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Showing papers on "Continuous automaton published in 2012"


Journal ArticleDOI
Jarkko Kari1
TL;DR: A one-dimensional solution that is based on multiplying numbers by a suitable constant is described and the automaton to multiply by constant 3/2 is shown to be related to some difficult open questions in number theory.

34 citations


Journal ArticleDOI
TL;DR: A modified traffic CA is proposed that washes out finite islands in the same way as the Gacs, Kurdyumov and Levin automaton, but is also guaranteed to converge to a uniform configuration on rings of odd size.
Abstract: The density classification task asks to design a cellular automaton that converges to the uniform configuration that corresponds to the state that is in majority in the initial configuration. We investigate connections of this problem to state-conserving cellular automata. We propose a modified traffic CA that washes out finite islands in the same way as the Gacs, Kurdyumov and Levin automaton, but is also guaranteed to converge to a uniform configuration on rings of odd size. We find experimentally several good classifiers that are close to state-conserving cellular automata, and we observe that the best performing known density classifier by Wolz and de Oliveira is only a simple swap away from a state-conserving automaton.

22 citations


Journal ArticleDOI
TL;DR: In this paper, a three-level description of cellular automata is presented, motivated by the approach of kinetic theory of gases, and a simple domino cellular automaton with avalanches is constructed.
Abstract: Motivated by the approach of kinetic theory of gases, a three-level description (microscopic, mesoscopic and macroscopic) of cellular automaton is presented. To provide an analytical treatment, a simple domino cellular automaton with avalanches is constructed. Formulas concerning exact relations for density, clusters, avalanches and other parameters in a stationary state are derived. Some relations approximately valid for deviations from the stationary state are found, and the adequate Ito equation is constructed. It provides the time evolution description of the density on the macroscopic level. The results support an idea of application of the Ito equation to some natural time series.

20 citations


Journal ArticleDOI
TL;DR: Motzkin numbers are derived from a special case of Random Domino Automaton – recently proposed a slowly driven system being a stochastic toy model of earthquakes and a generalisation of 1D Drossel–Schwabl forest-fire model.

18 citations


Book ChapterDOI
01 Jan 2012
TL;DR: This paper revisits label, a technique to satisfy the synthesis conditions through renaming of problematic labels, and for the first time, the problem is formally characterized and its optimality addressed.
Abstract: The theory of regions was introduced by Ehrenfeucht and Rozenberg in the early nineties to explain how to derive (synthesize) an event-based model (e.g., a Petri net) from an automaton. To be applicable, the theory relies on stringent conditions on the input automaton. Although some relaxation on these restrictions was done in the last decade, in general not every automaton can be synthesized while preserving its behavior. A crucial step for a non-synthesizable automaton is to transform it in order to satisfy the synthesis conditions. This paper revisits label splitting, a technique to satisfy the synthesis conditions through renaming of problematic labels. For the first time, the problem is formally characterized and its optimality addressed. Some extensions and applications of the label splitting are presented to illustrate the significance of this technique.

16 citations


Book ChapterDOI
Jarkko Kari1
14 Aug 2012
TL;DR: It is remarked that the automaton F×3 that multiplies by 3 can be slightly modified to simulate the Collatz function and several open problems concerning pattern generation by cellular automata are state.
Abstract: We discuss one-dimensional reversible cellular automata F×3 and F×3/2 that multiply numbers by 3 and 3/2, respectively, in base 6. They have the property that the orbits of all non-uniform 0-finite configurations contain as factors all finite words over the state alphabet {0,1,…,5}. Multiplication by 3/2 is conjectured to even have an orbit of 0-finite configurations that is dense in the usual product topology. An open problem by K. Mahler about Z-numbers has a natural interpretation in terms the automaton F×3/2. We also remark that the automaton F×3 that multiplies by 3 can be slightly modified to simulate the Collatz function. We state several open problems concerning pattern generation by cellular automata.

