11,157 research outputs found
Discontinuities in recurrent neural networks
This paper studies the computational power of various discontinuous
real computational models that are based on the classical analog
recurrent neural network (ARNN). This ARNN consists of finite number
of neurons; each neuron computes a polynomial net-function and a
sigmoid-like continuous activation-function.
The authors introducePostprint (published version
On the possible Computational Power of the Human Mind
The aim of this paper is to address the question: Can an artificial neural
network (ANN) model be used as a possible characterization of the power of the
human mind? We will discuss what might be the relationship between such a model
and its natural counterpart. A possible characterization of the different power
capabilities of the mind is suggested in terms of the information contained (in
its computational complexity) or achievable by it. Such characterization takes
advantage of recent results based on natural neural networks (NNN) and the
computational power of arbitrary artificial neural networks (ANN). The possible
acceptance of neural networks as the model of the human mind's operation makes
the aforementioned quite relevant.Comment: Complexity, Science and Society Conference, 2005, University of
Liverpool, UK. 23 page
Strong Turing Degrees for Additive BSS RAM's
For the additive real BSS machines using only constants 0 and 1 and order
tests we consider the corresponding Turing reducibility and characterize some
semi-decidable decision problems over the reals. In order to refine,
step-by-step, a linear hierarchy of Turing degrees with respect to this model,
we define several halting problems for classes of additive machines with
different abilities and construct further suitable decision problems. In the
construction we use methods of the classical recursion theory as well as
techniques for proving bounds resulting from algebraic properties. In this way
we extend a known hierarchy of problems below the halting problem for the
additive machines using only equality tests and we present a further
subhierarchy of semi-decidable problems between the halting problems for the
additive machines using only equality tests and using order tests,
respectively
Perfect Computational Equivalence between Quantum Turing Machines and Finitely Generated Uniform Quantum Circuit Families
In order to establish the computational equivalence between quantum Turing
machines (QTMs) and quantum circuit families (QCFs) using Yao's quantum circuit
simulation of QTMs, we previously introduced the class of uniform QCFs based on
an infinite set of elementary gates, which has been shown to be computationally
equivalent to the polynomial-time QTMs (with appropriate restriction of
amplitudes) up to bounded error simulation. This result implies that the
complexity class BQP introduced by Bernstein and Vazirani for QTMs equals its
counterpart for uniform QCFs. However, the complexity classes ZQP and EQP for
QTMs do not appear to equal their counterparts for uniform QCFs. In this paper,
we introduce a subclass of uniform QCFs, the finitely generated uniform QCFs,
based on finite number of elementary gates and show that the class of finitely
generated uniform QCFs is perfectly equivalent to the class of polynomial-time
QTMs; they can exactly simulate each other. This naturally implies that BQP as
well as ZQP and EQP equal the corresponding complexity classes of the finitely
generated uniform QCFs.Comment: 11page
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