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Higher-Dimensional Timed Automata [article]

Uli Fahrenberg
2018 arXiv   pre-print
We introduce a new formalism of higher-dimensional timed automata, based on van Glabbeek's higher-dimensional automata and Alur's timed automata.  ...  We also show how to use tensor products to combat state-space explosion and how to extend the setting to higher-dimensional hybrid automata.  ...  We have also seen how tensor product of HDTA can be used for parallel composition, and that HDTA can easily be generalized to higher-dimensional hybrid automata.  ... 
arXiv:1802.07038v1 fatcat:kav2n3442negjgigq5avg5xmv4

Page 4764 of Mathematical Reviews Vol. , Issue 94h [page]

1994 Mathematical Reviews  
Summary: “Higher-dimensional automata can model concurrent computations. The topological structure of the higher-dimensional automata determines certain properties of the concurrent com- putation.  ...  We introduce bicomplexes as an algebraic tool for de- scribing these automata and develop a simple homology theory for higher-dimensional automata.  ... 

Two-dimensional cellular automata

Norman H. Packard, Stephen Wolfram
1985 Journal of statistical physics  
A largely phenomenological study of two-dimensional cellular automata is reported. Qualitative classes of behavior similar to those in one-dimensional cellular automata are found.  ...  Growth from simple seeds in two-dimensional cellular automata can produce patterns with complicated boundaries, characterized by a variety of growth dimensions.  ...  Shaw for writing the kernel of our software simulation system for two-dimensional cellular automata in Ridge assembly language. We thank  ... 
doi:10.1007/bf01010423 fatcat:4tdguoisl5fmraggit5gstkkne

Page 5993 of Mathematical Reviews Vol. , Issue 94j [page]

1994 Mathematical Reviews  
Since the reversibility problem of higher-dimensional (d > 2) cellular automata is undecidable, there is no recursive bound for the neighborhood sizes of inverse CAs of higher-dimensional reversible CAs  ...  A method of obtaining rational speeds of configuration growth in one-dimensional cellu- lar automata is known.  ... 

Conjugacy of one-dimensional one-sided cellular automata is undecidable [article]

Joonatan Jalonen, Jarkko Kari
2017 arXiv   pre-print
It also immediately follows that these results hold for one-dimensional two-sided cellular automata.  ...  following decision problems are undecidable: Given two one-dimensional one-sided cellular automata F and G over a full shift: Are F and G conjugate?  ...  equicontinuity are undecidable for one-and higher-dimensional cellular automata.  ... 
arXiv:1710.08111v1 fatcat:cdizyyuryfaoriboabubkmshsm

Are complex systems hard to evolve?

Andy Adamatzky, Larry Bull
2009 Complexity  
Behavioural complexity of the gates evolved is characterised in terms of cellular automata behaviour.  ...  Then the logical function is considered to be a cell state transition of some cellular automata. Complexity of the cellular automata was compared to complexity of evolution.  ...  NAND-automata occupy an even higher level of complexity because they exhibit a few different domains in configurations at the same time steps (Fig. 3b) .  ... 
doi:10.1002/cplx.20269 fatcat:jjlcnqckobexlmcvyv2zj46krq

Conjugacy of One-Dimensional One-Sided Cellular Automata is Undecidable [chapter]

Joonatan Jalonen, Jarkko Kari
2017 Lecture Notes in Computer Science  
It also immediately follows that these results hold for one-dimensional two-sided cellular automata.  ...  following decision problems are undecidable: Given two one-dimensional one-sided cellular automata F and G over a full shift: Are F and G conjugate?  ...  equicontinuity are undecidable for one-and higher-dimensional cellular automata.  ... 
doi:10.1007/978-3-319-73117-9_16 fatcat:afsytbockbbbfhjd6hirucfhnq

Algebraic properties of linear cellular automata

L. Le Bruyn, M. Van den Bergh
1991 Linear Algebra and its Applications  
We discuss the phenomenon of self-replication and its connection with higher-order cellular automata and the state transition graph. 1.  ...  Cellular automata are systems evolving on lattices according to a local transition rule.  ...  Margolus of linear higher-order reversible automata (and to create many new examples of reversible cellular automata) as well as to describe the state transition graph of these higher-order cellular automata  ... 
doi:10.1016/0024-3795(91)90116-e fatcat:qsbrldsvwvg4bbixolpmjrwom4

