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Course Information
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COSC 494/594
Unconventional Computation
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Introduction
Fall 2015
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Instructor: Bruce MacLennan
Course website: web.eecs.utk.edu/~mclennan/Classes/494-­UC or 594-­UC
Lecture Notes are posted on it (read: LNUC-­I.pdf)
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Email: maclennan@utk.edu
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Prereqs: linear algebra (basic CS, physics)
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Grading:
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Homework (ev ery w eek or two)
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Projec t or two
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Term paper (on s ome k ind of unc onv entional c omputation)
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Pres entation (for 594)
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Unconventional Computation
Course Outline
Unconventional Computation
I. Introduction
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II. Physics of c omputation
III. Quantum c omputation
Unconventional (or non-­standard) c omputation refers t o t he use of non-­traditional t echnologies and c omputing paradigms
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IV. Molecular c omputation
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V. Analog c omputation?
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Physical limits t o:
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1.E-­14
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
90 (nm DRAM hp)
65
45
32
fJ
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Practical limit for CMOS?
1.E-­18
aJ
Room-­temperature 100 kT reliability limit
One electron volt
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Significant c hallenges
1.E-­20
Will broaden & deepen c oncept of c omputation in natural & artificial s ystems
1.E-­21
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1.E-­17
Requires a new approach t o c omputation
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1.E-­16
density of binary logic devices
speed of operation
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Trend of ITRS '97-­'03 Gate Energy Trends
Min. Transistor Switching Energy
Based on ITRS ’97-03 roadmaps
250
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Unconventional Computation
1.E-­15
CVV/2 energy, J
The end of Moore’s Law is in s ight!
Is this possible?
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Post-­Moore’s Law Computation
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Why would you want to do this?
Hypercomputation or s uper-­Turing c omputation
refers t o c omputation “beyond t he Turing limit”
VI. Grad presentations on other unconventional computing paradigms
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1.E-­19
Room-­temperature kT thermal energy
Room-­temperature von Neumann -­ Landauer limit
1.E-­22
1995
5
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2000
2005
2010
2015
2020
zJ
2025
Year
Unconventional Computation
2030
2035
2040
2045
Fig. from M. Frank, "Introduction to Reversible Computing” 6
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Unconventional Computation
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X := Y / Z
Differences in Spatial Scale
Differences
in Time
Scale
2.71828
0 0 1 0 1 1 1 0 0 1 1 0 0 0 1 0 1 0 0
…
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…
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(Images from Wikipedia)
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Convergence of Scales
Computation on s cale of physical processes
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Fewer levels between c omputation & realization
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Less t ime f or implementation of operations
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Computation will be more like underlying physical processes
Post-­Moore’s Law c omputing ⇒
greater assimilation of c omputation t o physics
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Computation is Physical
— Susan Stepney (2004)
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Cartesian Duality in CS
“Computation is physical;; it is necessarily embodied in a device whose behaviour is guided by t he laws of physics and c annot be completely c aptured by a c losed mathematical model. This f act of embodiment is becoming ever more apparent as we push t he bounds of those physical laws.”
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Unconventional Computation
Unconventional Computation
(Images from Wikipedia)
Implications of Convergence
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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 t reated independently of hardware
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Focus on f ormal rather t han material
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Post-­Moore’s Law c omputing:
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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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Example: Diffusion
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its physical realization
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its physical environment
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Representation & information processing emerge as regularities in dynamics of physical system
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Many physical systems have sigmoidal behavior
Free in many physical systems
Negative feedback for: Resources become saturated or depleted
delimitation
separation
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creation of structure
Free from
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evaporation
dispersion
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degradation
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Embodied computation uses free sigmoidal behavior
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stabilization
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Positive feedback for growth & extension
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Growth process saturates
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broadcasting information
massively parallel search for optimization, constraint satisfaction etc.
Expensive with c onventional computation
Unconventional Computation
Example:
Negative Feedback
Sigmoids in ANNs & universal approx.
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Can be used for many computational tasks
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Many c omputations performed “ for f ree” by physical s ubstrate
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Occurs naturally in many fluids
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Example: Saturation
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Information often implicit in:
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(Images from Bar-­Y am & Wikipedia)
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Many algorithms use randomness
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symmetry breaking
deadlock avoidance
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exploration
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For free from:
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“Respect the Medium”
escape from local optima
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Example: Randomness
noise
uncertainty
Imprecision
Conventional c omputer t echnology “ tortures the medium” to implement computation
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Embodied c omputation “ respects t he medium”
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Goal of embodied computation:
Exploit t he physics, don’t c ircumvent it
“Free variability”
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(Image from Anderson)
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Some Non-­Turing Characteristics o f Embodied Computation
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But is it Computing?
