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A decision procedure for well-formed linear quantum cellular automata [article]

Christoph Durr, Huong LeThanh, Miklos Santha
2000 arXiv   pre-print
We give an efficient algorithm which decides if a linear quantum cellular automaton is well-formed.  ...  In this paper we introduce a new quantum computation model, the linear quantum cellular automaton.  ...  Acknowledgements We are thankful to Stéphane Boucheron, Bruno Durand, Richard Jozsa and John Watrous for several helpful conversations.  ... 
arXiv:cs/9906024v2 fatcat:upvnhm5bobfj3hnqidvz5vulg4

A decision procedure for well-formed linear quantum cellular automata [chapter]

Christoph Dürr, Huong Thanh, Miklos Santha
1996 Lecture Notes in Computer Science  
We give an efficient algorithm which decides if a linear quantum cellular automaton is well-formed.  ...  In this paper we introduce a new quantum computation model, the linear quantum cellular automaton.  ...  Acknowledgements We are thankful to Stéphane Boucheron, Bruno Durand, Richard Jozsa and John Watrous for several helpful conversations.  ... 
doi:10.1007/3-540-60922-9_24 fatcat:frzcozujzrdb7n5da7donqdfxm

Page 561 of Mathematical Reviews Vol. , Issue 97A [page]

1997 Mathematical Reviews  
The purpose of the fifth chapter is to take a systematic look at the algorithmic (un)solvability of decision questions for cellular automata, particularly on Euclidean universes.  ...  Chapter 3 introduces linear cellular automata and studies their basic properties. Semi-totalistic rules are considered in the next chapter.  ... 

An algebraic study of unitary one dimensional quantum cellular automata [article]

Pablo Arrighi
2006 arXiv   pre-print
We provide algebraic criteria for the unitarity of linear quantum cellular automata, i.e. one dimensional quantum cellular automata.  ...  We derive these both by direct combinatorial arguments, and by adding constraints into the model which do not change the quantum cellular automata's computational power.  ...  Acknowledgments P.J.A would like to thank Shu Yan Chan, Christoph Dürr, Simon Perdrix, and Estrella Sicardi for a number of insightful conversations, and acknowledges the direct help of Thierry Gallay  ... 
arXiv:quant-ph/0512040v2 fatcat:u7tgakye2ra27hdinoqrnrvtfe

A decision procedure for unitary linear quantum cellular automata [article]

Christoph Durr
1999 arXiv   pre-print
Linear quantum cellular automata were introduced recently as one of the models of quantum computing.  ...  In this paper we give an efficient algorithm to decide if a linear quantum cellular automaton is unitary.  ...  We wish also to thank the anonymous referees for helpful comments and in particular for simplifying section 6.  ... 
arXiv:quant-ph/9604007v5 fatcat:5e2f2irl4bdxhd2ky4uq75baxy

Page 3216 of Mathematical Reviews Vol. , Issue 98E [page]

1998 Mathematical Reviews  
linear quantum cellular automata.  ...  We give an efficient algorithm which decides whether a linear quantum cellular automaton is well-formed.  ... 

Quantum Cellular Automata Controlled Self-Organizing Networks [chapter]

Laszlo Gyongyosi, Sandor Imre
2011 Cellular Automata - Innovative Modelling for Science and Engineering  
The quantum cellular machine model with the power of quantum computing can be used for the development of a real-life based network organism.  ...  Quantum cellular automata models are based on the working mechanism of classical cellular automata models and use the power of reversible quantum computation.  ...  quantum versions of cellular automata.  ... 
doi:10.5772/15750 fatcat:i6hajfibdjg4nkmn4ow5jmehuq

