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Inverse Problems Are Solvable on Real Number Signal Processing Hardware [article]

Holger Boche and Adalbert Fono and Gitta Kutyniok
2022 arXiv   pre-print
Turing machines provide the fundamental model of today's digital computers.  ...  Although a corresponding real world computing device does not exist at the moment, research and development towards real number computing hardware, usually referred to by the term "neuromorphic computing  ...  Turing machines that are able to work with arbitrary real numbers are so-called Oracle Turing machines [42] .  ... 
arXiv:2204.02066v2 fatcat:efvvpd2z7bbkhdjdyme6eusiaa

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Hava T. Siegelmann
2012 Minds and Machines  
We further propose it as standard in the field of analog computation, functioning in a role similar to that of the universal Turing machine in digital computation.  ...  In particular an analog of the Church-Turing thesis of digital computation is stated where the neural network takes place of the Turing machine.  ...  Turing Machines and Turing Machines with polynomial advice.  ... 
doi:10.1023/a:1021376718708 fatcat:zgqiws34c5danpy4tf3frjc5r4

Page 5 of Neural Computation Vol. 8, Issue 1 [page]

1996 Neural Computation  
However a Turing machine with a con- stant bound s on its number of tape cells is just a special case of a finite automaton, and hence this result does not show that a PPN of finite size can have the computational  ...  power of an arbitrary Turing machine.  ... 

Page 1435 of Mathematical Reviews Vol. , Issue 2000b [page]

2000 Mathematical Reviews  
can be properly learned with a polynomial number of polynomial-size membership and equivalence queries, but can be properly learned in polynomial time with such queries if and only if P= NP.  ...  machine U) is determined by the smallest code of a Turing machine that does not halt, but for which this fact cannot be proven in ZFC.  ... 

Turing on Super-Turing and adaptivity

Hava T. Siegelmann
2013 Progress in Biophysics and Molecular Biology  
Biological processes are often compared to computation and modeled on the Universal Turing Machine.  ...  We argue that the Super--Turing model is both capable of modeling adaptive computation, and furthermore, a possible answer to the computational model searched for by Turing himself.  ...  1995] and Turing machines with a real coin [Siegelmann 1999 ].  ... 
doi:10.1016/j.pbiomolbio.2013.03.013 pmid:23583352 fatcat:i2jlnfyswjbjrbyy755zvygz5a

Page 9241 of Mathematical Reviews Vol. , Issue 2001M [page]

2001 Mathematical Reviews  
Thus, posi- tive Turing and Turing reducibility to NP differ sharply unless the polynomial hierarchy collapses.  ...  In particular, we show that for any a < /2 and any b <1, SAT cannot be computed by a random-access deterministic Turing machine using n“ time, n°!  ... 

The simple dynamics of super Turing theories

Hava T. Siegelmann
1996 Theoretical Computer Science  
This system, which we term as the analog shift map, when viewed as a computational model has super-Turing power and is equivalent to neural networks and the class of analog machines.  ...  A possible such model, constituting a chaotic dynamical system, is presented.  ...  Now the Turing machine with a polynomial advice will act as follows: (a) The initial bi-infinite string is where x is the input string.  ... 
doi:10.1016/s0304-3975(96)00087-4 fatcat:bdo77spgkbgtpi76jury4fba7a

Optimization problems with low SWaP tactical Computing [article]

Mee Seong Im, Venkat R. Dasari, Lubjana Beshaj, Dale Shires
2019 arXiv   pre-print
In a resource-constrained, contested environment, computing resources need to be aware of possible size, weight, and power (SWaP) restrictions.  ...  Due to these restrictions, only a small subset of less complicated and fast computable algorithms can be used for tactical, adaptive computing.  ...  time complexity class, N P is the class of languages decidable in polynomial time on a nondeterministic Turing machine, PSpace is the class of decision problems solvable by a Turing machine using a polynomial  ... 
arXiv:1902.05070v1 fatcat:t3xyo62h3fbalal7p5yvno3pb4

Page 4395 of Mathematical Reviews Vol. , Issue 2002F [page]

2002 Mathematical Reviews  
Furthermore, we show that our consistent inductive inference coincides with the ordinary inductive inference when we deal with recursive real-valued functions on a fixed closed rational interval.”  ...  A class has teaching dimension polynomial in the number of instances iff it is learnable from polynomially many membership queries; such a class is called teachable from examples.  ... 