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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 c omputation
Non-­Turing Computation
Embodied c omputation may s eem imprecise
& difficult t o discriminate f rom other physical processes
Expanding c oncept of c omputation beyond TM requires an expanded definition
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Frames of Relevance
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All models have an associated f rame of relevance
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determined by model’s simplifying assumptions
by aspects & degrees to which model is similar to modelled system
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Determine questions model is s uited t o answer
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Using outside FoR may reflect model & simplifying assumptions more t han modelled system
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Models & Simplifying Assumptions
CT computation is a model of c omputation
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Turing computation is a model of computation
A model is like its s ubject in relevant ways
Unlike it in irrelevant ways
A model is s uited t o pose & answer c ertain classes of questions
Thus every model exists in a f rame of relevance (FoR)
FoR defines domain of reliable use of model Fall 2015
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Example: FoR of Maps
The FoR of Turing Computation
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Historical roots: issues of f ormal c alculability & 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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Alternate Frames of Relevance for Expanded Notions of Computation
Idealizing Assumptions
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Finite but unbounded resources
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Discreteness & definiteness
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applying natural processes in computation
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Sequential t ime
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alternative realizations of formal processes
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Computational t ask = evaluation of well-­defined function
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Computational power defined in t erms of s ets of functions
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Natural Computation
Nanocomputati on
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direct realizations of non-­Turing computations
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unique characteristics
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Quantum & Quantum-­like Computation
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Molecular Computation
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Relevant Issues Outside TC FoR
Natural Computation
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Natural c omputation = c omputation occurring in nature or inspired by it
Occurs in nervous s ystems, DNA, microorganisms, animal groups
Good models f or robust, efficient & effective artificial s ystems (autonomous robots etc.)
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Real-­time c ontrol
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Continuous c omputation
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Robustness
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Generality, f lexibility & adaptability
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Non-­functional c omputation
Different issues are relevant
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Relevant Issues Outside TC FoR
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Error, noise & uncertainty are unavoidable
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must be part of model of computation
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may be used productively
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Real-­time (RT) response c onstraints
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Asymptotic c omplexity is usually irrelevant
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Microscopic reversibility may occur
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Real-­Time Control
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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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Relevant: relation of RT response rate t o RT rates of its c omponents
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Continuous Computation
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Computational processes often c ontinuous
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More or less powerful t han TMs?
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Are continuous quantities
Vary continuously in real time
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Turing-­computable reals vs. standard reals
Standard reals vs. non-­standard reals
Results depend on “ metaphysical issues” ⇒
outside FoR of model
Naïve real analysis is s ufficient f or models of natural c omputation
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Comparis on OK
Can we compare models with different FoRs?
Yes: c an t ranslate one t o other’s FoR
Typically make incompatible s implifying assumptions
Results may depend on s pecifics of translation
E.g., how are c ontinuous quantities represented in TC?
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Within-­Frame Comparison
Cross-­Frame Comparisons
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“Metaphysical issues”:
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Obviously c an be approximated by discrete quantities v arying at discrete t imes,
but …
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“Metaphysics” of Reals
Inputs & outputs often:
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Input size typically constant or of limited variability
Computational resources are bounded
Model
1
Model
2
Common
Frame o f R elev anc e
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Cross-­Frame Comparison
Translated Comparison
Meaningles s C omparis on
Meaningful C omparis on,
But Relev ant?
trans -­
lation
Model
2
Model
1
FoR
A
Model
1
FoR
B
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FoR
A
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Relev ant?
Model
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FoR
A
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trans -­
lation
Model
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Model
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FoR
C
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Super-­Turing c omputation is important, but so is Non-­Turing computation
Model
2
FoR
B
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Digital VLSI becoming a v icious c ycle?
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A limit to t he number of bits and MIPS
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How fundamentally t o 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
What is c omputation in broad s ense?
What FoRs are appropriate f or non-­Turing computation?
Models of non-­Turing c omputation
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FoR
B
Notion of Super-­Turing c omputation is relative to FoR of Turing computation
Some Issues in
Non-­Turing Computation
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Model
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Super-­Turing vs. Non-­Turing
Translation to Third Frame
trans -­
lation
Model
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Alternative t echnologies are s urpassed before they c an be developed
False assumption t hat binary logic is t he only way t o c ompute
How to break out of t he v icious c ycle?
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Possible Physical Realizations
of Computation
What is Computation?
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What distinguishes c omputing (physically realized information processing) f rom other physical processes?
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Computation is a mechanistic process, the purpose or f unction of which is t he abstract manipulation (processing) of abstract objects
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Purpose is f ormal rather t han material
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Does not exclude embodied c omputation, which relies more on physical processes Fall 2015
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Any abstract manipulation of abstract objects is a potential c omputation
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But it must be physically realizable
Any reasonably c ontrollable, mathematically described, physical process c an be used f or computation
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Speed, but:
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faster is not always better
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slower processes may have other advantages
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Feasibility of required t ransducers
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Natural c omputation s hows alternate modes of c omputation, e.g.:
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natural computation shows ways of achieving, even with imperfect components
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Familiarity of binary logic maintains v icious cycle
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Accuracy, s tability & c ontrollability as required f or t he application
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Value of general-­purpose c omputers f or all modes of c omputation
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not appropriate to natural computation, nanocomputation, quantum / quantum-­like computation
central issues of these include continuity, indeterminacy, parallelism
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Broader definition of computation is needed
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Facilitates new implementati on technologies
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Turing model of computation exists in a frame of relevance
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“Universality” is relative t o f rame of relevance
E.g., s peed of emulation is essential t o real-­
time applications (natural c omputation)
Merely c omputing t he s ame f unction may be irrelevant
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Conclusions
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information processing & control in brain
emergent self-­organization in animal societies
Openness t o usable physical processes
Library of well-­matched c omputational methods & physical realizations
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
Improves understandi ng of computati on in nature
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