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The Extended Analog Computer and Turing machine

Monika Piekarz
2007 Annales UMCS Informatica  
As a model of analog computer we use the model proposed by Rubel in 1993 called the Extended Analog Computer (EAC) while as a model of classical computer, the Turing machines.  ...  Showing that the Extended Analog Computer can robustly generate result of any Turing machine we use the method of simulation proposed by D.S. Graça, M.L. Campagnolo and J. Buescu [1] in 2005.  ...  The Extend Analog Computer defined above has some interesting properties. The EAC is that one which expands the scope of the General Purpose Analog Computer (GPAC) [12] .  ... 
dblp:journals/umcs/Piekarz07 fatcat:gufqaitxinacffdbl4cbyfswd4

Simulation of Turing Machine with uEAC-Computable Functions

Yilin Zhu, Feng Pan, Lingxi Li, Xuemei Ren, Qi Gao
2015 Mathematical Problems in Engineering  
The micro-Extended Analog Computer (uEAC) is an electronic implementation inspired by Rubel's EAC model.  ...  Then its computational capabilities are investigated by proving that a Turing machineMcan be simulated with uEAC-computable functions, even in the presence of bounded noise.  ...  However, Mills and his colleagues designed and built an electronic implementation inspired by the EAC, the micro-Extended Analog Computer (uEAC), and the current version was designed in 2005.  ... 
doi:10.1155/2015/236806 fatcat:6u5jwcn7fvawfgewmcp2iwpgm4

The case for hypercomputation

Mike Stannett
2006 Applied Mathematics and Computation  
We examine some 20 physical and mathematical models of computation that are either known or suspected to have super-Turing or hypercomputational capabilities, and argue that there is nothing in principle  ...  The weight of evidence supporting the case for hypercomputation is compelling.  ...  Turing machines are very specifically discrete conceptual devices, and we cannot avoid the fact that real computers are analog devices operating in an analog world.  ... 
doi:10.1016/j.amc.2005.09.067 fatcat:4e4st6y7vzhnrdpp56y2f4ku6e

Contents [chapter]

2019 The Discrete Charm of the Machine  
Analog Computer 129 9 Turing's Machine 132 9.1 The Ingredients of a Turing Machine 132 9.2 The All-Analog Machine 133 9.3 The Partly Digital Computer 134 9.4 A Reminiscence: The Stored-Program  ...  11.1 Analog Attacks on NP-CompleteProblems 164 11.2 The Missing Law 169 11.3 The Church-Turing Thesis 170 11.4 The Extended Church-Turing Thesis 171 11.5 Locality: From Einstein to Bell 172 11.6 Behind  ... 
doi:10.1515/9780691184173-toc fatcat:dag5fd75wbbtfkd2od2ycpjzpq

The Ackermann Award 2017

Anuj Dawar, Daniel Leivant, Marc Herbstritt
2017 Annual Conference for Computer Science Logic  
The Ackermann Award is the EACSL Outstanding Dissertation Award for Logic in Computer Science. It is presented during the annual conference of the EACSL (CSL'xx).  ...  This contribution reports on the 2017 edition of the award.  ...  Nicolai Kraus from Germany Detailed reports on their work appeared in the CSL proceedings and are also available on the EACSL homepage.  ... 
doi:10.4230/lipics.csl.2017.1 dblp:conf/csl/DawarL17 fatcat:dexzvosz6jhxnjnfzex4sobyzq

Conference: Morphological, Natural, Analog and Other Unconventional Forms of Computing for Cognition and Intelligence, Berkeley 2019

Marcin J. Schroeder, Gordana Dodig-Crnkovic
2020 Proceedings (MDPI)  
The Conference "Morphological, Natural, Analog, and Other Unconventional Forms of Computing for Cognition and Intelligence" (MORCOM 2019) was focused on this theme from the perspective of unconventional  ...  forms of computing.  ...  It means that symmetric Turing machines have the same computing power as Turing machines.  ... 
doi:10.3390/proceedings47010022 fatcat:3cjtym4cazfcrbmj7hm5vm36se

Analog computation beyond the Turing limit

Jerzy Mycka
2006 Applied Mathematics and Computation  
The main purpose of this paper is quite uncontroversial. First, we recall some models of analog computations (including these allowed to perform Turing uncomputable tasks).  ...  Additionally, the inner restrictions of analog models of computations are indicated.  ...  Another important model of analog computation is RubelÕs Extended Analog Computer (EAC) [27] .  ... 
doi:10.1016/j.amc.2005.09.074 fatcat:xwg6delq3fhwrfcc5jjuejfieu

A Survey on Analog Models of Computation [article]