Is Complexity Important for Philosophy of Mind? [article]

Kristina Šekrst, Sandro Skansi
2021 arXiv   pre-print
The Church-Turing thesis is therefore revisited and rephrased in order to capture the ontological background of spatial and temporal complexity.  ...  Third, to emphasize ontological differences between different time complexities, which seem to provide a solid base towards better understanding of artificial intelligence in general.  ...  = PSPACE, where PSPACE is a set of all decision problems solvable by a Turing machine using a polynomial amount of space. There is one more counterintuitive result.  ... 
arXiv:2112.03877v1 fatcat:4ncdakcy4bg2xaagkrumlhzxki

Experience, generations, and limits in machine learning

Mark Burgin, Allen Klinger
2004 Theoretical Computer Science  
That yields three basic models for learning systems: polynomially bounded turing machines, Turing machines, and inductive Turing machines of the ÿrst order.  ...  This paper extends traditional models of machine learning beyond their one-level structure by introducing previously obtained problem knowledge into the algorithm or automaton involved.  ...  Learner models and learning potency The basic models for learning systems here are: a polynomially bounded Turing machine (PBTM), Turing machine (TM), and inductive Turing machine of the ÿrst order (ITM1  ... 
doi:10.1016/j.tcs.2003.12.005 fatcat:6dzytvnyynbc3kj5zl2rzqurx4

Experience, generations, and limits in machine learning

M BURGIN
2004 Theoretical Computer Science  
That yields three basic models for learning systems: polynomially bounded turing machines, Turing machines, and inductive Turing machines of the ÿrst order.  ...  This paper extends traditional models of machine learning beyond their one-level structure by introducing previously obtained problem knowledge into the algorithm or automaton involved.  ...  Learner models and learning potency The basic models for learning systems here are: a polynomially bounded Turing machine (PBTM), Turing machine (TM), and inductive Turing machine of the ÿrst order (ITM1  ... 
doi:10.1016/s0304-3975(03)00632-7 fatcat:zzcjrqzsabgmflrbdl6knlx3vu

On the Power of Threshold Measurements as Oracles [chapter]

Edwin Beggs, José Félix Costa, Diogo Poças, John V. Tucker
2013 Lecture Notes in Computer Science  
Corresponding author. 1 Scientific activity seen as a Turing machine can be found in computational learning theory (see [10] ).  ...  The Turing machines compute with the help of qualitative information provided by the oracle.  ...  polynomial time by an oracle Turing machine coupled with a threshold oracle of infinite precision, then A ∈ P / log 2 .  ... 
doi:10.1007/978-3-642-39074-6_3 fatcat:nb54lps42je6hnxpdexohrhz7u

A Hierarchy for $$ BPP //\log \!\star $$ B P P / / log ⋆ Based on Counting Calls to an Oracle [chapter]

Edwin Beggs, Pedro Cortez, José Félix Costa, John V Tucker
2016 Emergent Computation  
Algorithms whose computations involve making physical measurements can be modelled by Turing machines with oracles that are physical systems and oracle queries that obtain data from observation and measurement  ...  The hierarchy rests on the theorem that the number of calls to the physical oracle correlates with the size of the responses to queries.  ...  The research of José Félix Costa is supported by Fundação para a Ciência e Tecnologia, projeto FCT I.P.:UID/FIL/00678/2013.  ... 
doi:10.1007/978-3-319-46376-6_3 fatcat:j4iadonkcvactbyomm3ige6du4

An introduction to computational complexity in Markov Chain Monte Carlo methods [article]

Izhar Asael Alonzo Matamoros
2020 arXiv   pre-print
In this work, we provide a general overview, references, and discussion about all these theoretical subjects.  ...  Definition 10 A probabilistic Turing machine (PTM) is a kind of Nondeterministic Turing Machine, with coin flip choices instead of nondeterministic choices.  ...  In the same scheme, the NP class, accepts a non deterministic Turing machine (NTM) in polynomial time.  ... 
arXiv:2004.07083v1 fatcat:zpahbc65bncdtchrkt5abawrwe
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