answer set solving in practice
play

Answer Set Solving in Practice Torsten Schaub University of Potsdam - PowerPoint PPT Presentation

Sep 28, 2022 •126 likes •1.92k views

Answer Set Solving in Practice Torsten Schaub University of Potsdam Torsten Schaub (KRR@UP) ASP in Practice 1 / 69 Outline 1 Motivation 2 Introduction 3 Modeling by Example Graph Coloring Queens Traveling Salesperson 4 Meta Programming 5

  1. Introduction Basic idea Consider the logical formula Φ and its three Φ q ∧ ( q ∧ ¬ r → p ) (classical) models: { p , q } , { q , r } , and { p , q , r } Formula Φ has one stable model, ← P Φ q often called answer set: ← q , ∼ r p { p , q } Informally, a set X of atoms is an stable model of a logic program P if X is a (classical) model of P and if all atoms in X are justified by some rule in P (rooted in intuitionistic logics HT (Heyting, 1930) and G3 (G¨ odel, 1932)) Torsten Schaub (KRR@UP) ASP in Practice 8 / 69

  2. Introduction Basic idea Consider the logical formula Φ and its three Φ q ∧ ( q ∧ ¬ r → p ) (classical) models: { p , q } , { q , r } , and { p , q , r } Formula Φ has one stable model, ← P Φ q often called answer set: ← q , ∼ r p { p , q } Informally, a set X of atoms is an stable model of a logic program P if X is a (classical) model of P and if all atoms in X are justified by some rule in P (rooted in intuitionistic logics HT (Heyting, 1930) and G3 (G¨ odel, 1932)) Torsten Schaub (KRR@UP) ASP in Practice 8 / 69

  3. Introduction ASP versus SAT ASP SAT Model generation Bottom-up Constructive Logic Classical Logic Closed (and open) Open world reasoning world reasoning Modeling language — Complex reasoning modes Satisfiability testing Satisfiability Satisfiability Enumeration/Projection — Optimization — Intersection/Union — (Turing +) NP ( NP ) NP Torsten Schaub (KRR@UP) ASP in Practice 9 / 69

  4. Introduction ASP versus SAT ASP SAT Model generation Bottom-up Constructive Logic Classical Logic Closed (and open) Open world reasoning world reasoning Modeling language — Complex reasoning modes Satisfiability testing Satisfiability Satisfiability Enumeration/Projection — Optimization — Intersection/Union — (Turing +) NP ( NP ) NP Torsten Schaub (KRR@UP) ASP in Practice 9 / 69

  5. Introduction Formal Definition Syntax A rule, r , is an expression of the form a ← b 1 , . . . , b m , ∼ c 1 , . . . , ∼ c n , where 0 ≤ m , n and each a , b i , c j is an atom A logic program is a finite set of rules Semantics The reduct, P X , of a program P relative to a set X of atoms is defined by P X = { a ← b 1 , . . . , b m | r ∈ P and { c 1 , . . . , c n } ∩ X = ∅} The ⊆ –smallest model of P X is denoted by Cn ( P X ) A set X of atoms is an stable model of a program P , if X = Cn ( P X ) Torsten Schaub (KRR@UP) ASP in Practice 10 / 69

  6. Introduction Formal Definition Syntax A rule, r , is an expression of the form a ← b 1 , . . . , b m , ∼ c 1 , . . . , ∼ c n , where 0 ≤ m , n and each a , b i , c j is an atom A logic program is a finite set of rules Semantics The reduct, P X , of a program P relative to a set X of atoms is defined by P X = { a ← b 1 , . . . , b m | r ∈ P and { c 1 , . . . , c n } ∩ X = ∅} The ⊆ –smallest model of P X is denoted by Cn ( P X ) A set X of atoms is an stable model of a program P , if X = Cn ( P X ) Torsten Schaub (KRR@UP) ASP in Practice 10 / 69

  7. Introduction Formal Definition Syntax A rule, r , is an expression of the form a ← b 1 , . . . , b m , ∼ c 1 , . . . , ∼ c n , where 0 ≤ m , n and each a , b i , c j is an atom A logic program is a finite set of rules Semantics The reduct, P X , of a program P relative to a set X of atoms is defined by P X = { a ← b 1 , . . . , b m | r ∈ P and { c 1 , . . . , c n } ∩ X = ∅} The ⊆ –smallest model of P X is denoted by Cn ( P X ) A set X of atoms is an stable model of a program P , if X = Cn ( P X ) Torsten Schaub (KRR@UP) ASP in Practice 10 / 69

  8. Introduction Formal Definition Syntax A rule, r , is an expression of the form a ← b 1 , . . . , b m , ∼ c 1 , . . . , ∼ c n , where 0 ≤ m , n and each a , b i , c j is an atom A logic program is a finite set of rules Semantics The reduct, P X , of a program P relative to a set X of atoms is defined by P X = { a ← b 1 , . . . , b m | r ∈ P and { c 1 , . . . , c n } ∩ X = ∅} The ⊆ –smallest model of P X is denoted by Cn ( P X ) A set X of atoms is an stable model of a program P , if X = Cn ( P X ) Torsten Schaub (KRR@UP) ASP in Practice 10 / 69