15 citations


Patent
Mehryar Mohri1, Michael Riley1
30 Jul 2012
TL;DR: In this article, a potential for each state of an input automaton to a set of destination states of a weighted automaton is first determined, and then the N-best paths are found in the result of an on-the-fly determinization of the input automata.
Abstract: Systems and methods for identifying the N-best strings of a weighted automaton. A potential for each state of an input automaton to a set of destination states of the input automaton is first determined. Then, the N-best paths are found in the result of an on-the-fly determinization of the input automaton. Only the portion of the input automaton needed to identify the N-best paths is determinized. As the input automaton is determinized, a potential for each new state of the partially determinized automaton is determined and is used in identifying the N-best paths of the determinized automaton, which correspond exactly to the N-best strings of the input automaton.

14 citations


Journal ArticleDOI
TL;DR: Among the classes of automata, the class of single bottom automata is considered, and the composition of a single loop automaton and a strongly connected automaton together with its automorphism group is provided.

13 citations


Journal ArticleDOI
TL;DR: The computability of NCCAs in which the pairwise number flows are performed at fully asynchronous timings is explored, and the Brownian-like flow of the numbers allows for efficient embedding of logic circuits into the novel asynchronous NCCA.

13 citations


Journal ArticleDOI
TL;DR: This survey overviews the past studies on RCAs, and can see even very simple RCAs have computation-universality.
Abstract: A reversible cellular automaton (RCA) is a subclass of a CA such that its global function is injective. It is considered as an abstract spatiotemporal model of a reversible physical system. In spite of the strong constraint of reversibility, an RCA has a high ability of information processing. In this survey, we overview the past studies on RCAs, and discuss how computing is performed in them. We can see even very simple RCAs have computation-universality.

8 citations


Journal ArticleDOI
TL;DR: A graph-theoretic approach is presented to test the minimality of a deterministic automaton and it is shown that different minimality conditions of an automaton can be characterized in graph- theoretic terms.

Book ChapterDOI
03 Jul 2012
TL;DR: This work proposes a linear pseudo-minimization algorithm specific to Aho-Corasick automata, which produces an automaton whose size is between the size of the input automaton and the one of its associated minimal automaton.
Abstract: A classical construction of Aho and Corasick solves the pattern matching problem for a finite set of words X in linear time, where the size of the input X is the sum of the lengths of its elements. It produces an automaton that recognizes A*X, where A is a finite alphabet, but which is generally not minimal. As an alternative to classical minimization algorithms, which yields a ${\mathcal O}(n\log n)$ solution to the problem, we propose a linear pseudo-minimization algorithm specific to Aho-Corasick automata, which produces an automaton whose size is between the size of the input automaton and the one of its associated minimal automaton. Moreover this algorithm generically computes the minimal automaton: for a large variety of natural distributions the probability that the output is the minimal automaton of A*X tends to one as the size of X tends to infinity.

Dissertation
03 Feb 2012
TL;DR: The maxmin-m model is proposed as a suitable model for the asynchronous computation of cellular automata and its complexity is empirically shown to obey a bell form as a function of m (where m ranges from 1 to n).
Abstract: This thesis aims to better represent a framework for asynchrony. Traditional asynchronous models, particularly those used to simulate cellular automata, have used stochasticity or randomness to generate update times. We claimthat, while they may make good representations of their application, such asynchronousmethods rid themodel of the essence of interesting asynchronous processes. Thus, we attempt to better harness the aspects internal to the decision process of such discretely dynamic cells as those in cellular automata.We propose the maxmin-m model as a suitable model for the asynchronous computation of cellular automata. The model uses maxmin-plus algebra, a special case of which is max-plus algebra. This algebra arises naturally from the cellular automaton requirement that a cell receives the state of its neighbours before updating. The maxmin-m model allows each cell to update after it receives m out of a possible n neighbours' states.The max-plus model shows that, while update times may be asynchronous in real time, there is no loss of information, since the corresponding asynchronous process is bijectively related to the synchronous model. In turn, the cellular automaton output, measured by the Shannon and word entropies, is shown to vary little from the synchronous model. Moreover, this type of asynchrony is simple, i.e. it is deterministically obtained due to the linearity of max-plus algebra.Indeed, the maxmin-m model is also shown to be deterministic and always reaches periodic behaviour. In the long time limit, this model is shown to be represented by a max-plus model, supporting its determinism further. Consequently, the complexity of such a model may be thought to be limited. However, we show through large scale experiments that the case where m is approximately n/2 generates most complex behaviour in terms of large periods and transients to the aforementioned periodic orbits. In particular, the complexity is empirically shown to obey a bell form as a function of m (where m ranges from 1 to n). The resulting cellular automaton simulations indicate a correspondence from the complexity of the update times. Therefore, cellular automaton behaviour may be predictable with the type of asynchrony employed in this thesis.