Book announcements

2000 Discrete Applied Mathematics  
in Cellular Automata 4.5 The Firing Squad Synchronization Problem 4.6 Parallel Formal-Language Recognition by Cellular Automata 4.7 Parallel Arithmetic by Cellular Automata 4.8 Evolving Cellular  ...  Computation in Cellular Automata: A Selected Review 4.1 Introduction 4.2 Von Neumann's Self-Reproducing Cellular Automation 4.3 Universal Computation in Cellular Automata 4.4 Dynamics and Computation  ... 
doi:10.1016/s0166-218x(00)90007-6 fatcat:cemhaoz7rzdmdoec7pjjqiur2a

Foundations of Reversible Computation [chapter]

Bogdan Aman, Gabriel Ciobanu, Robert Glück, Robin Kaarsgaard, Jarkko Kari, Martin Kutrib, Ivan Lanese, Claudio Antares Mezzina, Łukasz Mikulski, Rajagopal Nagarajan, Iain Phillips, G. Michele Pinna (+3 others)
2020 Lecture Notes in Computer Science  
The approach extends to any form of quantum learning giving rise to linear decision boundaries.  ...  decision procedure.  ... 
doi:10.1007/978-3-030-47361-7_1 fatcat:3qgnwqrqnvdltkqjbuzfgx7wty

Page 2914 of Mathematical Reviews Vol. , Issue 2000d [page]

2000 Mathematical Reviews  
Finally, the author shows how a decision procedure for super- entailment can enhance tests for query finiteness.  ...  Bornholdt); (4) Computation in cellular automata: a selected review (M. Mitchell); (5) The theory of quantum computation: an introduction (T.  ... 

Barriers and bounds to Rationality

Herbert A Simon
2000 Structural Change and Economic Dynamics  
Special attention is devoted to the use of cellular automa in identifying the nature of non-linearities compatible with aggregation; in assessing the role of a central actor in a in a decentralized market  ...  In conclusion, the article suggests that a new theoretical paradigm is emerging, in which the search for invariant laws would be substituted by attention for historical conditions and localized patterns  ...  decision procedure.  ... 
doi:10.1016/s0954-349x(99)00022-3 fatcat:ecjr2oc4anfzjek33stipg7gw4

A Decision Procedure for Unitary Linear Quantum Cellular Automata

Christoph Dürr, Miklos Santha
2002 SIAM journal on computing (Print)  
Linear quantum cellular automata were introduced recently as one of the models of quantum computing.  ...  In this paper we give an efficient algorithm to decide if a linear quantum cellular automaton is unitary.  ...  Acknowledgments We are thankful to Laurent Rosaz, Huong LêThanh and Umesh Vazirani for several helpful conversations.  ... 
doi:10.1137/s0097539797327702 fatcat:hbwlfscsyvcpnj3bwxaitcpxxq

Page 1263 of Mathematical Reviews Vol. , Issue 99b [page]

1991 Mathematical Reviews  
decision procedure for well-formed linear quantum cellular automata.  ...  A new quantum computation model, the linear quantum cellu- lar automata (LQCA), is introduced.  ... 

Page 4089 of Mathematical Reviews Vol. , Issue 89G [page]

1989 Mathematical Reviews  
quantum mechanical cellular automata are investigated.  ...  Markku Lehto (SF-JVSK-P) 89g:81027 81C99 58F40 68Q80 Gréssing, Gerhard (A-ATOM) Comparison of classical and quantum lattice properties with the aid of cellular automata. Phys. Lett.  ... 

Multivaluedness Aspects in Self-Organization, Complexity and Computations Investigations by Strong Anticipation [chapter]

Alexander Makarenko
2017 Studies in Systems, Decision and Control  
Further prospects for development of automata theory and hyper computation are proposed.  ...  General new possibilities are the presumable multivaluedness of the dynamics of automata. Possible interpretations of such behavior of cellular automata are discussed.  ...  The author would like to give the appreciation for D. Krusinsky, Yu. Yatsuk, V. Biliuga, A. Stashenko and S. Lazarenko for computer realizations of models and V.  ... 
doi:10.1007/978-3-319-58996-1_3 fatcat:45guk2uunfdtpo4rhp5kxubtfe
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