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The Matrix Model of Computation (MMC). Sergio Pissanetzky. The MMC consists of two sparse matrices: M = (C, Q) C = Matrix of Services Q = Matrix of Sequences The model has two forms: ● imperative form ● canonical form. PROGRAM. - PowerPoint PPT Presentation
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The Matrix Model of Computation
(MMC)
Sergio Pissanetzky
The MMC consists of two sparse matrices:
M = (C, Q)
C = Matrix of Services
Q = Matrix of Sequences
The model has two forms:
● imperative form
● canonical form
* C* C* C* C* C* C* C* C* C+ A C+ A A C+ A C+ A C+ A A C+ A C+ A A C+ A C+ A C
tc = a * fz
tj = b * fx
tf = d * vz
tk = b * fy
tb = a * fy
te = d * vy
tl = b * fz
ta = a * fx
td = d * vx
wz = vz + tl
tg = ta + td
wx = vx + tj
sx = rx + tg
th = tb + te
wy = vy + tk
ti = tc + tf
sz = rz + ti
sy = ry + th
tc tj tf tk tb te tl ta td wz tg wx sx th wy ti sz syPROGRAM DATA
a, fz
b, fx
d, vz
b, fy
a, fy
d, vy
b, fz
a, fx
d, vx
vz
vx
rx
vy
rz
ry
The MMC is simple, yet very rich in features
Universal Natural ontology
Mathematically formal Dynamic mode
Turing – equivalent Self – organizing
Quantum – equivalent Connectionist
Relational database Massively parallel
Computer program Data channel
Algebra of operations Transformations, refactorings
Formal algorithms Training modes
The Scope Constriction Algorithm
(SCA)
CC
CC
CC
CC
CA C
A A CA C
A CA A C
A CA A C
A CA C
Profile ofmatrix C
tc tj tf tk tb te tl ta td wz tg wx sx th wy ti sz sy
CC
CC
CC
CC
CA C
A A CA C
A CA A C
A CA A C
A CA C
Data channel
tc tj tf tk tb te tl ta td wz tg wx sx th wy ti sz sy
“Turbulent” flow
CC
CC
CC
CC
CA C
A A CA C
A CA A C
A CA A C
A CA C
Service Commutation
tc tj tf tk tb te tl ta td wz tg wx sx th wy ti sz sy
CC
A A CA C
CA C
CC
A A CA C
CA C
CC
A A CA C
CA C
td ta tg sx tj wx te tb th sy tk wy tf tc ti sz tl wztd = d * vx
ta = a * fx
tg = ta + td
sx = rx + tg
tj = b * fx
wx = vx + tj
te = d * vy
tb = a * fy
th = tb + te
sy = ry + th
tk = b * fy
wy = vy + tk
tf = d * vz
tc = a * fz
ti = tc + tf
sz = rz + ti
tl = b * fz
wz = vz + tl
PROGRAM DATAd, vx
a, fx
rx
b,fx
vx
d, vy
a, fy
ry
b, fy
vy
d, vz
a, fz
rz
b, fz
vz
“Laminar” flow
G
G
G
H
H
H
G gx;sx = gx.go(a, d, fx, rx, vx);H hx;wx = hx.go(b, fx, vx);G gy;sy = gy.go(a, d, fy, ry, vy);H hy;wy = hy.go(b, fy, vy);G gz;sz = gz.go(a, d, fz, rz, vz);H hz;wz = hz.go(b, fz, vz);
The refactored code
Where did the objects come from?
CONCLUSIONS AND OUTLOOK
● Objects and inheritance occur naturally in systems. They can be revealed by the SCA algorithm.
● Impact on Computer Science, Software Engineering,Refactoring, the Semantic Web, Artificial Intelligence, Biology, Neuroscience, Linguistics.
● Conjecture: Our mind uses the same process tomake objects.
