second cellular automaton. In this case, the active cell of the second cellular automaton realizes another local function at each time step and is inhomogeneous. The algorithm for the work of a cell of a combined cellular automaton for implementing a generator and its hardware implementation are presented.

Research on the single-host parallel computing with the local time step scheme for modeling of hydro-sediment-morphodynamic processes

2021 ◽  
Author(s):  
Zixiong Zhao ◽  
Peng Hu ◽  
Wei Li ◽  
Zhixian Cao ◽  
Zhiguo He
Keyword(s):  
Parallel Computing ◽  
Local Time ◽  
High Performance ◽  
Water Model ◽  
Time Step ◽  
Time Stepping ◽  
Computational Performance ◽  
Cuda Programming ◽  
Single Host ◽  
Algorithmic Acceleration

<p>In recent decades, computational hydraulics and sediment modelling have a great development due to compute technology. Applying a finite-volume Godunov-type hydrodynamic shallow water model with hydro-sediment-morphodynamic processes, this work demonstrates and analysis the ability of single-host parallel computing technology with algorithmic acceleration technology. This model is implemented for high-performance computing using the NVIDIA’s Compute Unified Device Architecture (CUDA) programming framework, using a domain decomposition technique and across multiple cores through an efficient implementation of the Open Multi-Processing (Open MP) architecture, and using an algorithmic acceleration technology named local time stepping scheme (LTS), which is capable of obtain much efficiency improvement via different time step sizes for different grid sizes. The model is applied for three cases, through which we compare the effectiveness of CPU, Open MP, Open MP+LTS, CUDA, and CUDA+LTS, demonstrating high computational performance across CUDA+LTS which can lead to speedups of 40 times with respect to CPU and high-precision results across CUDA +LTS.</p><p>KEY WORDS: Hydro-sediment-morphological modeling; local time step; Open MP; CUDA.</p>

scholarly journals A Generalized Local Time-Step Scheme for Efficient FVTD Simulations in Strongly Inhomogeneous Meshes

2004 ◽  
Vol 52 (3) ◽  
pp. 1067-1076 ◽  
Author(s):  
C. Fumeaux ◽  
D. Baumann ◽  
P. Leuchtmann ◽  
R. Vahldieck
Keyword(s):  
Local Time ◽  
Time Step
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