cellular automata

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Self-verifying cellular automata

Self-verifying cellular automata

Abstract.We study the computational capacity of self-verifying cellular automata with an em- phasis on one-way information flow (SVOCA). A self-verifying device is a nondeterministic device whose nondeterminism is symmetric in the following sense. Each computation path can give one of the answers yes, no, or do not know. For every input word, at least one computation path must give either the answer yes or no, and the answers given must not be contradictory. We show that realtime SVOCA are strictly more powerful than realtime deterministic one-way cellular automata, since they can accept non-semilinear unary languages. It turns out that SVOCA can strongly be sped-up from lineartime to realtime. They are even capable to simulate any lineartime computa- tion of deterministic two-way cellular automata. Closure properties and decidability problems are considered as well.
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Cellular automata modeling of propagation and absorption of acoustic waves in impedance tube

Cellular automata modeling of propagation and absorption of acoustic waves in impedance tube

Figure 10 – Sound Absorption Coefficient Curves of Sample 5 Figures 7 to 10 show that by introducing the parameters in Table 1 into the presented Cellular Automata model, the sound absorption coefficients of materials at 125dB can be obtained. It can be found out that as a whole, the simulated and experimental results fit quite well, but there still exists relatively large errors at some frequencies.

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Efficient universal pushdown cellular automata and their application to complexity

Efficient universal pushdown cellular automata and their application to complexity

Abstract. In order to obtain universal classical cellular automata an in nite space is required. Therefore, the number of required processors depends on the length of input data and, additionally, may increase during the computation. On the other hand, Turing machines are universal devices which have one processor only and ad- ditionally an in nite storage tape.

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Cellular automata model on AIS-based for variable two-way waterway

Cellular automata model on AIS-based for variable two-way waterway

forward the concept of “Tidal Reversible Channel”, but the effect of changing lane hasn’t been solved and discussed in their works. For the virtues of discretization in space, time and state, and easy implementation in algorithm on a computer, cellular automata (CA) model has been widely developed and used in traffic flow study. Feng (2013) presented a ship traffic CA model which took marine characteristics into account. In order to simulate ship traffic from the micro view and reveal the effect of lane- changing to waterway transit capacity, the paper establishes a variable two-way waterway CA model on the basis of Feng (2013). The work can be applied to the optimization, organization and management of ship traffic.
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Automata 2013 : exploratory papers ; 19th International Workshop on Cellular Automata and Discrete Complex Systems, Giessen, Germany, Sept. 17-19, 2013

Automata 2013 : exploratory papers ; 19th International Workshop on Cellular Automata and Discrete Complex Systems, Giessen, Germany, Sept. 17-19, 2013

Cellular Automata (CAs) present an attractive and effective modeling tech- nique for a variety of problems. In order to use CAs in any practical mod- eling task, one needs to understand the underlying rules, relevant to the given phenomenon, and translate them into a CA local rule. Additionally, the state space, tessellation and neighborhood structure need to be pinned down beforehand. This narrows the application area for CAs, since there are problems for which only the initial and final states are known (e.g. [2,13,14]). Such problems motivate the research towards automated CA identification. Various methods have been used, including genetic algorithms [6, 11, 12, 15], genetic programming [3, 4, 10], gene expression programming [7], ant intel- ligence [9], machine learning [5] as well as direct search/construction ap- proaches [1, 16–18].
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Should big cities grow? Scenario-based cellular automata urban growth modeling and policy applications

Should big cities grow? Scenario-based cellular automata urban growth modeling and policy applications

A B S T R A C T The formation of ‘Urban Networks’ has become a wide-spread phenomenon around the world. In the study of metropolitan regions, there are competing or diverging views about management and control of environmental and land-use factors as well as about scales and arrangements of settlements. Especially in China, these matters alongside of regulatory aspects, infrastructure applications, and resource allocations, are important because of population concentrations and the overlapping of urban areas with other land resources. On the other hand, the increasing sophistication of models operating on iterative computational power and widely-available spatial information and analytical techniques make it possible to simulate and investigate the spatial distribution of urban territories at a regional scale. This research applies a scenario-based Cellular Automata model to a case study of the Changjiang Delta Region, which produces useful and predictive scenario-based projections within the region, using quantitative methods and baseline conditions that address issues of regional urban development. The contribution of the research includes the improvement of computer simulation of urban growth, the application of urban form and other indices to evaluate complex urban conditions, and a heightened understanding of the performance of an urban network in the Changjiang Delta Region composed of big, medium, and small-sized cities and towns.
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Lane-changing rules in two-lane traffic simulation using cellular automata Part. II: A systematic approach

