the matrix model of computation (mmc)

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.