  9. Introduction Formal Definition Syntax A rule, r , is an expression of the form a ← b 1 , . . . , b m , ∼ c 1 , . . . , ∼ c n , where 0 ≤ m , n and each a , b i , c j is an atom A logic program is a finite set of rules Semantics The reduct, P X , of a program P relative to a set X of atoms is defined by P X = { a ← b 1 , . . . , b m | r ∈ P and { c 1 , . . . , c n } ∩ X = ∅} The ⊆ –smallest model of P X is denoted by Cn ( P X ) A set X of atoms is an stable model of a program P , if X = Cn ( P X ) Torsten Schaub (KRR@UP) ASP in Practice 10 / 69

  10. Introduction Formal Definition Syntax A rule, r , is an expression of the form a ← b 1 , . . . , b m , ∼ c 1 , . . . , ∼ c n , where 0 ≤ m , n and each a , b i , c j is an atom A logic program is a finite set of rules Semantics The reduct, P X , of a program P relative to a set X of atoms is defined by P X = { a ← b 1 , . . . , b m | r ∈ P and { c 1 , . . . , c n } ∩ X = ∅} The ⊆ –smallest model of P X is denoted by Cn ( P X ) A set X of atoms is an stable model of a program P , if X = Cn ( P X ) Torsten Schaub (KRR@UP) ASP in Practice 10 / 69

  11. Introduction Formal Definition Syntax A rule, r , is an expression of the form a ← b 1 , . . . , b m , ∼ c 1 , . . . , ∼ c n , where 0 ≤ m , n and each a , b i , c j is an atom A logic program is a finite set of rules Semantics The reduct, P X , of a program P relative to a set X of atoms is defined by P X = { a ← b 1 , . . . , b m | r ∈ P and { c 1 , . . . , c n } ∩ X = ∅} The ⊆ –smallest model of P X is denoted by Cn ( P X ) A set X of atoms is an stable model of a program P , if X = Cn ( P X ) Torsten Schaub (KRR@UP) ASP in Practice 10 / 69

  12. Introduction Declarative problem solving “What is the problem?” instead of “How to solve the problem?” Problem Solution ✻ Modeling Interpreting ❄ ✲ Representation Output Solving Torsten Schaub (KRR@UP) ASP in Practice 11 / 69

  13. Introduction Declarative problem solving “What is the problem?” instead of “How to solve the problem?” Problem Solution ✻ Modeling Interpreting ❄ ✲ Representation Output Solving Torsten Schaub (KRR@UP) ASP in Practice 11 / 69

  14. Introduction Language Constructs Variables (over the Herbrand Universe) p(X) :- q(X) over constants { a , b , c } stands for p(a) :- q(a), p(b) :- q(b), p(c) :- q(c) Conditional Literals p :- q(X) : r(X) given r(a), r(b), r(c) stands for p :- q(a), q(b), q(c) Disjunction p(X) ; q(X) :- r(X) Integrity Constraints :- q(X), p(X) Choice 2 { p(X,Y) : q(X) } 7 :- r(Y) Aggregates s(Y) :- r(Y), 2 #count { p(X,Y) : q(X) } 7 also: #sum, #times, #avg, #min, #max, #even, #odd Torsten Schaub (KRR@UP) ASP in Practice 12 / 69

  15. Introduction Language Constructs Variables (over the Herbrand Universe) p(X) :- q(X) over constants { a , b , c } stands for p(a) :- q(a), p(b) :- q(b), p(c) :- q(c) Conditional Literals p :- q(X) : r(X) given r(a), r(b), r(c) stands for p :- q(a), q(b), q(c) Disjunction p(X) ; q(X) :- r(X) Integrity Constraints :- q(X), p(X) Choice 2 { p(X,Y) : q(X) } 7 :- r(Y) Aggregates s(Y) :- r(Y), 2 #count { p(X,Y) : q(X) } 7 also: #sum, #times, #avg, #min, #max, #even, #odd Torsten Schaub (KRR@UP) ASP in Practice 12 / 69

  16. Introduction Language Constructs Variables (over the Herbrand Universe) p(X) :- q(X) over constants { a , b , c } stands for p(a) :- q(a), p(b) :- q(b), p(c) :- q(c) Conditional Literals p :- q(X) : r(X) given r(a), r(b), r(c) stands for p :- q(a), q(b), q(c) Disjunction p(X) ; q(X) :- r(X) Integrity Constraints :- q(X), p(X) Choice 2 { p(X,Y) : q(X) } 7 :- r(Y) Aggregates s(Y) :- r(Y), 2 #count { p(X,Y) : q(X) } 7 also: #sum, #times, #avg, #min, #max, #even, #odd Torsten Schaub (KRR@UP) ASP in Practice 12 / 69

  17. Introduction Language Constructs Variables (over the Herbrand Universe) p(X) :- q(X) over constants { a , b , c } stands for p(a) :- q(a), p(b) :- q(b), p(c) :- q(c) Conditional Literals p :- q(X) : r(X) given r(a), r(b), r(c) stands for p :- q(a), q(b), q(c) Disjunction p(X) ; q(X) :- r(X) Integrity Constraints :- q(X), p(X) Choice 2 { p(X,Y) : q(X) } 7 :- r(Y) Aggregates s(Y) :- r(Y), 2 #count { p(X,Y) : q(X) } 7 also: #sum, #times, #avg, #min, #max, #even, #odd Torsten Schaub (KRR@UP) ASP in Practice 12 / 69