Lane-changing rules in two-lane traffic simulation using cellular automata Part. II: A systematic approach

We start out from real world data ~Sec. II!, followed by a short review of traditional approaches to this problem in traf- fic science ~Sec. III!. Section IV outlines our approach. In Secs. V–VII we describe simulation results with different rules. Section VIII looks closer into the mechanism of flow breakdown near maximum flow in the two-lane models. Sec- tion IX is a discussion of our work, followed by a section showing how other multilane models for cellular automata fit into our scheme ~Sec. X!. The paper concludes with a short summary ~Sec. XII!.

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Of cells and cities: a comparative Econometric and Cellular Automata approach to Urban Growth Modeling

Of cells and cities: a comparative Econometric and Cellular Automata approach to Urban Growth Modeling

3.4 The CA application for urban growth While Cellular Automata had their origins in the fifties in an attempt to compute the relationship of computing machines and human nervous sys- tems [8], they later developed into a more complex attempt of understanding spatial interactions between agents such as Conway’s ‘Game of Life’ [4]. De- velopment of planning, and the integration of spatial explicit dynamics [?], were a further background to understand the growth of cities with Cellu- lar Automata [12]. A new era for Cellular Automata had emerged, taking advantage of geo-information as tools for regional decision support systems [9] and offering an insight on the discrete future dynamics of cities [1]. The discrete functions are mostly carried out through five dimension with which the cellular automata interacts [?]: (i) lattice of cells (agglomeration of indi- vidual cell neighborhood), (ii) state of cells (e.g. urban or non-urban), (iii) time interval (spatiotemporal datasets of urban measurement), (iv) transi- tion rules (defining the capacity of a cell to change from one state to another given a set of rules) and (v) neighborhood.
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The urban sprawl dynamics: does a neural network understand the spatial logic better than a cellular automata?

The urban sprawl dynamics: does a neural network understand the spatial logic better than a cellular automata?

Among them some applications, mainly based on Cellular Automata, have opened more promising directions for the goal: Clarke, Hoppen and Gaydos (1997) modelled the historical development of San Francisco area; (Batty, Xie and Sun 1999; Wu 1998) built several urban models and in particular a model on the residential development in the fringe of Buffalo; Portugali, Benenson and Omer (1994; 1997) have focused their research on models of socio-spatial segregation; the many contributions of Engelen, Ulje and White (White and Engelen 2000) have produced several CA based models with integration of several economic theories.
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Basic discrete concepts for simulating natural systems : an approach to
describe diffusion and chemical kinetics using a combination of graphs and cellular automata

Basic discrete concepts for simulating natural systems : an approach to describe diffusion and chemical kinetics using a combination of graphs and cellular automata

It has often been stated that cellular automata are a way to simulate complex phenom- ena with a simple set of assumptions [Adami, 1998]. In many areas of science cellular automata are used to simulate complex and dynamic systems [Wolfram, 2002]. For ex- ample R EINHARD K OENIG uses cellular automata to simulate the development of cities on a large scale [Koenig, 2012]. But small scale applications are equally as feasible. S TANISLAW U LAM postulated the abstract idea of cellular automata while studying the growth of crystals. The scale of the atomic units in the automata should be chosen carefully, but can be chosen freely. In the field of cellular biology it has been suggested, that cellular automata (dynamic cellular automata) can be used to simulate chemical in- teractions and the progression of biochemical pathways [Wishart et al., 2005]. But until now, systems using cellular automata have been treated shabbily in the different fields of biology.
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Cellular automata with sparse communication

