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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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.

Abstract. In order to obtain universal classical **cellular** **automata** an innite 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 innite storage tape.

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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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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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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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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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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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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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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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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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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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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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w UK_a_`pm_aY\jei[2YPWoUKet;T2^aWlT Y\jdU']yfRpmk2VUKbifbdTVU!_cUZhzbsvYPkm pmk]fRp2kmVUK bif?bdTVU'jl^cnRTbÆx Y\jdUU$bpm^a}7YP_cUKkbbifbdTVUfPjl^cnR^akmYP_XqtfmUK_Xed^ak2WoU[r]

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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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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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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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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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