  18. Introduction Language Constructs Variables (over the Herbrand Universe) p(X) :- q(X) over constants { a , b , c } stands for p(a) :- q(a), p(b) :- q(b), p(c) :- q(c) Conditional Literals p :- q(X) : r(X) given r(a), r(b), r(c) stands for p :- q(a), q(b), q(c) Disjunction p(X) ; q(X) :- r(X) Integrity Constraints :- q(X), p(X) Choice 2 { p(X,Y) : q(X) } 7 :- r(Y) Aggregates s(Y) :- r(Y), 2 #count { p(X,Y) : q(X) } 7 also: #sum, #times, #avg, #min, #max, #even, #odd Torsten Schaub (KRR@UP) ASP in Practice 12 / 69

  19. Introduction Language Constructs Variables (over the Herbrand Universe) p(X) :- q(X) over constants { a , b , c } stands for p(a) :- q(a), p(b) :- q(b), p(c) :- q(c) Conditional Literals p :- q(X) : r(X) given r(a), r(b), r(c) stands for p :- q(a), q(b), q(c) Disjunction p(X) ; q(X) :- r(X) Integrity Constraints :- q(X), p(X) Choice 2 { p(X,Y) : q(X) } 7 :- r(Y) Aggregates s(Y) :- r(Y), 2 #count { p(X,Y) : q(X) } 7 also: #sum, #times, #avg, #min, #max, #even, #odd Torsten Schaub (KRR@UP) ASP in Practice 12 / 69

  20. Introduction Language Constructs Variables (over the Herbrand Universe) p(X) :- q(X) over constants { a , b , c } stands for p(a) :- q(a), p(b) :- q(b), p(c) :- q(c) Conditional Literals p :- q(X) : r(X) given r(a), r(b), r(c) stands for p :- q(a), q(b), q(c) Disjunction p(X) ; q(X) :- r(X) Integrity Constraints :- q(X), p(X) Choice 2 { p(X,Y) : q(X) } 7 :- r(Y) Aggregates s(Y) :- r(Y), 2 #count { p(X,Y) : q(X) } 7 also: #sum, #times, #avg, #min, #max, #even, #odd Torsten Schaub (KRR@UP) ASP in Practice 12 / 69

  21. Introduction Language Constructs Variables (over the Herbrand Universe) p(X) :- q(X) over constants { a , b , c } stands for p(a) :- q(a), p(b) :- q(b), p(c) :- q(c) Conditional Literals p :- q(X) : r(X) given r(a), r(b), r(c) stands for p :- q(a), q(b), q(c) Disjunction p(X) ; q(X) :- r(X) Integrity Constraints :- q(X), p(X) Choice 2 { p(X,Y) : q(X) } 7 :- r(Y) Aggregates s(Y) :- r(Y), 2 #count { p(X,Y) : q(X) } 7 also: #sum, #times, #avg, #min, #max, #even, #odd Torsten Schaub (KRR@UP) ASP in Practice 12 / 69

  22. Introduction Declarative problem solving “What is the problem?” instead of “How to solve the problem?” Problem Solution ✻ Modeling Interpreting ❄ ✲ Representation Output Solving Torsten Schaub (KRR@UP) ASP in Practice 13 / 69

  23. Introduction Declarative problem solving “What is the problem?” instead of “How to solve the problem?” Problem Solution ✻ Modeling Interpreting ❄ ✲ Representation Output Solving Torsten Schaub (KRR@UP) ASP in Practice 13 / 69

  24. Introduction Reasoning Modes Satisfiability Enumeration † Projection † Intersection ‡ Union ‡ Optimization † without solution recording ‡ without solution enumeration Torsten Schaub (KRR@UP) ASP in Practice 14 / 69

  25. Modeling by Example Outline 1 Motivation 2 Introduction 3 Modeling by Example Graph Coloring Queens Traveling Salesperson 4 Meta Programming 5 Conflict-Driven Answer Set Solving 6 Potassco 7 Summary Torsten Schaub (KRR@UP) ASP in Practice 15 / 69

  26. Modeling by Example Declarative problem solving “What is the problem?” instead of “How to solve the problem?” Problem Solution ✻ Modeling Interpreting ❄ ✲ Representation Output Solving Torsten Schaub (KRR@UP) ASP in Practice 16 / 69

  27. Modeling by Example Declarative problem solving “What is the problem?” instead of “How to solve the problem?” Problem Solution ✻ Modeling Interpreting ❄ ✲ Representation Output Solving Torsten Schaub (KRR@UP) ASP in Practice 16 / 69

  28. Modeling by Example ASP Solving Process ✲ ✲ ✲ Program Grounder Solver Models Torsten Schaub (KRR@UP) ASP in Practice 17 / 69

  29. Modeling by Example ASP Solving Process ✲ ✲ ✲ Program Grounder Solver Models Torsten Schaub (KRR@UP) ASP in Practice 17 / 69

  30. Modeling by Example ASP Solving Process ✲ ✲ ✲ Program Grounder Solver Models Torsten Schaub (KRR@UP) ASP in Practice 17 / 69

  31. Modeling by Example ASP Solving Process ✲ ✲ ✲ Program Grounder Solver Models Torsten Schaub (KRR@UP) ASP in Practice 17 / 69