Cellular automata with sparse communication

Abstract. We investigate cellular automata whose internal inter-cell communication is bounded. The communication is quantitatively measured by the number of uses of the links between cells. Bounds on the sum of all communications of a computation as well as bounds on the maximal number of communications that may appear between each two cells are considered. It is shown that even the weakest non-trivial device in question, that is, one-way cellular automata where each two neighboring cells may communicate constantly often only, accept rather complicated languages. We investigate the computational capacity of the devices in question and prove an infinite strict hierarchy depending on the bound on the total number of communications during a computation. Despite their sparse communi- cation even for the weakest devices, by reduction of Hilbert’s tenth problem undecidability of several problems is derived. Finally, the question whether a given real-time one-way cel- lular automaton belongs to the weakest class is shown to be undecidable. This result can be adapted to answer an open question posed in [Vollmar, R.: Zur Zustands¨anderungskom- plexit¨at von Zellularautomaten. In: Beitr¨age zur Theorie der Polyautomaten—zweite Folge, Braunschweig (1982) 139–151 (in German)].
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Cellular Automata on Group Sets

Cellular Automata on Group Sets

Among others the following questions are investigated: Which prop- erties of the local transition function are necessary and sufficient for the global transition function to be equivariant under translations (com- mute with the induced action on global configurations)? Is the com- position of global transition functions itself a global transition function and if it is, of which cellular automaton (see chapter 1)? Can global transition functions be pulled or pushed onto quotients, products, re- strictions, and extensions of their cell spaces and if they can, how do the corresponding cellular automata change (see chapter 2)? Are global transition functions for a well chosen topology (or uniformity) on the set of global configurations characterised by equivariance under transla- tions and (uniform) continuity? Is the inverse of a bijective global tran- sition function itself a global transition function (see chapter 3)? On which cell spaces are global transition functions surjective if and only if they are pre-injective (see chapter 5)? How can such cell spaces be char- acterised (see chapter 4)? Can these questions be answered for restric- tions of global transition functions to translation invariant and compact subsets of the set of global configurations (see chapters 6 and 7)? Is there an optimal-time algorithm for the firing squad synchronisation problem on (continuous) graph-shaped cell spaces (see chapter 8)? equivariance and composition
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Identification of cellular automata: theoretical remarks

Identification of cellular automata: theoretical remarks

As far as stochastic Cellular Automata are concerned, we might compare this kind of systems with another one: chess matches, which can be structured in the same way. First, let us analyze what aspects are in common: • cells in Cellular Automaton space are the same as chess on a chessboard; the state of every piece is its position. Even if it would seem more natural comparing cells with chessboard squares, these ones do not change, they only host different pieces without being involved in any kind of changing. On the contrary pieces, moving on the chessboard, change their state.
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On time computability of functions in one-way cellular automata

On time computability of functions in one-way cellular automata

Ç UVS7IMQ*S,XVMb7b=MYu–gYK WK-^TYXdUVSp\n KDOoT \jTYb b7Q*ODKtS7I*TS Udb=PaK-^ UVM[c*UdLh ‘ W„S7IK L-TYbeK]UVSwUdbtQ*XVS7UdOTSeK XV\vP?K-^UVMkc*UdLDu¨MY^FTYXdX ¬#û¬AÍDUdWrS7IKu'MXdXVM [r]

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Modelling of Rain Radar Image Space-Time Dynamics with Cellular Automata

Modelling of Rain Radar Image Space-Time Dynamics with Cellular Automata

This  work  focuses  on  the  presentation  of  an  approach  for  assessing  and  characterizing  rain  cell  dynamics  based  exclu­  sively  on  the  analysis  of  the  radar  reflectivity  images,  and  without  an  a  priori  assumption  on  the  structure  of  rain  cells.  This  research  has  been  addressed by  using cellular automata.  Rain  cell  dynamics  are  simulated  by  using  probabilistic  CA  rules  and  tracking  vectors,  which  indicate  a  global  advection  direction and velocity. The proposed method seems to capture  with fairly good accuracy the dynamical behavior of rain cells  in the studied examples. Moreover, this method offers a global  approach  to  determine  the  motion  for  rain  cells  of  WRIs.  A  straightforward linkage between rain cell dynamics in terms of 
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Real-time language recognition by alternating cellular automata

Real-time language recognition by alternating cellular automata

w UK_a_`pm_aY\jei[2YPWoUKet†;T2^aWlT Y\jdU']yfRpmk2VUKbifbdTVU!_cUZhzbsvYPkm pmkŸ]„fRp2kmVUK bif?bdTVU'jl^cnRTŸbÆx Y\jdUƒU$bŸpm^a}7YP_cUKkŸbŽbif•bdTVUƒfPjl^cnR^akmYP_XqtfmUK_Xed^ak2WoU[r]