Journal ArticleDOI
TL;DR: It is shown that a sequence over a finite field F q of characteristic p is p-automatic if and only if it occurs as a column of the spacetime diagram of a linear cellular automaton with memory over F q .
Abstract: We show that a sequence over a finite field $\mathbb F_q$ of characteristic $p$ is $p$-automatic if and only if it occurs as a column of the spacetime diagram, with eventually periodic initial conditions, of a linear cellular automaton with memory over $\mathbb F_q$. As a consequence, the subshift generated by a length-$p$ substitution can be realized as a topological factor of a linear cellular automaton.

Journal ArticleDOI
TL;DR: A coarse-grained cellular automaton is proposed to simulate traffic systems and indicates the presence of a phase transition in the parameter space, between two macroscopic phases: passable and jammed.
Abstract: A coarse-grained cellular automaton is proposed to simulate traffic systems. There, cells represent road sections. A cell can be in two states: jammed or passable. Numerical calculations are performed for a piece of square lattice with open boundary conditions, for the same piece with some cells removed and for a map of a small city. The results indicate the presence of a phase transition in the parameter space, between two macroscopic phases: passable and jammed. The results are supplemented by exact calculations of the stationary probabilities of states for the related Kripke structure constructed for the traffic system. There, the symmetry-based reduction of the state space allows to partially reduce the computational limitations of the numerical method.

Book ChapterDOI
TL;DR: A history of notable discoveries in the 2x2 rule is provided, and the fundamental patterns of the automaton are described, including a proof that the speed limits for diagonal and orthogonal spaceships in this rule are c/3 and c/2, respectively.
Abstract: The B36/S125 (or "2x2") cellular automaton is one that takes place on a 2D square lattice much like Conway's Game of Life. Although it exhibits high-level behaviour that is similar to Life, such as chaotic but eventually stable evolution and the existence of a natural diagonal glider, the individual objects that the rule contains generally look very different from their Life counterparts. In this article, a history of notable discoveries in the 2x2 rule is provided, and the fundamental patterns of the automaton are described. Some theoretical results are derived along the way, including a proof that the speed limits for diagonal and orthogonal spaceships in this rule are c/3 and c/2, respectively. A Margolus block cellular automaton that 2x2 emulates is investigated, and in particular a family of oscillators made up entirely of 2 x 2 blocks are analyzed and used to show that there exist oscillators with period 2^m(2^k - 1) for any integers m,k \geq 1.

Journal ArticleDOI
TL;DR: A general hybrid automaton for systems consisting of multiple rigid-bodies with convexdifferentiable surfaces is presented and a Simulink-based simulation package for multi-rigid body systems based on the hybrid-automaton modelling framework is presented.

Book ChapterDOI
11 Sep 2012
TL;DR: It is shown that the model described by an asynchronous cellular automaton can reproduce the features of four groups into which biological and other model neurons are classified, and underlying bifurcations of the four groups are analyzed.
Abstract: A spiking neuron model described by an asynchronous cellular automaton is introduced. Our model can be implemented in an asynchronous sequential logic circuit and its control parameter is adjustable after implementation in an FPGA. It is shown that our model can reproduce the features of four groups into which biological and other model neurons are classified. In addition, underlying bifurcations of the four groups are analyzed, and the results yield basic guides to synthesis of our model.