  32. Modeling by Example ASP Solving Process ✲ ✲ ✲ Program Grounder Solver Models Torsten Schaub (KRR@UP) ASP in Practice 17 / 69

  33. Modeling by Example ASP Solving Process ✲ ✲ ✲ Program Grounder Solver Models ✻ Torsten Schaub (KRR@UP) ASP in Practice 17 / 69

  34. Modeling by Example Graph Coloring Outline 1 Motivation 2 Introduction 3 Modeling by Example Graph Coloring Queens Traveling Salesperson 4 Meta Programming 5 Conflict-Driven Answer Set Solving 6 Potassco 7 Summary Torsten Schaub (KRR@UP) ASP in Practice 18 / 69

  35. Modeling by Example Graph Coloring ASP Solving Process ✲ ✲ ✲ Program Grounder Solver Models Torsten Schaub (KRR@UP) ASP in Practice 19 / 69

  36. Modeling by Example Graph Coloring Graph Coloring node(1..6). edge(1,2). edge(1,3). edge(1,4). edge(2,4). edge(2,5). edge(2,6). edge(3,1). edge(3,4). edge(3,5). edge(4,1). edge(4,2). edge(5,3). edge(5,4). edge(5,6). edge(6,2). edge(6,3). edge(6,5). col(r). col(b). col(g). 1 { color(X,C) : col(C) } 1 :- node(X). :- edge(X,Y), color(X,C), color(Y,C). Torsten Schaub (KRR@UP) ASP in Practice 20 / 69

  37. Modeling by Example Graph Coloring Graph Coloring node(1..6). edge(1,2). edge(1,3). edge(1,4). edge(2,4). edge(2,5). edge(2,6). edge(3,1). edge(3,4). edge(3,5). edge(4,1). edge(4,2). edge(5,3). edge(5,4). edge(5,6). edge(6,2). edge(6,3). edge(6,5). col(r). col(b). col(g). 1 { color(X,C) : col(C) } 1 :- node(X). :- edge(X,Y), color(X,C), color(Y,C). Torsten Schaub (KRR@UP) ASP in Practice 20 / 69

  38. Modeling by Example Graph Coloring Graph Coloring node(1..6). edge(1,2). edge(1,3). edge(1,4). edge(2,4). edge(2,5). edge(2,6). edge(3,1). edge(3,4). edge(3,5). edge(4,1). edge(4,2). edge(5,3). edge(5,4). edge(5,6). edge(6,2). edge(6,3). edge(6,5). col(r). col(b). col(g). 1 { color(X,C) : col(C) } 1 :- node(X). :- edge(X,Y), color(X,C), color(Y,C). Torsten Schaub (KRR@UP) ASP in Practice 20 / 69

  39. Modeling by Example Graph Coloring Graph Coloring node(1..6). edge(1,2). edge(1,3). edge(1,4). edge(2,4). edge(2,5). edge(2,6). edge(3,1). edge(3,4). edge(3,5). edge(4,1). edge(4,2). edge(5,3). edge(5,4). edge(5,6). edge(6,2). edge(6,3). edge(6,5). col(r). col(b). col(g). 1 { color(X,C) : col(C) } 1 :- node(X). :- edge(X,Y), color(X,C), color(Y,C). Torsten Schaub (KRR@UP) ASP in Practice 20 / 69

  40. Modeling by Example Graph Coloring Graph Coloring node(1..6). edge(1,2). edge(1,3). edge(1,4). edge(2,4). edge(2,5). edge(2,6). edge(3,1). edge(3,4). edge(3,5). edge(4,1). edge(4,2). edge(5,3). edge(5,4). edge(5,6). edge(6,2). edge(6,3). edge(6,5). col(r). col(b). col(g). 1 { color(X,C) : col(C) } 1 :- node(X). :- edge(X,Y), color(X,C), color(Y,C). Torsten Schaub (KRR@UP) ASP in Practice 20 / 69

  41. Modeling by Example Graph Coloring ASP Solving Process ✲ ✲ ✲ Program Grounder Solver Models Torsten Schaub (KRR@UP) ASP in Practice 21 / 69

  42. Modeling by Example Graph Coloring Graph Coloring: Grounding $ gringo -t color.lp node(1). node(2). node(3). node(4). node(5). node(6). edge(1,2). edge(1,3). edge(1,4). edge(2,4). edge(2,5). edge(2,6). edge(3,1). edge(3,4). edge(3,5). edge(4,1). edge(4,2). edge(5,3). edge(5,4). edge(5,6). edge(6,2). edge(6,3). edge(6,5). col(r). col(b). col(g). 1 {color(1,r), color(1,b), color(1,g)} 1. 1 {color(2,r), color(2,b), color(2,g)} 1. 1 {color(3,r), color(3,b), color(3,g)} 1. 1 {color(4,r), color(4,b), color(4,g)} 1. 1 {color(5,r), color(5,b), color(5,g)} 1. 1 {color(6,r), color(6,b), color(6,g)} 1. :- color(1,r), color(2,r). :- color(2,g), color(5,g). ... :- color(6,r), color(2,r). :- color(1,b), color(2,b). :- color(2,r), color(6,r). :- color(6,b), color(2,b). :- color(1,g), color(2,g). :- color(2,b), color(6,b). :- color(6,g), color(2,g). :- color(1,r), color(3,r). :- color(2,g), color(6,g). :- color(6,r), color(3,r). :- color(1,b), color(3,b). :- color(3,r), color(1,r). :- color(6,b), color(3,b). :- color(1,g), color(3,g). :- color(3,b), color(1,b). :- color(6,g), color(3,g). :- color(1,r), color(4,r). :- color(3,g), color(1,g). :- color(6,r), color(5,r). :- color(1,b), color(4,b). :- color(3,r), color(4,r). :- color(6,b), color(5,b). :- color(1,g), color(4,g). :- color(3,b), color(4,b). :- color(6,g), color(5,g). :- color(2,r), color(4,r). :- color(3,g), color(4,g). :- color(2,b), color(4,b). :- color(3,r), color(5,r). :- color(2,g), color(4,g). :- color(3,b), color(5,b). :- color(2,r), color(5,r). :- color(3,g), color(5,g). Torsten Schaub (KRR@UP) ASP in Practice 22 / 69 :- color(2,b), color(5,b). :- color(4,r), color(1,r).

