2012/8/22
Course Information
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COSC 494/594
Unconventional Computation
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Unconventional Computation
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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:
Introduction
Fall 2012
Instructor: Bruce MacLennan
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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)
Fall 2012
Unconventional Computation
Course Outline
Unconventional Computation
I.  Introduction
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II.  Physics of computation
III.  Quantum computation
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V.  Analog computation?
VI. Grad presentations on other unconventional
computing paradigms
Unconventional Computation
Unconventional (or non-standard) computation
refers to the use of non-traditional technologies
and computing paradigms
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IV.  Molecular computation
Fall 2012
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3
Why would you want to do this?
Hypercomputation or super-Turing computation
refers to computation “beyond the Turing limit”
Is this possible?
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Unconventional Computation
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Gate Energy
Trends
Trend of ITRS
Min.'97-'03
Transistor
Switching
Energy
Post-Moore’s Law Computation
Based on ITRS ’97-03 roadmaps
1.E-14
250
180
1.E-15
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
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speed of operation
45
fJ
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Practical limit for CMOS?
1.E-18
Na
ïve
lin
ear
ex
Room-temperature 100 kT reliability limit
One electron volt
1.E-19
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Significant challenges
1.E-20
Will broaden & deepen concept of computation
in natural & artificial systems
1.E-21
Unconventional Computation
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Requires a new approach to computation
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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)
1.E-17
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90
1.E-16
CVV/2 energy, J
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130
tra
p
Room-temperature kT thermal energy
ola
tio
n
Room-temperature von Neumann - Landauer limit
1.E-22
1995
5
aJ
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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2012/8/22
X := Y / Z
Differences in Spatial Scale
Differences
in Time
Scale
2.71828
0010111001100010100
…
Fall 2012
…
Unconventional Computation
(Images from Wikipedia)‫‏‬
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Convergence of Scales
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
— Susan Stepney (2004)
Unconventional Computation
Unconventional Computation
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Cartesian Duality in CS
“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.”
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Unconventional Computation
Unconventional Computation
(Images from Wikipedia)‫‏‬
Implications of Convergence
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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
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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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Unconventional Computation
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2012/8/22
Strengths of
“Embodied Computation”
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Example:
Diffusion
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its physical realization
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its physical environment
Many computations performed “for free” by
physical substrate
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Representation & information processing
emerge as regularities in dynamics of physical
system
Unconventional Computation
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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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Unconventional Computation
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Occurs naturally in many
fluids
Can be used for many
computational tasks
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broadcasting information
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massively parallel search
for optimization, constraint
satisfaction etc.
Expensive with conventional
computation
Free in many physical
systems
Unconventional Computation
Example:
Negative
Feedback
Example: Saturation
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Information often implicit in:
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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
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degradation
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(Images from Bar-Yam & Wikipedia)‫‏‬
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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
“Respect the Medium”
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For free from:
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noise
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uncertainty
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Imprecision
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
“Free variability”
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Unconventional Computation
(Image from Anderson)
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Unconventional Computation
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2012/8/22
Some Non-Turing Characteristics of
Embodied Computation
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But is it Computing?
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Unconventional 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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Unconventional Computation
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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
Non-Turing Computation
& difficult to discriminate from other physical
processes
Expanding concept of computation beyond TM
requires an expanded definition
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Frames of Relevance
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All models have an associated frame of
relevance
determined by model’s simplifying assumptions
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by aspects & degrees to which model is similar to
modelled system
A model is like its subject in relevant ways
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Unlike it in irrelevant ways
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Using outside FoR may reflect model &
simplifying assumptions more than modelled
system
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Turing computation is a model of
computation
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Determine questions model is suited to answer
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Models & Simplifying Assumptions
CT computation is a model of computation
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Unconventional Computation
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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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2012/8/22
Example: FoR of Maps
The FoR of Turing Computation
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2010/03/22
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Historical roots: issues of formal calculability &
provability in axiomatic mathematics; hence:
Finite but unbounded resources
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Discreteness & definiteness
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Sequential time
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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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Computational task = evaluation of well-defined
function
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Computational power defined in terms of sets of
functions
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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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Relevant Issues Outside TC FoR
Natural Computation
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Unconventional Computation
Alternate Frames of Relevance
for Expanded Notions of
Computation
Idealizing Assumptions
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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.)