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Land Use Dynamics: a Cellular Automata

Land Use Dynamics: a Cellular Automata

3. Validation The validation of the cellular automaton is understood as the assessment of how close the simulations get to reality. Simulating the real behaviour of a city is a complex and arduous task; it is necessary to keep in mind the different factors that intervene in the evolution of a territory. The most important factor is human intervention as humans model the urban-natural system "as they please" according to their own needs. It should also be noted that the cellular automaton created here does not distinguish between cells, that is, it does not know which cells will undergo a transformation from one map and the successive map. Since we did not apply spatial constraints all the cells are in the same conditions, that is, they all have the same probability of undergoing a transformation.
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Systems of Parallel Communicating Restarting Automata

Systems of Parallel Communicating Restarting Automata

At first, we give some preliminaries and basic notations in Section 2 that are used within this work. In Section 3, the most popular representatives of parallel communicating systems are presented giving their definitions, examples, and results that can be found in the literature. This should give a first impression of the structure, the used communication protocols, the principles of operation, and their properties. We will use these explanations sometimes for the purpose of comparisons. Section 4 gives a short overview of the model of the restarting au- tomaton, which is used as the basic device for the systems investigated in Section 5. Section 5 is the main part of this work. There, PCRA systems are introduced and investigated. At first, these systems are defined and explained. The commu- nication protocol is presented and important differences to the systems given in Section 3 are emphasized. Moreover, a first detailed example is given. Then, after defining some more useful technical material in Subsection 5.1, we will see some other example systems for various well-known formal languages in Subsection 5.2. More examples are given throughout the further subsections whenever it seems helpful. Afterwards, we consider properties that are typically interesting for sys- tems of parallel communicating components. In Subsection 5.3, we investigate an essential property of the communication, namely whether a centralized communi- cation structure is a restriction for the computational power of our systems. In Subsection 5.4, we study the effect of the ‘nonforgetting property’ on our systems. For single restarting automata (that are in general ‘forgetting’), this property is an extension that in fact increases the computational power. In Subsection 5.5, we show some closure properties for language classes that are characterized by our systems. We will see that some of them are so-called ‘abstract families of languages’ (AFLs). Then, in Section 5.6 we investigate the computational power of PCRA systems. In this context our systems are compared with single restarting automata and with other types of parallel communicating systems, and we obtain some correlations to popular complexity classes. Moreover, systems of shrinking restarting automata are considered there. In Section 5.7 it is shown that, although the word problem is decidable in quadratic time for deterministic systems and in exponential time for nondeterministic systems, many other questions are not de- cidable even for systems with weak types of restarting automata as components.
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Non-structural subtype entailment in automata theory

Non-structural subtype entailment in automata theory

A similar automata theoretic approach is already known for satisfiablity but not for entailment [9, 16]. Our extension to entailment yields a new characterization of NSSE that uses regular expressions and word equations [11, 17]. Word equations raise the real difficulty behind NSSE since they spoil the usual pumping arguments from automata theory. They also clarify why NSSE differs so significantly from seemingly similar entailment problems [13, 14].

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Learning One-Clock Timed Automata

Learning One-Clock Timed Automata

In her seminal work [ 10 ], Angluin introduced the L ∗ algorithm for learning a regu- lar language from queries and counterexamples within a query-answering framework. The Angluin-style learning therefore is also termed active learning or query learning, which is distinguished from passive learning, i.e., generating a model from a given data set. Following this line of research, an increasing number of efficient active learning methods (cf. [ 38 ]) have been proposed to learn, e.g., Mealy machines [ 34 , 30 ], I/O au- tomata [ 2 ], register automata [ 25 , 1 , 15 ], nondeterministic finite automata [ 12 ], B¨uchi automata [ 19 , 28 ], symbolic automata [ 29 , 18 , 11 ] and Markov decision processes [ 36 ], to name just a few. Full-fledged libraries, tools and applications are also available for automata-learning tasks [ 13 , 27 , 20 , 21 ].
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