  43. Modeling by Example Graph Coloring Graph Coloring: Grounding $ gringo -t color.lp node(1). node(2). node(3). node(4). node(5). node(6). edge(1,2). edge(1,3). edge(1,4). edge(2,4). edge(2,5). edge(2,6). edge(3,1). edge(3,4). edge(3,5). edge(4,1). edge(4,2). edge(5,3). edge(5,4). edge(5,6). edge(6,2). edge(6,3). edge(6,5). col(r). col(b). col(g). 1 {color(1,r), color(1,b), color(1,g)} 1. 1 {color(2,r), color(2,b), color(2,g)} 1. 1 {color(3,r), color(3,b), color(3,g)} 1. 1 {color(4,r), color(4,b), color(4,g)} 1. 1 {color(5,r), color(5,b), color(5,g)} 1. 1 {color(6,r), color(6,b), color(6,g)} 1. :- color(1,r), color(2,r). :- color(2,g), color(5,g). ... :- color(6,r), color(2,r). :- color(1,b), color(2,b). :- color(2,r), color(6,r). :- color(6,b), color(2,b). :- color(1,g), color(2,g). :- color(2,b), color(6,b). :- color(6,g), color(2,g). :- color(1,r), color(3,r). :- color(2,g), color(6,g). :- color(6,r), color(3,r). :- color(1,b), color(3,b). :- color(3,r), color(1,r). :- color(6,b), color(3,b). :- color(1,g), color(3,g). :- color(3,b), color(1,b). :- color(6,g), color(3,g). :- color(1,r), color(4,r). :- color(3,g), color(1,g). :- color(6,r), color(5,r). :- color(1,b), color(4,b). :- color(3,r), color(4,r). :- color(6,b), color(5,b). :- color(1,g), color(4,g). :- color(3,b), color(4,b). :- color(6,g), color(5,g). :- color(2,r), color(4,r). :- color(3,g), color(4,g). :- color(2,b), color(4,b). :- color(3,r), color(5,r). :- color(2,g), color(4,g). :- color(3,b), color(5,b). :- color(2,r), color(5,r). :- color(3,g), color(5,g). Torsten Schaub (KRR@UP) ASP in Practice 22 / 69 :- color(2,b), color(5,b). :- color(4,r), color(1,r).

  44. Modeling by Example Graph Coloring ASP Solving Process ✲ ✲ ✲ Program Grounder Solver Models Torsten Schaub (KRR@UP) ASP in Practice 23 / 69

  45. Modeling by Example Graph Coloring Graph Coloring: Solving $ gringo color.lp | clasp 0 clasp version 2.1.0 Reading from stdin Solving... Answer: 1 edge(1,2) ... col(r) ... node(1) ... color(6,b) color(5,g) color(4,b) color(3,r) color(2,r) color(1,g) Answer: 2 edge(1,2) ... col(r) ... node(1) ... color(6,r) color(5,g) color(4,r) color(3,b) color(2,b) color(1,g) Answer: 3 edge(1,2) ... col(r) ... node(1) ... color(6,g) color(5,b) color(4,g) color(3,r) color(2,r) color(1,b) Answer: 4 edge(1,2) ... col(r) ... node(1) ... color(6,r) color(5,b) color(4,r) color(3,g) color(2,g) color(1,b) Answer: 5 edge(1,2) ... col(r) ... node(1) ... color(6,g) color(5,r) color(4,g) color(3,b) color(2,b) color(1,r) Answer: 6 edge(1,2) ... col(r) ... node(1) ... color(6,b) color(5,r) color(4,b) color(3,g) color(2,g) color(1,r) SATISFIABLE Models : 6 Time : 0.002s (Solving: 0.00s 1st Model: 0.00s Unsat: 0.00s) CPU Time : 0.000s Torsten Schaub (KRR@UP) ASP in Practice 24 / 69