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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
Different issues are relevant
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2012/8/22
Relevant Issues Outside TC FoR
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Real-Time Control
Error, noise & uncertainty are unavoidable
must be part of model of computation
-  may be used productively
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Real-time (RT) response constraints
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Asymptotic complexity is usually irrelevant
Microscopic reversibility may occur
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e.g., reversible chemical reactions
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want statistical or macroscopic progress
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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
Computation proceeds asynchronously in
continuous-time parallelism
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Continuous Computation
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“Metaphysical issues”:
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Are continuous quantities
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Turing-computable reals vs. standard reals
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Vary continuously in real time
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Standard reals vs. non-standard reals
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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Unconventional Computation
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Results depend on “metaphysical issues” ⇒
outside FoR of model
Naïve real analysis is sufficient for models of
natural computation
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Within-Frame Comparison
Cross-Frame Comparisons
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“Metaphysics” of Reals
Inputs & outputs often:
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Unconventional Computation
Comparison OK
Can we compare models with different
FoRs?
Yes: can translate one to other’s FoR
Typically make incompatible simplifying
assumptions
Model
1
Results may depend on specifics of
translation
E.g., how are continuous quantities
represented in TC?
Unconventional Computation
Model
2
Common
Frame of Relevance
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Cross-Frame Comparison
Translated Comparison
Meaningless Comparison
Meaningful Comparison,
But Relevant?
translation
Model
2
Model
1
FoR
A
Model
1
FoR
B
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FoR
A
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Relevant?
Model
1
FoR
A
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translation
Model
1ʹ′
Model
2ʹ′
FoR
C
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FoR
B
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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
Model
2
FoR
B
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Fall 2012
Unconventional Computation
What is computation in broad sense?
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Digital VLSI becoming a vicious cycle?
What FoRs are appropriate for non-Turing
computation?
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A limit to the number of bits and MIPS
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Models of non-Turing computation
How fundamentally to incorporate error,
uncertainty, imperfection, reversibility?
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How systematically to exploit new physical
processes?
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Expanding the Range of
Physical Computation
Some Issues in
Non-Turing Computation
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Model
2
Super-Turing vs. Non-Turing
Translation to Third Frame
translation
Model
1ʹ′
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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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Unconventional Computation
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2012/8/22
Possible Physical Realizations
of Computation
What is Computation?
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What distinguishes computing (physically
realized information processing) from other
physical processes?
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Computation is a mechanistic process, the
purpose or function of which is the abstract
manipulation (processing) of abstract objects
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Purpose is formal rather than material
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Does not exclude embodied computation, which
relies more on physical processes
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Unconventional Computation
Any abstract manipulation of abstract objects
is a potential 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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Unconventional Computation
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Speed, but:
faster is not always better
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slower processes may have other advantages
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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
Unconventional Computation
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Familiarity of binary logic maintains vicious
cycle
Natural computation shows alternate modes
of computation, e.g.:
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information processing & control in brain
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emergent self-organization in animal societies
Openness to usable physical processes
Library of well-matched computational
methods & physical realizations
Fall 2012
Unconventional Computation
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Value of general-purpose computers for all
modes of computation
Turing model of computation exists in a frame
of relevance
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not appropriate to natural computation,
nanocomputation, quantum / quantum-like
computation
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central issues of these include continuity,
indeterminacy, parallelism
“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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Broader definition of computation is needed
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Facilitates new implementation technologies
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Conclusions
General-Purpose Computation
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Matching Computational
& Physical Processes
Some Requirements
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de novo applications of math models
applications suggested by natural computation
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Improves understanding of computation in
nature
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