Posted Content
TL;DR: A two-state, three-dimensional, deterministic, reversible cellular automaton is shown to be capable of approximately circular orbits, wavelike undulations, and particle-like configurations that decay in accordance with a half-life law.
Abstract: A two-state, three-dimensional, deterministic, reversible cellular automaton is shown to be capable of approximately circular orbits, wavelike undulations, and particle-like configurations that decay in accordance with a half-life law.

Journal ArticleDOI
TL;DR: This paper proposes a behavioral model, named controller automata, to combine timed automata by focusing on the control passing between components, and shows that this problem can be avoided and a controller automaton can be faithfully translated into a timed automaton.
Abstract: Timed automata are commonly recognized as a formal behavioral model for real-time systems. For compositional system design, parallel composition of timed automata as proposed by Larsen et al. [22] is useful. Although parallel composition provides a general method for system construction, in the low level behavior, components often behave sequentially by passing control via communication. This paper proposes a behavioral model, named controller automata, to combine timed automata by focusing on the control passing between components. In a controller automaton, to each state a timed automaton is assigned. A timed automaton at a state may be preempted by the control passing to another state by a global labeled transition. A controller automaton properly extends the expressive power because of the stack, but this can make the reachability problem undecidable. Given a strict partial order over states, we show that this problem can be avoided and a controller automaton can be faithfully translated into a timed automaton.

Journal ArticleDOI
TL;DR: In this paper, a discussion of complex dynamics of the elementary cellular automaton rule 54 is presented, and an equation which shows some degree of self-similarity is obtained, showing that rule 54 exhibits Bernoulli shift and is topologically mixing.
Abstract: This work deals with a discussion of complex dynamics of the elementary cellular automaton rule 54. An equation which shows some degree of self-similarity is obtained. It is shown that rule 54 exhibits Bernoulli shift and is topologically mixing on its closed invariant subsystem. Finally, many complex Bernoulli shifts are explored for the finite symbolic sequences with periodic boundary conditions.

Proceedings ArticleDOI
29 May 2012
TL;DR: A cellular automaton classifier with a tree structure is constructed by combing with the CART algorithm and is shown to be more accurate than those obtained through the multiple attractor cellular automata.
Abstract: The partition of a pattern space as the view of a cell space is a uniform partition, it is difficult to adapt to the needs of spatial non-uniform partition. In this paper, a cellular automaton classifier with a tree structure is constructed by combing with the CART algorithm. The construction method of the characteristic matrix of the multiple attractor cellular automata is studied based on the particle swarm optimization method, and this method can build the nodes of the multiple attractor cellular automata. This kind of classifier can solve the non-uniform partition problem and obtain a good classification performance while using a pseudo-exhaustive field with less bits. The experiment results show that our algorithm is more accurate than those obtained through the multiple attractor cellular automata.

Journal ArticleDOI
TL;DR: A decision algorithm for the analysis of the stability of a class of planar switched linear systems, modeled by hybrid automata, shows that for every pair of an ingoing and an outgoing transition related to a location, the exact gain in the norm of the vector induced by the dynamics in that location can be computed.

Proceedings ArticleDOI
06 Jul 2012
TL;DR: In this paper, cellular automata with boundaries are addressed by using the theories of semi-tensor product and Drazin inverse of matrices, and a necessary and sufficient condition for the reversibility is given.
Abstract: In this paper, cellular automata with boundaries are addressed by using the theories of semi-tensor product and Drazin inverse of matrices. For a cellular automaton with boundaries, a dynamical system model is constructed, then a necessary and sufficient condition for the reversibility is given, and a concept of generalized inverse cellular automaton that characterizes the local energy conservation is presented. Besides, a representation for the (generalized) inverse cellular automaton together with a unified algorithm to calculate it is given. Some examples are given to illustrate the algorithm.