  46. Modeling by Example Graph Coloring Graph Coloring: Solving $ gringo color.lp | clasp 0 clasp version 2.1.0 Reading from stdin Solving... Answer: 1 edge(1,2) ... col(r) ... node(1) ... color(6,b) color(5,g) color(4,b) color(3,r) color(2,r) color(1,g) Answer: 2 edge(1,2) ... col(r) ... node(1) ... color(6,r) color(5,g) color(4,r) color(3,b) color(2,b) color(1,g) Answer: 3 edge(1,2) ... col(r) ... node(1) ... color(6,g) color(5,b) color(4,g) color(3,r) color(2,r) color(1,b) Answer: 4 edge(1,2) ... col(r) ... node(1) ... color(6,r) color(5,b) color(4,r) color(3,g) color(2,g) color(1,b) Answer: 5 edge(1,2) ... col(r) ... node(1) ... color(6,g) color(5,r) color(4,g) color(3,b) color(2,b) color(1,r) Answer: 6 edge(1,2) ... col(r) ... node(1) ... color(6,b) color(5,r) color(4,b) color(3,g) color(2,g) color(1,r) SATISFIABLE Models : 6 Time : 0.002s (Solving: 0.00s 1st Model: 0.00s Unsat: 0.00s) CPU Time : 0.000s Torsten Schaub (KRR@UP) ASP in Practice 24 / 69

  47. Modeling by Example Queens Outline 1 Motivation 2 Introduction 3 Modeling by Example Graph Coloring Queens Traveling Salesperson 4 Meta Programming 5 Conflict-Driven Answer Set Solving 6 Potassco 7 Summary Torsten Schaub (KRR@UP) ASP in Practice 25 / 69

  48. Modeling by Example Queens The n-Queens Problem 5 Z0Z0Z Place n queens on an n × n 4 0Z0Z0 chess board Queens must not attack one 3 Z0Z0Z another 2 0Z0Z0 Q Q Q 1 Z0Z0Z Q Q 1 2 3 4 5 Torsten Schaub (KRR@UP) ASP in Practice 26 / 69

  49. Modeling by Example Queens Defining the Field queens.lp row (1..n). col (1..n). Create file queens.lp Define the field n rows n columns Torsten Schaub (KRR@UP) ASP in Practice 27 / 69

  50. Modeling by Example Queens Defining the Field Running . . . $ clingo queens.lp -c n=5 Answer: 1 row (1) row (2) row (3) row (4) row (5) \ col (1) col (2) col (3) col (4) col (5) SATISFIABLE Models : 1 Time : 0.000 Prepare : 0.000 Prepro. : 0.000 Solving : 0.000 Torsten Schaub (KRR@UP) ASP in Practice 28 / 69

  51. Modeling by Example Queens Placing some Queens queens.lp row (1..n). col (1..n). { queen(I,J) : row(I) : col(J) } . Guess a solution candidate by placing some queens on the board Torsten Schaub (KRR@UP) ASP in Practice 29 / 69

  52. Modeling by Example Queens Placing some Queens Running . . . $ clingo queens.lp -c n=5 3 Answer: 1 row (1) row (2) row (3) row (4) row (5) \ col (1) col (2) col (3) col (4) col (5) Answer: 2 row (1) row (2) row (3) row (4) row (5) \ col (1) col (2) col (3) col (4) col (5) queen(1,1) Answer: 3 row (1) row (2) row (3) row (4) row (5) \ col (1) col (2) col (3) col (4) col (5) queen(2,1) SATISFIABLE Models : 3+ ... Torsten Schaub (KRR@UP) ASP in Practice 30 / 69

  53. Modeling by Example Queens Placing some Queens: Answer 1 Answer 1 5 Z0Z0Z 4 0Z0Z0 3 Z0Z0Z 2 0Z0Z0 1 Z0Z0Z 1 2 3 4 5 Torsten Schaub (KRR@UP) ASP in Practice 31 / 69

  54. Modeling by Example Queens Placing some Queens: Answer 2 Answer 2 5 Z0Z0Z 4 0Z0Z0 3 Z0Z0Z 2 0Z0Z0 1 L0Z0Z 1 2 3 4 5 Torsten Schaub (KRR@UP) ASP in Practice 32 / 69

  55. Modeling by Example Queens Placing some Queens: Answer 3 Answer 3 5 Z0Z0Z 4 0Z0Z0 3 Z0Z0Z 2 QZ0Z0 1 Z0Z0Z 1 2 3 4 5 Torsten Schaub (KRR@UP) ASP in Practice 33 / 69

  56. Modeling by Example Queens Placing n Queens queens.lp row (1..n). col (1..n). { queen(I,J) : row(I) : col(J) }. :- not n { queen(I,J) } n. Place exactly n queens on the board Torsten Schaub (KRR@UP) ASP in Practice 34 / 69

  57. Modeling by Example Queens Placing n Queens Running . . . $ clingo queens.lp -c n=5 2 Answer: 1 row (1) row (2) row (3) row (4) row (5) \ col (1) col (2) col (3) col (4) col (5) \ queen(5,1) queen(4,1) queen(3,1) \ queen(2,1) queen(1,1) Answer: 2 row (1) row (2) row (3) row (4) row (5) \ col (1) col (2) col (3) col (4) col (5) \ queen(1,2) queen(4,1) queen(3,1) \ queen(2,1) queen(1,1) ... Torsten Schaub (KRR@UP) ASP in Practice 35 / 69

  58. Modeling by Example Queens Placing n Queens: Answer 1 Answer 1 5 L0Z0Z 4 QZ0Z0 3 L0Z0Z 2 QZ0Z0 1 L0Z0Z 1 2 3 4 5 Torsten Schaub (KRR@UP) ASP in Practice 36 / 69

