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Small Universal Cellular Automata in Hyperbolic Spaces

Author : Maurice Margenstern

Publisher : Springer Science & Business Media

Page : 328 pages

File Size : 42,53 MB

Release : 2013-03-14

Category : Technology & Engineering

ISBN : 3642366635

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Book Description

Hyperbolic geometry is an essential part of theoretical astrophysics and cosmology. Besides specialists of these domains, many specialists of new domains start to show a growing interest both to hyperbolic geometry and to cellular automata. This is especially the case in biology and computer science. This book gives the reader a deep and efficient introduction to an algorithmic approach to hyperbolic geometry. It focuses the attention on the possibilities to obtain in this frame the power of computing everything a computer can compute, that is to say: universality. The minimal ways to get universality are investigated in a large family of tilings of the hyperbolic plane. In several cases the best results are obtained.In all cases, the results are close to the theoretical best values. This gives rise to fantastic illustrations: the results are jewels in all meanings of the word. ------------------------ Maurice MARGENSTERN is professor emeritus at the University of Lorraine, he is a member of LITA, the research unit of computer science in the campus of Metz of this university. Professor Margenstern is amongst top world experts in theory of computation, mathematical machines and geometry. He is a pioneer in cellular automata in hyperbolic spaces.





Advances in Unconventional Computing

Author : Andrew Adamatzky

Publisher : Springer

Page : 868 pages

File Size : 32,3 MB

Release : 2016-07-18

Category : Technology & Engineering

ISBN : 3319339249

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Book Description

The unconventional computing is a niche for interdisciplinary science, cross-bred of computer science, physics, mathematics, chemistry, electronic engineering, biology, material science and nanotechnology. The aims of this book are to uncover and exploit principles and mechanisms of information processing in and functional properties of physical, chemical and living systems to develop efficient algorithms, design optimal architectures and manufacture working prototypes of future and emergent computing devices. This first volume presents theoretical foundations of the future and emergent computing paradigms and architectures. The topics covered are computability, (non-)universality and complexity of computation; physics of computation, analog and quantum computing; reversible and asynchronous devices; cellular automata and other mathematical machines; P-systems and cellular computing; infinity and spatial computation; chemical and reservoir computing. The book is the encyclopedia, the first ever complete authoritative account, of the theoretical and experimental findings in the unconventional computing written by the world leaders in the field. All chapters are self-contains, no specialist background is required to appreciate ideas, findings, constructs and designs presented. This treatise in unconventional computing appeals to readers from all walks of life, from high-school pupils to university professors, from mathematicians, computers scientists and engineers to chemists and biologists.



Computing with New Resources

Author : Cristian S. Calude

Publisher : Springer

Page : 486 pages

File Size : 29,64 MB

Release : 2014-12-09

Category : Computers

ISBN : 3319133500

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Book Description

Professor Jozef Gruska is a well known computer scientist for his many and broad results. He was the father of theoretical computer science research in Czechoslovakia and among the first Slovak programmers in the early 1960s. Jozef Gruska introduced the descriptional complexity of grammars, automata, and languages, and is one of the pioneers of parallel (systolic) automata. His other main research interests include parallel systems and automata, as well as quantum information processing, transmission, and cryptography. He is co-founder of four regular series of conferences in informatics and two in quantum information processing and the Founding Chair (1989-96) of the IFIP Specialist Group on Foundations of Computer Science.



Reversibility and Universality

Author : Andrew Adamatzky

Publisher : Springer

Page : 484 pages

File Size : 21,8 MB

Release : 2018-02-26

Category : Technology & Engineering

ISBN : 3319732161

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Book Description

This book is a tribute to Kenichi Morita’s ideas and achievements in theoretical computer science, reversibility and computationally universal mathematical machines. It offers a unique source of information on universality and reversibility in computation and is an indispensable book for computer scientists, mathematicians, physicists and engineers. Morita is renowned for his works on two-dimensional language accepting automata, complexity of Turing machines, universality of cellular automata, regular and context-free array grammars, and undecidability. His high-impact works include findings on parallel generation and parsing of array languages by means of reversible automata, construction of a reversible automaton from Fredkin gates, solving a firing squad synchronization problem in reversible cellular automata, self-reproduction in reversible cellular spaces, universal reversible two-counter machines, solution of nondeterministic polynomial (NP) problems in hyperbolic cellular automata, reversible P-systems, a new universal reversible logic element with memory, and reversibility in asynchronous cellular automata. Kenichi Morita’s achievements in reversibility, universality and theory of computation are celebrated in over twenty high-profile contributions from his colleagues, collaborators, students and friends. The theoretical constructs presented in this book are amazing in their diversity and depth of intellectual insight, addressing: queue automata, hyperbolic cellular automata, Abelian invertible automata, number-conserving cellular automata, Brownian circuits, chemical automata, logical gates implemented via glider collisions, computation in swarm networks, picture arrays, universal reversible counter machines, input-position-restricted models of language acceptors, descriptional complexity and persistence of cellular automata, partitioned cellular automata, firing squad synchronization algorithms, reversible asynchronous automata, reversible simulations of ranking trees, Shor’s factorization algorithms, and power consumption of cellular automata.