Sabbatical Leave

Henry G. Bennett, Schiller Scroggs
1932 Journal of Higher Education  
Time evolution is generated according to a set of quantum cellular automata (QCA) rules which can be implemented through application of global control pulses on either species.  ...  Submitted for the DAMOP05 Meeting of The American Physical Society Noise diagnostics using one-dimensional quantum cellular automata YOUNG SOON KIM 1 , Myongji University, MATTHEW DAVIDSON, Catholic University  ... 
doi:10.2307/1974516 fatcat:rgpw3jfug5c4pfx5ynqtpmmdvy

Prisoner's Dilemma in One-Dimensional Cellular Automata: Visualization of Evolutionary Patterns [article]

Marcelo Alves Pereira, Alexandre Souto Martinez, Aquino Lauri Espindola
2007 arXiv   pre-print
Here we consider players in cells of one-dimensional cellular automata. Each player interacts with other z players.  ...  Fig. 3 . 3 Time evolution of the PD in a one-dimensional cellular automata for z asymmetric. Time evolves from top to bottom. Each vertical line is the evolution of the states of the i automata.  ...  Fig. 6 . 6 (a) Time evolution of the PD in a one-dimensional cellular automata for z symmetric. Time evolves from top to bottom. Each vertical line is the evolution of the states of the i automata.  ... 
arXiv:0708.3520v2 fatcat:y7xzfayvwva7ldcpfedd6t3ja4

Are quantum fields cellular automata?

Karl Svozil
1986 Physics Letters A  
In this case, it has to be assumed that for some (yet unknown) reason, dimensional reduction to D=4 occurs, such that the four-dimensional phenomenology is a "shadow" of a higher-dimensional world.  ...  A third possibility to circumvent the no-go theorem may be a higher-dimensional configuration space with dimension D> 4.  ... 
doi:10.1016/0375-9601(86)90436-6 fatcat:ick5bgqzwjahpjsncn4f6xecsu

Performance Enhancement for Tsunami Wave Simulation using Hexagonal Cellular Automata

E. SyedMohamed, S. Rajasekaran
2013 International Journal of Computer Applications  
The algorithm is efficient and easily implemented, allowing less computational time and cost. Experimental results of this model prove its value in tsunami wave spread as real time.  ...  In this paper tsunami wave models have been widely studied using cellular automata(CA) that has special features for simulating complex phenomena .The influential factors for tsunami wave are divided into  ...  The Size of Discrete Time Step Since cellular automata evolve in discrete time steps, it is a basic point to decide the size of such step of time .  ... 
doi:10.5120/13142-0541 fatcat:3alnlezwbjdo5bp7kznqcyskry

Grain Growth of AZ31 Magnesium Alloy Based on Three-Dimensional Cellular Automata

Yanfeng Li, Cuirong Liu, Zhibing Chu, Wei Li, Zhisheng Wu, Shan Gao, Wenwu He, Michael Aizenshtein
2020 Advances in Materials Science and Engineering  
The angle between the two-dimensional slices of three-dimensional grains is approximately 120°, which is consistent with that of the traditional two-dimensional cellular automata.  ...  Based on the thermodynamic conversion mechanism and energy transition principle, a three-dimensional cellular automata model of grain growth is established from the aspects of grain orientation, grain  ...  time. e angle between the two-dimensional cross section of grains is approximately 120֩, which is consistent with that of the traditional two-dimensional cellular automata. (2) With the GaussAmp nonlinear  ... 
doi:10.1155/2020/7615643 fatcat:rdl4yhrn3ratzc3bnftsyd6x2u

Complex Computing with Cellular Automata [chapter]

J. Signorini
1989 Springer Proceedings in Physics  
Cellular Automata is a discrete space and time, physical parameters which take a limited set of values the ideal of physical systems.  ...  At the same time, borrowed the idea of cellular automata, can form a highly parallel algorithm, is a rich potential for development of new numerical methods.  ...  Time Cellular Automata is a dynamic system that changes in the time dimension is discrete, namely the time t is an integer value, and continuous equal spacing.  ... 
doi:10.1007/978-3-642-75259-9_6 fatcat:cgihbwavbff77lulpbu7j4c64y

Page 5461 of Mathematical Reviews Vol. , Issue 88j [page]

1988 Mathematical Reviews  
Summary: “Infinite one-dimensional cellular automata are stud- ied using information theory.  ...  This paper in- troduces anew the following two-dimensional automaton.  ... 
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