  59. Modeling by Example Queens Placing n Queens: Answer 2 Answer 2 5 Z0Z0Z 4 QZ0Z0 3 L0Z0Z 2 QZ0Z0 1 LQZ0Z 1 2 3 4 5 Torsten Schaub (KRR@UP) ASP in Practice 37 / 69

  60. Modeling by Example Queens Horizontal and vertical Attack queens.lp row (1..n). col (1..n). { queen(I,J) : row(I) : col(J) }. :- not n { queen(I,J) } n. :- queen(I,J), queen(I,JJ), J != JJ. :- queen(I,J), queen(II,J), I != II. Forbid horizontal attacks Forbid vertical attacks Torsten Schaub (KRR@UP) ASP in Practice 38 / 69

  61. Modeling by Example Queens Horizontal and vertical Attack queens.lp row (1..n). col (1..n). { queen(I,J) : row(I) : col(J) }. :- not n { queen(I,J) } n. :- queen(I,J), queen(I,JJ), J != JJ. :- queen(I,J), queen(II,J), I != II. Forbid horizontal attacks Forbid vertical attacks Torsten Schaub (KRR@UP) ASP in Practice 38 / 69

  62. Modeling by Example Queens Horizontal and vertical Attack Running . . . $ clingo queens.lp -c n=5 Answer: 1 row (1) row (2) row (3) row (4) row (5) \ col (1) col (2) col (3) col (4) col (5) \ queen(5,5) queen(4,4) queen(3,3) \ queen(2,2) queen(1,1) ... Torsten Schaub (KRR@UP) ASP in Practice 39 / 69

  63. Modeling by Example Queens Horizontal and vertical Attack: Answer 1 Answer 1 5 Z0Z0L 4 0Z0L0 3 Z0L0Z 2 0L0Z0 1 L0Z0Z 1 2 3 4 5 Torsten Schaub (KRR@UP) ASP in Practice 40 / 69

  64. Modeling by Example Queens Diagonal Attack queens.lp row (1..n). col (1..n). { queen(I,J) : row(I) : col(J) }. :- not n { queen(I,J) } n. :- queen(I,J), queen(I,JJ), J != JJ. :- queen(I,J), queen(II ,J), I != II. :- queen(I,J), queen(II,JJ), (I,J) != (II,JJ), I-J == II-JJ. :- queen(I,J), queen(II,JJ), (I,J) != (II,JJ), I+J == II+JJ. Forbid diagonal attacks Torsten Schaub (KRR@UP) ASP in Practice 41 / 69

  65. Modeling by Example Queens Diagonal Attack Running . . . $ clingo queens.lp -c n=5 Answer: 1 row (1) row (2) row (3) row (4) row (5) \ col (1) col (2) col (3) col (4) col (5) \ queen(4,5) queen(1,4) queen(3,3) \ queen(5,2) queen(2,1) SATISFIABLE Models : 1+ Time : 0.000 Prepare : 0.000 Prepro. : 0.000 Solving : 0.000 Torsten Schaub (KRR@UP) ASP in Practice 42 / 69

  66. Modeling by Example Queens Diagonal Attack: Answer 1 Answer 1 5 ZQZ0Z 4 0Z0ZQ 3 Z0L0Z 2 QZ0Z0 1 Z0ZQZ 1 2 3 4 5 Torsten Schaub (KRR@UP) ASP in Practice 43 / 69

  67. Modeling by Example Queens Optimizing queens-opt.lp 1 { queen(I ,1..n) } 1 :- I = 1..n. 1 { queen (1..n,J) } 1 :- J = 1..n. :- 2 { queen(D-J,J) }, D = 2..2*n. :- 2 { queen(D+J,J) }, D = 1-n..n-1. Encoding can be optimized Much faster to solve Torsten Schaub (KRR@UP) ASP in Practice 44 / 69

  68. Modeling by Example Traveling Salesperson Outline 1 Motivation 2 Introduction 3 Modeling by Example Graph Coloring Queens Traveling Salesperson 4 Meta Programming 5 Conflict-Driven Answer Set Solving 6 Potassco 7 Summary Torsten Schaub (KRR@UP) ASP in Practice 45 / 69

  69. Modeling by Example Traveling Salesperson Traveling Salesperson node(1..6). edge(1,2;3;4). edge(2,4;5;6). edge(3,1;4;5). edge(4,1;2). edge(5,3;4;6). edge(6,2;3;5). cost(1,2,2). cost(1,3,3). cost(1,4,1). cost(2,4,2). cost(2,5,2). cost(2,6,4). cost(3,1,3). cost(3,4,2). cost(3,5,2). cost(4,1,1). cost(4,2,2). cost(5,3,2). cost(5,4,2). cost(5,6,1). cost(6,2,4). cost(6,3,3). cost(6,5,1). Torsten Schaub (KRR@UP) ASP in Practice 46 / 69

