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Priscila M. V. Lima , Felipe M. G. França and Guilherme M. B. Domingues UFRJ

Priscila M. V. Lima , Felipe M. G. França and Guilherme M. B. Domingues UFRJ 1 st EELA Grid School Itacuruç á , June 4 th , 2006. G-SATyrus: A Gridfied SAT-based Neuro-Symbolic Problem Solving Architecture Task 3.3: Additional Applications. SATyrus. SAT yrus:

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Priscila M. V. Lima , Felipe M. G. França and Guilherme M. B. Domingues UFRJ

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  1. Priscila M. V. Lima, Felipe M. G. França and Guilherme M. B. Domingues UFRJ 1st EELA Grid School Itacuruçá, June 4th, 2006 G-SATyrus: A Gridfied SAT-based Neuro-Symbolic Problem Solving ArchitectureTask 3.3: Additional Applications

  2. Itacuruçá, June 25th, 2006 SATyrus SATyrus: • SATisfiability-based, neuro-symbolic architecture; • Exact formulation synthesizer. Target Problem, e.g., colouring Constraints Modeling SATyrus compiler Energy Function Optimizer, e.g., stochastic HONNs Global/Local optima

  3. Itacuruçá, June 25th, 2006 SATyrus Target Problem, e.g., colouring Graph Colouring consists on determining the minimum assignment of colours to the vertices of G=(V, A); G=(V, A)

  4. Itacuruçá, June 25th, 2006 SATyrus Target Problem, e.g., colouring Constraints Modeling Integrity Constraints: • (i) Every vertex must have one colour assigned to it: • ∀i, ∀k| 1 ≤ i ≤ n, 1 ≤ k ≤ n: ∨(vcik). • So, letφ5 = ∧i(∨k (vcik)). • (ii) Two neighbouring vertices cannot have the same colour: • ∀i, ∀i’, ∀k| 1 ≤ i ≤ n, 1 ≤ i’ ≤ n, 1 ≤ k ≤ n, i ≠ i’: ¬(neighii’) ∨ ¬(vcik ∧vci’k). • So, letφ6 = ∧i∧i’≠i∧k(¬(neighii’) ∨ ¬(vcik ∧vci’k)).

  5. Itacuruçá, June 25th, 2006 SATyrus Target Problem, e.g., colouring Constraints Modeling Integrity Constraints (cont.): • (iii) A vertex cannot have more than one colour: • ∀i, ∀k, ∀k’ | 1 ≤ i ≤ n, 1 ≤ k ≤ n, 1 ≤ k’ ≤ n, k ≠ k’: ¬(vcik∧ vcik’). • So, letφ7 = ∧i∧k∧k’≠k ¬(vcik∧ vcik’). • (iv) If a colourkis assigned to a vertex in matrixVcolour, then the corresponding unit in matrixCcolourmust be activated: • ∀i, ∀k | 1 ≤ i ≤ n, 1 ≤ k ≤ n: ¬vcik∨ ck. • So, letφ8 = ∧i∧k(¬vcik∨ ck).

  6. Itacuruçá, June 25th, 2006 SATyrus Target Problem, e.g., colouring Constraints Modeling Optimality Constraint: • (v) The number of activated elements in matrix Ccolour: • ∀k | 1 ≤ k ≤ n : ck. • So, let φ9 = ∨k ck.

  7. Itacuruçá, June 25th, 2006 SATyrus Target Problem, e.g., colouring Constraints Modeling Constraints’ penalties: • Constraints (iii):  • Constraints (i), (ii) and (iv):  • Constraints (v): 1

  8. Itacuruçá, June 25th, 2006 SATyrus Target Problem, e.g., colouring Constraints Modeling %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;} SATyrus compiler

  9. Itacuruçá, June 25th, 2006 SATyrus Target Problem, e.g., colouring Constraints Modeling SATyrus compiler Energy Function

  10. Itacuruçá, June 25th, 2006 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.

  11. Itacuruçá, June 25th, 2006 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);

  12. Itacuruçá, June 25th, 2006 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);

  13. Itacuruçá, June 25th, 2006 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.

  14. Itacuruçá, June 25th, 2006 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 agileinter-domain communication capabilities;

  15. Itacuruçá, June 25th, 2006 SATyrus Thanks. priscila@nce.ufrj.br felipe@cos.ufrj.br

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