2012/8/22
COSC 494/594
Unconventional Computation
Introduction
Fall 2012
Unconventional Computation
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Course Information
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Instructor: Bruce MacLennan
Course website:
web.eecs.utk.edu/~mclennan/Classes/494-UC or 594-UC
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Email: maclennan@eecs.utk.edu
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Prereqs: linear algebra (basic CS, physics)
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Grading:
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Homework (every week or two)
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Project or two
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Term paper (on some kind of unconventional computation)
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Presentation (for 594)
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Course Outline
I.  Introduction
II.  Physics of computation
III.  Quantum computation
IV.  Molecular computation
V.  Analog computation?
VI. Grad presentations on other unconventional
computing paradigms
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Unconventional Computation
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Unconventional (or non-standard) computation
refers to the use of non-traditional technologies
and computing paradigms
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Why would you want to do this?
Hypercomputation or super-Turing computation
refers to computation “beyond the Turing limit”
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Is this possible?
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Post-Moore’s Law Computation
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The end of Moore’s Law is in sight!
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Physical limits to:
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density of binary logic devices
-
speed of operation
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Requires a new approach to computation
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Significant challenges
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Will broaden & deepen concept of computation
in natural & artificial systems
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Gate Energy
Trends
Trend of ITRS
Min.'97-'03
Transistor
Switching
Energy
Based on ITRS ’97-03 roadmaps
1.E-14
250
180
1.E-15
130
90
CVV/2 energy, J
1.E-16
LP min gate energy, aJ
HP min gate energy, aJ
100 k(300 K)
ln(2) k(300 K)
1 eV
k(300 K)
Node numbers
(nm DRAM hp)
65
45
32
1.E-17
fJ
22
Practical limit for CMOS?
1.E-18
Na
ïve
lin
ear
ex
Room-temperature 100 kT reliability limit
One electron volt
1.E-19
1.E-20
1.E-21
aJ
tra
pol
atio
n
Room-temperature kT thermal energy
Room-temperature von Neumann - Landauer limit
1.E-22
1995
2000
2005
2010
2015
2020
zJ
2025
2030
2035
2040
2045
Year
2005/05/05
M. Frank, "Introduction to Reversible Computing"
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Differences in Spatial Scale
2.71828
0010111001100010100
…
Fall 2012
…
Unconventional Computation
(Images from Wikipedia)‫‏‬
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X := Y / Z
Differences
in Time
Scale
Fall 2012
P[0] := N
i := 0
while i < n do
if P[i] >= 0 then
q[n-(i+1)] := 1
P[i+1] := 2*P[i] - D
else
q[n-(i+1)] := -1
P[i+1] := 2*P[i] + D
end if
i := i + 1
end while
Unconventional Computation
(Images from Wikipedia)‫‏‬
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Convergence of Scales
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Implications of Convergence
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Computation on scale of physical processes
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Fewer levels between computation & realization
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Less time for implementation of operations
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Computation will be more like underlying
physical processes
Post-Moore’s Law computing
greater assimilation of computation to physics
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Computation is Physical
“Computation is physical; it is necessarily
embodied in a device whose behaviour is
guided by the laws of physics and cannot be
completely captured by a closed mathematical
model. This fact of embodiment is becoming
ever more apparent as we push the bounds of
those physical laws.”
— Susan Stepney (2004)
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Cartesian Duality in CS
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Programs as idealized mathematical objects
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Software treated independently of hardware
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Focus on formal rather than material
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Post-Moore’s Law computing:
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less idealized
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more dependent on physical realization
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More difficult
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But also presents opportunities…
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Strengths of
“Embodied Computation”
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Information often implicit in:
-
its physical realization
-
its physical environment
Many computations performed “for free” by
physical substrate
Representation & information processing
emerge as regularities in dynamics of physical
system
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Unconventional Computation
Example:
Diffusion
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Occurs naturally in many
fluids
Can be used for many
computational tasks
-
broadcasting information
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massively parallel search
for optimization, constraint
satisfaction etc.
Expensive with conventional
computation
Free in many physical
systems
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Example: Saturation
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Sigmoids in ANNs &
universal approx.
Many physical systems
have sigmoidal
behavior
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Growth process
saturates
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Resources become
saturated or depleted
Embodied computation
uses free sigmoidal
behavior
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(Images from Bar-Yam & Wikipedia)‫‏‬
Example:
Negative
Feedback
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Positive feedback for
growth & extension
Negative feedback for:
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stabilization
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delimitation
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separation
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creation of structure
Free from
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evaporation
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dispersion
-
degradation
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Many algorithms use
randomness
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escape from local optima
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symmetry breaking
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deadlock avoidance
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exploration
Example:
Randomness
For free from:
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noise
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uncertainty
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Imprecision
“Free variability”
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(Image from Anderson)
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“Respect the Medium”
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Conventional computer technology “tortures the
medium” to implement computation
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Embodied computation “respects the medium”
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Goal of embodied computation:
Exploit the physics, don’t circumvent it
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But is it Computing?
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Some Non-Turing Characteristics of
Embodied Computation
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Operates in real time and real space
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with real matter and real energy
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and hence non-ideal aspects of physical realization
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Often does not terminate
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Often has no distinct inputs or outputs
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Often purpose is not to get an answer from an input
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Often purpose is not to control fixed agent
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Different notions of equivalence and universality
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Is EC a Species of Computing?
