AlanTuring: ACenturyofComputingusers.metu.edu.tr/bozsahin/turing-metu-econ.pdf · AlanTuring:...

Alan Turing:A Century of Computing

Cem Bozşahin

Cognitive Science Department, The Informatics Institute, METU

www.ii.metu.edu.tr

Department of Economics Seminars, METU

28.5.2012

Bozşahin Alan Turing Centenary

Alan Mathison Turing: 1912–1954

Bozşahin Alan Turing Centenary 2/23

What was Turing up to?

He tried just about everything

ChemistryCryptology (Enigma)Bio-genetics (morphogenesis)Abstract computing (algorithms)Applied computing (programming)Mind-body problem (round-the-house chess)Turing testArtificial lifeFoundations of mathematicsArtificial IntelligenceMarathon

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AMT the athlete

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Perhaps the right question is:

How was Turing trying to do everything he did?

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Mark I, 1948. Manchester’s Ferranti Bros.

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Mark I, 2011

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Turing Machine

. . . b b a a a a . . . Input/Output Tape

q0q1

q2

q3 . . .

qn

Finite Control

q1

Reading and Writing Head(moves in both directions)

Bozşahin Alan Turing Centenary 8/23

A TM

aL L LI

#

#L #

aR # L

#R

#

R

a

I#Ra

#I

IR L#

a

#

a

a

a

#

# aaR #CaL #

not I

‘#’

x

L

R

L

R

find first x on left

x

x

find first x on right

move right

move left

write x

blank

#

A Turing machine to compute f(n,m)=n x m

It copies the second string a number of times given by the first string.

From Lewis and Papadimitriou (1981).

Representation: maps #I #I #m n

to aI aI m n

first__ __

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k-tape TM

1

2

k

FSM

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Putnam-Gold TM

1

2

3

FSM

TM

deneme

E E H

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Non-Turing extensions to Computing

Analog devices (where everything represents itself)Quantum computing

Bankers bewareNew measures of complexity

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What is essential to Turing?

P-G machine is a TMThe nature of relation between representation and computing.Complexity is defined over representation rather than physicaltime and space.One more move of a TM makes the solution one step moreinvolved.

Bozşahin Alan Turing Centenary 13/23

TM

. . . b b a a a a . . . Input/Output Tape

q0q1

q2

q3 . . .

qn

Finite Control

q1

Reading and Writing Head(moves in both directions)

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k-TTM

1

2

k

FSM

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Problems

Formulable but unsolvable problems

diagonal(X):a: if halt(X,X) goto a otherwise halt.

diagonal(diagonal) ?

Expressible but unformulable problems

What is the next number after π?

The difference is TM representability.

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Foundations of Math and AMT

Turing’s universal combinatorUfg = g(ffg)

U = (λxλy .y(xxy))(λxλy .y(xxy))

Uf = [ (λxλy .y(xxy))(λxλy .y(xxy)) ] f[λy .y([ λx1λy1.y1(x1x1y1) ] [ λx2λy2.y2(x2x2y2) ] y) ] ff ([ λx1λy1.y1(x1x1y1) ] [ λx2λy2.y2(x2x2y2) ] f )f (Uf )

Uf = f (Uf )

Recursion without names, programs without variables!

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Turing Test

(Ann Witbrock; Copeland, B.J., Artificial Intelligence BlackwellPublishers, Oxford, 1993.)

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Searle and Turing

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Programming and Searle

ConceptualIntentional System

ArticulatoryPerceptual System

Person

Performance System

PhonologicalForm

LogicalForm

Grammar

Lexicon(meaning bearing items)

(meaning bearing phrases)

Virtual Machine

Interpretive systemTransductive system

Computer

I/O CPU

Alphabet (finite vocabulary)

Well−formed

programs

(source code)

meaningful

computation

(interp. code)

Grammar

Lexicon(finitely characterizable tokens)

(finitely characterizable sentences)

Bozşahin Alan Turing Centenary 20/23

does it look like a TM?AMT: intelligent behavior can arise from manipulation ofrepresentation.With representations, we can build models. Without them wetalk about them.Turing representability is the key to Turing’s computing.

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AMT @ 13

“I always seem to want to make things from the thing that iscommonest in nature.”

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AMT @ 9

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