FP6−2004−Infrastructures−6-SSA-026409

www.eu-eela.org

E-infrastructure shared between Europe and Latin America

G-SATyrus: A Gridfied SAT-based Neuro-Symbolic Problem Solving Architecture

Task 3.3: Additional Applications

Priscila M. V. Lima, Felipe M. G. França and Guilherme M. B. DominguesUFRJ1st EELA Grid SchoolItacuruçá, June 4th, 2006

Itacuruçá, June 25th, 2006FP6−2004−Infrastructures−6-SSA-026409

E-infrastructure shared between Europe and Latin America

SATyrus:

• SATisfiability-based,

neuro-symbolic

architecture;

• Exact formulation

synthesizer.

SATyrus

Target Problem, e.g., colouring

Constraints Modeling

SATyrus compiler

Energy Function

Optimizer, e.g., stochastic HONNs

Global/Local optima

Itacuruçá, June 25th, 2006FP6−2004−Infrastructures−6-SSA-026409

E-infrastructure shared between Europe and Latin America

SATyrus

G=(V, A)

Graph Colouring consists on determining the minimum assignment of colours to the vertices of G=(V, A);

Target Problem, e.g., colouring

Itacuruçá, June 25th, 2006FP6−2004−Infrastructures−6-SSA-026409

E-infrastructure shared between Europe and Latin America

SATyrus

Integrity Constraints:

(i) Every vertex must have one colour assigned to it:

∀i, k | 1 ≤ i ≤ n, 1 ≤ k ≤ n: (vcik). ∀ ∨So, let φ5 = i( k (vcik)).∧ ∨

(ii) Two neighbouring vertices cannot have the same colour:

∀i, i’, k | 1 ≤ i ≤ n, 1 ≤ i’ ≤ n, 1 ≤ k ∀ ∀

Target Problem, e.g., colouring

Constraints Modeling

Itacuruçá, June 25th, 2006FP6−2004−Infrastructures−6-SSA-026409

E-infrastructure shared between Europe and Latin America

SATyrus

Integrity Constraints (cont.):

(iii) A vertex cannot have more than one colour:

∀i, k, k’ | 1 ≤ i ≤ n, 1 ≤ k ≤ n, 1 ≤ k’ ∀ ∀

Target Problem, e.g., colouring

Constraints Modeling

Itacuruçá, June 25th, 2006FP6−2004−Infrastructures−6-SSA-026409

E-infrastructure shared between Europe and Latin America

SATyrus

Optimality Constraint:

(v) The number of activated elements in matrix Ccolour:

∀k | 1 ≤ k ≤ n : ck.

So, let φ9 = ∨k ck.

Target Problem, e.g., colouring

Constraints Modeling

Itacuruçá, June 25th, 2006FP6−2004−Infrastructures−6-SSA-026409

E-infrastructure shared between Europe and Latin America

SATyrus

Target Problem, e.g., colouring

Constraints Modeling

Constraints’ penalties:

Constraints (iii):

Constraints (i), (ii) and (iv): Constraints (v): 1

Itacuruçá, June 25th, 2006FP6−2004−Infrastructures−6-SSA-026409

E-infrastructure shared between Europe and Latin America

SATyrus

%GRAPH COULORING(SATyrus specification)num=6;neigh(num,num);vc(num,num);colour(num);integrity group type alfa:Forall {i,k}; 1 <= I <= num,1 <= k <= num:vc[i][k];integrity group type beta:Forall {i,l,k}; 1 <= I <= num,1 <= l <= num,1 <= k <= num; I != l:(not neigh[i][l] or not vc[i][k]or not vc[l][k]);integrity group type beta:Forall {i,k,m}; 1 <= I <= num,1 <= k <= num;1$<=$m$<=$num;k$!=$m:(not vc[i][k] or not vc[i][m]); integrity group type beta:Forall {i,k}; 1 <= I <= num,1 <= k <= num: (not vc[i][k] or

colour[k]);optimality group type costo:Forall {k}; 1 <= k <= num: colour[k];PENALTY { beta is level 2; alfa is level 1; costo is level 0;}

Target Problem, e.g., colouring

Constraints Modeling

SATyrus compiler

Itacuruçá, June 25th, 2006FP6−2004−Infrastructures−6-SSA-026409

E-infrastructure shared between Europe and Latin America

SATyrus

Target Problem, e.g., colouring

Constraints Modeling

SATyrus compiler

Energy Function

Itacuruçá, June 25th, 2006FP6−2004−Infrastructures−6-SSA-026409

E-infrastructure shared between Europe and Latin America

SATyrus

Motivations: Hard, composite, complex problems

• Energy Generation Expansion

LOA — Advanced Optimization Lab, CNPq, Brazil, 2006;

E.g., unification of short, medium and long term models.

• Airport Management (surface)

CAPES-COFECUB, UFRJ — ENAC&UT2, Toulouse, 2006 (submitted);

E.g., A-SMGCS support: routing, monitoring, signaling and control of mobile entities.

Itacuruçá, June 25th, 2006FP6−2004−Infrastructures−6-SSA-026409

E-infrastructure shared between Europe and Latin America

SATyrus

• Artificial Logical Reasoning

ARQ-PROP2, ARQ-FOL — Resolution based, ANN based

architectures (Lima, 1992) (Lima, 2000) (Lima, 2001a)

(Lima, 2001b) ;

• 3D Molecular Structure Reconstruction

Molecular reconstruction via integration of independent

models;

Equivalence between geometrical model and classic

molecular model proven (Glaucia Pereira, 2006);

Itacuruçá, June 25th, 2006FP6−2004−Infrastructures−6-SSA-026409

E-infrastructure shared between Europe and Latin America

SATyrus

• Grid OS

Dynamic and Distributed Scheduling of Execution, Storage and Communication Resources;

Distributed File/Storage System;

Intelligent/Reactive Communication System;

(Diego Carvalho, Guilherme Domingues and Pedro Henrique Rausch Bello);

Itacuruçá, June 25th, 2006FP6−2004−Infrastructures−6-SSA-026409

E-infrastructure shared between Europe and Latin America

SATyrus

First grid enabling strategy: Multistart

Single HONN under slow cooling; geometrical cooling (0.99)

versus

Multiple HONNs starting from different initial points;

cool runnings ;-)

• Adv.: copes with lack of agile inter-domain communication capabilities

(bag-of-tasks);

• Disadv.: problems limited by single CPU capabilities.

Itacuruçá, June 25th, 2006FP6−2004−Infrastructures−6-SSA-026409

E-infrastructure shared between Europe and Latin America

SATyrus

Second grid enabling strategy (perhaps EELA-2):

Fully Distributed

Single HONN under slow cooling spread throughout the grid;

• Adv.: interesting (and huge) problems, e.g., 3D molecular

reconstruction (110 PetaBytes), could be tackled; not limited by single

CPU capabilities.

• Disadv.: does not cope with lack of agile inter-domain communication

capabilities;

Itacuruçá, June 25th, 2006FP6−2004−Infrastructures−6-SSA-026409

E-infrastructure shared between Europe and Latin America

SATyrus

Thanks.

priscila@nce.ufrj.br

felipe@cos.ufrj.br