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The Turing Machine provides a precise
definition of computation
Embodied computation may seem imprecise
& difficult to discriminate from other physical
processes
Expanding concept of computation beyond TM
requires an expanded definition
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Non-Turing Computation
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Frames of Relevance
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CT computation is a model of computation
All models have an associated frame of
relevance
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determined by model’s simplifying assumptions
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by aspects & degrees to which model is similar to
modelled system
Determine questions model is suited to answer
Using outside FoR may reflect model &
simplifying assumptions more than modelled
system
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Models & Simplifying Assumptions
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Turing computation is a model of
computation
A model is like its subject in relevant ways
Unlike it in irrelevant ways
A model is suited to pose & answer certain
classes of questions
Thus every model exists in a frame of
relevance (FoR)
FoR defines domain of reliable use of model
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Example: FoR of Maps
2010/03/22
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The FoR of Turing Computation
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Historical roots: issues of formal calculability &
provability in axiomatic mathematics; hence:
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finite number of steps & finite but unlimited
resources
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computation viewed as function evaluation
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discreteness assumptions
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Idealizing Assumptions
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Finite but unbounded resources
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Discreteness & definiteness
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Sequential time
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Computational task = evaluation of well-defined
function
Computational power defined in terms of sets of
functions
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Alternate Frames of Relevance
for Expanded Notions of
Computation
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Natural Computation
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applying natural processes in computation
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alternative realizations of formal processes
Nanocomputation
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direct realizations of non-Turing computations
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unique characteristics
Quantum & Quantum-like Computation
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Natural Computation
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Natural computation = computation occurring in
nature or inspired by it
Occurs in nervous systems, DNA,
microorganisms, animal groups
Good models for robust, efficient & effective
artificial systems (autonomous robots etc.)
Different issues are relevant
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Relevant Issues Outside TC FoR
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Real-time control
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Continuous computation
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Robustness
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Generality, flexibility & adaptability
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Non-functional computation
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Relevant Issues Outside TC FoR
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Error, noise & uncertainty are unavoidable
must be part of model of computation
-  may be used productively
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Microscopic reversibility may occur
e.g., reversible chemical reactions
-  want statistical or macroscopic progress
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Computation proceeds asynchronously in
continuous-time parallelism
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Real-Time Control
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Real-time (RT) response constraints
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Asymptotic complexity is usually irrelevant
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Input size typically constant or of limited variability
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Computational resources are bounded
Relevant: relation of RT response rate to RT
rates of its components
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Continuous Computation
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Inputs & outputs often:
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Are continuous quantities
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Vary continuously in real time
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Computational processes often continuous
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More or less powerful than TMs?
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Obviously can be approximated by discrete
quantities varying at discrete times,
but …
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“Metaphysics” of Reals
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“Metaphysical issues”:
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Turing-computable reals vs. standard reals
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Standard reals vs. non-standard reals
Results depend on “metaphysical issues” ⇒
outside FoR of model
Naïve real analysis is sufficient for models of
natural computation
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Cross-Frame Comparisons
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Can we compare models with different
FoRs?
Yes: can translate one to other’s FoR
Typically make incompatible simplifying
assumptions
Results may depend on specifics of
translation
E.g., how are continuous quantities
represented in TC?
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Within-Frame Comparison
Comparison OK
Model
1
Model
2
Common
Frame of Relevance
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Cross-Frame Comparison
Meaningless Comparison
Model
2
Model
1
FoR
A
FoR
B
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Translated Comparison
Meaningful Comparison,
But Relevant?
translation
Model
1
FoR
A
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Model
1ʹ′
Model
2
FoR
B
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Translation to Third Frame
Relevant?
translation
Model
1
FoR
A
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translation
Model
1ʹ′
Model
2ʹ′
FoR
C
Model
2
FoR
B
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Super-Turing vs. Non-Turing
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Notion of Super-Turing computation is relative
to FoR of Turing computation
Super-Turing computation is important, but so
is Non-Turing computation
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Some Issues in
Non-Turing Computation
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What is computation in broad sense?
What FoRs are appropriate for non-Turing
computation?
Models of non-Turing computation
How fundamentally to incorporate error,
uncertainty, imperfection, reversibility?
How systematically to exploit new physical
processes?
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Expanding the Range of
Physical Computation
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Digital VLSI becoming a vicious cycle?
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A limit to the number of bits and MIPS
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Alternative technologies are surpassed before
they can be developed
False assumption that binary logic is the only
way to compute
How to break out of the vicious cycle?
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What is Computation?
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What distinguishes computing (physically
realized information processing) from other
physical processes?
Computation is a mechanistic process, the
purpose or function of which is the abstract
manipulation (processing) of abstract objects
Purpose is formal rather than material
Does not exclude embodied computation, which
relies more on physical processes
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Possible Physical Realizations
of Computation
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Any abstract manipulation of abstract objects
is a potential computation
de novo applications of math models
-  applications suggested by natural computation
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But it must be physically realizable
Any reasonably controllable, mathematically
described, physical process can be used for
computation
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Some Requirements
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Speed, but:
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faster is not always better
-
slower processes may have other advantages
Feasibility of required transducers
Accuracy, stability & controllability as
required for the application
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natural computation shows ways of achieving,
even with imperfect components
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Matching Computational
& Physical Processes
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Familiarity of binary logic maintains vicious
cycle
Natural computation shows alternate modes
of computation, e.g.:
information processing & control in brain
-  emergent self-organization in animal societies
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Openness to usable physical processes
Library of well-matched computational
methods & physical realizations
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General-Purpose Computation
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Value of general-purpose computers for all
modes of computation
“Universality” is relative to frame of relevance
E.g., speed of emulation is essential to realtime applications (natural computation)
Merely computing the same function may be
irrelevant
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Conclusions
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Turing model of computation exists in a frame
of relevance
-
not appropriate to natural computation,
nanocomputation, quantum / quantum-like
computation
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central issues of these include continuity,
indeterminacy, parallelism
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Broader definition of computation is needed
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Facilitates new implementation technologies
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Improves understanding of computation in
nature
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