Proceedings ArticleDOI
01 Dec 2012
TL;DR: This paper allows obstacles moving in discrete steps and verify that the finite automaton with just five printing symbols can escape or find the exit and shows the earlier results for static obstacles distributed over integer grid.
Abstract: A variety of interesting problems arise in the study of finite automata that move about in a two dimensional space. The model proposed by H. Muller [4] is used here to construct new automaton which can explore any labyrinth and escape through the moving or dynamic obstacles inside over the grid. The earlier results were shown for static obstacles distributed over integer grid and the automaton in this case was constructed to interact on the rectangular grid location endowed with four neighborhood directional states. In this paper we allow obstacles moving in discrete steps and verify that the finite automaton with just five printing symbols can escape or find the exit.

Journal Article
TL;DR: The rule matrix is obtained of a 2-dimensional cellular automaton generated by a new local rule of the nearest neighborhoods and prolonged next nearest neighborhoods under periodic boundary condition over the field.
Abstract: In this paper, we study a 2-dimensional cellular automaton generated by a new local rule of the nearest neighborhoods and prolonged next nearest neighborhoods under periodic boundary condition over the field . We obtain the rule matrix of this cellular automaton and characterize the cellular automaton with some of their important characteristics. We get some recurrence equations to compute the rank of the rule matrix related to the 2-dimensional cellular automaton. Keywords: Cellular automata, Rule matrix, Matrix algebra, Periodic Boundary Condition

01 Aug 2012
TL;DR: A refinement of the classical model of CA where the topology is considered as the communication medium and a solution by which each router can locally predict where to redirect the states to correctly and efficiently implement this broadcasting algorithm is provided.
Abstract: A cellular automaton (CA) is an infinite array of cells, each containing the same automaton. The dynamics of a CA is distributed over the cells where each computes its next state as a function of the previous states of its neighborhood. Thus, the transmission of such states between neighbors is considered as feasible directly, in no time. When considering the implementation of a cellular automaton on a many-cores System-on-Chip (SoC), this state transmission is no longer abstract and instantaneous, but has to follow the interconnection medium of the SoC. It is usually a grid or a mesh matching the underlying topology of the CA but finite. In order to consider such constraints at a higher level, we propose a refinement of the classical model of CA where the topology is considered as the communication medium. If the state of a cell depends on its neighbors up to a certain distance, then a given state must be broadcasted to all its neighbors at the same distance, as they all require it to compute their next state. It means routing and duplicating the state in the topology. We study the routing patterns needed to efficiently implement such state broadcasting algorithm. We provide a solution by which each router can locally predict where to redirect the states to correctly and efficiently implement this broadcasting algorithm.

Book ChapterDOI
24 Sep 2012
TL;DR: A cellular automaton is defined by composition and how its cycles are related is shown, to show how they are related to each other.
Abstract: We know that a few uniform cellular automata have maximum cycle lengths. However, there are many uniform cellular automata, and checking the cycles of all uniform cellular automata is impractical. In this paper, we define a cellular automaton by composition and show how its cycles are related.

Journal ArticleDOI
TL;DR: Algorithms for producing a Collatz sequence in the cases of the binary and ternary number systems and Logic circuits of iterative automata that implement the algorithms described are presented.
Abstract: Algorithms for producing a Collatz sequence are considered in the cases of the binary and ternary number systems. Advantages of this approach to the representation of such a sequence are considered. Logic circuits of iterative automata that implement the algorithms described are presented.

Book ChapterDOI
24 Sep 2012
TL;DR: A novel scheme to construct circuits on the cell space of an asynchronous cellular automaton that has partitioned cells is presented, conducted by worm configurations that contain instructions on how to operate.
Abstract: This paper presents a novel scheme to construct circuits on the cell space of an asynchronous cellular automaton that has partitioned cells. The construction process in this scheme is conducted by worm configurations that contain instructions on how to operate. Circuits are constructed by multiple worms, which move around in parallel on the cell space, resulting in an efficient process, as is shown.