Automata, Universality, Computation

Author : Andrew Adamatzky

Publisher : Springer

Page : 421 pages

File Size : 49,43 MB

Release : 2014-11-15

Category : Technology & Engineering

ISBN : 3319090399

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Book Description

This book is an intellectually stimulating excursion into mathematical machines and structures capable for a universal computation. World top experts in computer science and mathematics overview exciting and intriguing topics of logical theory of monoids, geometry of Gauss word, philosophy of mathematics in computer science, asynchronous and parallel P-systems, decidability in cellular automata, splicing systems, reversible Turing machines, information flows in two-way finite automata, prime generators in automaton arrays, Grossone and Turing machines, automaton models of atomic lattices. The book is full of visually attractive examples of mathematical machines, open problems and challenges for future research. Those interested in the advancement of a theory of computation, philosophy of mathematics, future and emergent computing paradigms, architectures and implementations will find the book vital for their research and development.



Reachability Problems

Author : Giorgio Delzanno

Publisher : Springer Science & Business Media

Page : 255 pages

File Size : 35,98 MB

Release : 2011-09-19

Category : Computers

ISBN : 3642242871

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Book Description

This book constitutes the refereed proceedings of the 5th International Workshop on Reachability Problems, RP 2011, held in Genoa, Italy, in September 2011. The 16 papers presented together with 4 invited talks were carefully reviewed and selected from 24 submissions. The workshop deals with reachability problems that appear in algebraic structures, computational models, hybrid systems, logic, and verification. Reachability is a fundamental problem that appears in several different contexts: finite- and infinite-state concurrent systems, computational models like cellular automata and Petri nets, decision procedures for classical, modal and temporal logic, program analysis, discrete and continuous systems, time critical systems, and open systems modelled as games.



Unconventional Computation and Natural Computation

Author : Jerome Durand-Lose

Publisher : Springer

Page : 262 pages

File Size : 31,39 MB

Release : 2012-09-02

Category : Computers

ISBN : 3642328946

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Book Description

This book constitutes the thoroughly refereed post-conference proceedings of the 11th International Conference on Unconventional Computation, UC 2012, held in Orléans, France, during September 3-7, 2012. The 28 revised full papers presented were carefully selected from numerous submissions. Conference papers are organized in 4 technical sessions, covering topics of hypercomputation, chaos and dynamical systems based computing, granular, fuzzy and rough computing, mechanical computing, cellular, evolutionary, molecular, neural, and quantum computing, membrane computing, amorphous computing, swarm intelligence; artificial immune systems, physics of computation, chemical computation, evolving hardware, the computational nature of self-assembly, developmental processes, bacterial communication, and brain processes



A Computable Universe

Author : Hector Zenil

Publisher : World Scientific

Page : 855 pages

File Size : 34,75 MB

Release : 2013

Category : Computers

ISBN : 9814374296

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Book Description

This volume discusses the foundations of computation in relation to nature. It focuses on two main questions: What is computation? and How does nature compute?



Reachability Problems

Author : Antonin Kucera

Publisher : Springer

Page : 208 pages

File Size : 42,23 MB

Release : 2010-08-21

Category : Computers

ISBN : 3642153496

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Book Description

Annotation. This book constitutes the research papers presented at the 4th International Workshop, RP 2010 held in Brno, Czech Republic, August 28-29, 2010 and was co-located with Joint MFCS and CSL 2010 (35th International Symposiums on Mathematical Foundations of Computer Science and 19th EACSL Annual Conferences on Computer Science Logic). The revised 9 full papers and the 4 invited talks of this workshop reflect reachability problems that appear in algebraic structures, computational models, hybrid systems and verification. Reachability is a fundamental problem in the context of many models and abstractions which are describing various computational processes. Topics of interest include reachability problems in infinite state systems, rewriting systems, dynamical and hybrid systems, reachability problems in logic and verification, reachability analysis in different computational models, counter, timed, cellular, communicating automata, Petri-Nets, computational aspects of algebraic structures (semigroups, groups and rings), frontiers between decidable and undecidable reachability problems, predictability in iterative maps and new computational paradigms.