Olivier Bournez, Amaury Pouly
2018 arXiv   pre-print
We present a survey on analog models of computations. Analog can be understood both as computing by analogy, or as working on the continuum.  ...  We consider both approaches, often intertwined, with a point of view mostly oriented by computation theory.  ...  extended definition of computation and computability theory including alternative (especially analog) models in addition to the Turing machines are needed [243, 242] .  ... 
arXiv:1805.05729v1 fatcat:abb33r5wpbd7tem557fm4vzlqu

The Interactive Nature of Computing: Refuting the Strong Church–Turing Thesis

Dina Goldin, Peter Wegner
2008 Minds and Machines  
We present Persistent Turing Machines (PTMs), that extend TMs to capture sequential interaction.  ...  The acceptance of interaction as a new paradigm is hindered by the Strong Church-Turing Thesis (SCT), the widespread belief that Turing Machines (TMs) capture all computation, so models of computation  ...  Acknowledgements We sincerely thank the anonymous reviewers for their comments, which were very helpful in revising this paper.  ... 
doi:10.1007/s11023-007-9083-1 fatcat:vfytwfsd6nf3ppjimqhrfs6mgy

"Empty space" computes

Jonathan W. Mills, Matt Parker, Bryce Himebaugh, Craig Shue, Brian Kopecky, Chris Weilemann
2006 Proceedings of the 3rd conference on Computing frontiers - CF '06  
For the past decade research at Indiana University has explored the design and applications of extended analog computers. The machines have become increasingly sophisticated and flexible.  ...  Rubel defined the extended analog computer to remove the limitations of Shannon's general purpose analog computer.  ...  computability of a Turing machine [11] .  ... 
doi:10.1145/1128022.1128025 dblp:conf/cf/MillsPHSKW06 fatcat:ybxui3rqtfh73jecb7rkaoikim

A note on discreteness and virtuality in analog computing

Giuseppe Trautteur, Guglielmo Tamburrini
2007 Theoretical Computer Science  
The capability for virtual behaviour, that is, the capability of interpreting, storing, transforming, creating the code, and thereby mimicking the behaviour of (Turing) machines, is used here to introduce  ...  The need for physically motivated discreteness and finiteness conditions emerges in models of both analog and digital computing that are genuinely concerned with physically realizable computational processes  ...  the Church-Turing thesis, and Roberto Cordeschi for stimulating discussions on the analog-digital divide.  ... 
doi:10.1016/j.tcs.2006.10.017 fatcat:2qefz7x4zvcmdk36q6rcvl32ny

Interactive foundations of computing

Peter Wegner
1998 Theoretical Computer Science  
Interaction machines extend the Chomsky hierarchy, are modeled by interaction grammars, and precisely capture fuzzy concepts like open systems and empirical computer science.  ...  Turing machines cannot model interaction machines (which extend Turing machines with interactive input/output) because interaction is not expressible by a finite initial input string.  ...  Both the pi calculus and interaction machines extend the Church-Turing model to interaction, but the pi calculus extends the lambda calculus while interaction machines extend Turing machines.  ... 
doi:10.1016/s0304-3975(97)00154-0 fatcat:jfv7xn5nlveqjagut2rkidjdem

A review of "Mem-computing NP-complete problems in polynomial time using polynomial resources" (arXiv:1411.4798) [article]

Igor L. Markov
2015 arXiv   pre-print
The reviewed paper describes an analog device that empirically solves small instances of the NP-complete Subset Sum Problem (SSP).  ...  The authors claim that this device can solve the SSP in polynomial time using polynomial space, in principle, and observe no exponential scaling in resource requirements.  ...  In the 1980s, Richard Feynman studied the Physical Church-Turing thesis in its extended form, with quantum physics included.  ... 
arXiv:1412.0650v3 fatcat:zugffhrefvbtzgmuhkcaoobqbq

Computational complexity with experiments as oracles

E. Beggs, J. F. Costa, B. Loff, J. V Tucker
2008 Proceedings of the Royal Society A  
We discuss combining physical experiments with machine computations and introduce a form of analogue-digital Turing machine.  ...  Using non-uniform complexity theory, and some probability, we prove theorems that show that these machines can compute more than classical Turing machines.  ...  Acknowledgements: The first and last named authors would like to thank the EPSRC for their support via grant EP/C525361/1.  ... 
doi:10.1098/rspa.2008.0085 fatcat:6eftdicdvbeljfcnzgesjbvpr4

What Is an Algorithm? [chapter]

Yuri Gurevich
2012 Lecture Notes in Computer Science  
We present a two-part exposition on the notion of algorithm and foundational analyses of computation. The first part is below, and the second is here:  ...  Acknowledgments Many thanks to Andreas Blass for numerous illuminating discussions, and to Serge Grigorieff and Oron Shagrir for useful suggestion.  ...  But then there are analog computers in practical use that work in real time and compute functions that are not Turing computable. Of course Turing would not be surprised by our examples.  ... 
doi:10.1007/978-3-642-27660-6_3 fatcat:5o2ak5hl65adfgy5uji2cobywe
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