  70. Modeling by Example Traveling Salesperson Traveling Salesperson node(1..6). edge(1,2;3;4). edge(2,4;5;6). edge(3,1;4;5). edge(4,1;2). edge(5,3;4;6). edge(6,2;3;5). cost(1,2,2). cost(1,3,3). cost(1,4,1). cost(2,4,2). cost(2,5,2). cost(2,6,4). cost(3,1,3). cost(3,4,2). cost(3,5,2). cost(4,1,1). cost(4,2,2). cost(5,3,2). cost(5,4,2). cost(5,6,1). cost(6,2,4). cost(6,3,3). cost(6,5,1). Torsten Schaub (KRR@UP) ASP in Practice 46 / 69

  71. Modeling by Example Traveling Salesperson Traveling Salesperson node(1..6). edge(1,2;3;4). edge(2,4;5;6). edge(3,1;4;5). edge(4,1;2). edge(5,3;4;6). edge(6,2;3;5). cost(1,2,2). cost(1,3,3). cost(1,4,1). cost(2,4,2). cost(2,5,2). cost(2,6,4). cost(3,1,3). cost(3,4,2). cost(3,5,2). cost(4,1,1). cost(4,2,2). cost(5,3,2). cost(5,4,2). cost(5,6,1). cost(6,2,4). cost(6,3,3). cost(6,5,1). Torsten Schaub (KRR@UP) ASP in Practice 46 / 69

  72. Modeling by Example Traveling Salesperson Traveling Salesperson 1 { cycle(X,Y) : edge(X,Y) } 1 :- node(X). 1 { cycle(X,Y) : edge(X,Y) } 1 :- node(Y). reached(Y) :- cycle(1,Y). reached(Y) :- cycle(X,Y), reached(X). :- node(Y), not reached(Y). #minimize { cycle(X,Y) : cost(X,Y,C) = C }. Torsten Schaub (KRR@UP) ASP in Practice 47 / 69

  73. Modeling by Example Traveling Salesperson Traveling Salesperson 1 { cycle(X,Y) : edge(X,Y) } 1 :- node(X). 1 { cycle(X,Y) : edge(X,Y) } 1 :- node(Y). reached(Y) :- cycle(1,Y). reached(Y) :- cycle(X,Y), reached(X). :- node(Y), not reached(Y). #minimize { cycle(X,Y) : cost(X,Y,C) = C }. Torsten Schaub (KRR@UP) ASP in Practice 47 / 69

  74. Modeling by Example Traveling Salesperson Traveling Salesperson 1 { cycle(X,Y) : edge(X,Y) } 1 :- node(X). 1 { cycle(X,Y) : edge(X,Y) } 1 :- node(Y). reached(Y) :- cycle(1,Y). reached(Y) :- cycle(X,Y), reached(X). :- node(Y), not reached(Y). #minimize { cycle(X,Y) : cost(X,Y,C) = C }. Torsten Schaub (KRR@UP) ASP in Practice 47 / 69

  75. Modeling by Example Traveling Salesperson Traveling Salesperson 1 { cycle(X,Y) : edge(X,Y) } 1 :- node(X). 1 { cycle(X,Y) : edge(X,Y) } 1 :- node(Y). reached(Y) :- cycle(1,Y). reached(Y) :- cycle(X,Y), reached(X). :- node(Y), not reached(Y). #minimize { cycle(X,Y) : cost(X,Y,C) = C }. Torsten Schaub (KRR@UP) ASP in Practice 47 / 69

  76. Modeling by Example Traveling Salesperson What is ASP good for? Combinatorial search problems in the realm of P , NP , and NP NP (some with substantial amount of data), like For instance, auctions, bio-informatics, computer-aided verification, configuration, constraint satisfaction, diagnosis, information integration, planning and scheduling, security analysis, semantic web, wire-routing, zoology and linguistics, and many more My favorite: Using ASP as a basis for a decision support system for NASA’s space shuttle (Gelfond et al., Texas Tech) Our own applications: Automatic synthesis of multiprocessor systems Inconsistency detection, diagnosis, repair, and prediction in large biological networks Home monitoring for risk prevention in ambient assisted living General game playing Torsten Schaub (KRR@UP) ASP in Practice 48 / 69

  77. Modeling by Example Traveling Salesperson What is ASP good for? Combinatorial search problems in the realm of P , NP , and NP NP (some with substantial amount of data), like For instance, auctions, bio-informatics, computer-aided verification, configuration, constraint satisfaction, diagnosis, information integration, planning and scheduling, security analysis, semantic web, wire-routing, zoology and linguistics, and many more My favorite: Using ASP as a basis for a decision support system for NASA’s space shuttle (Gelfond et al., Texas Tech) Our own applications: Automatic synthesis of multiprocessor systems Inconsistency detection, diagnosis, repair, and prediction in large biological networks Home monitoring for risk prevention in ambient assisted living General game playing Torsten Schaub (KRR@UP) ASP in Practice 48 / 69

  78. Modeling by Example Traveling Salesperson What is ASP good for? Combinatorial search problems in the realm of P , NP , and NP NP (some with substantial amount of data), like For instance, auctions, bio-informatics, computer-aided verification, configuration, constraint satisfaction, diagnosis, information integration, planning and scheduling, security analysis, semantic web, wire-routing, zoology and linguistics, and many more My favorite: Using ASP as a basis for a decision support system for NASA’s space shuttle (Gelfond et al., Texas Tech) Our own applications: Automatic synthesis of multiprocessor systems Inconsistency detection, diagnosis, repair, and prediction in large biological networks Home monitoring for risk prevention in ambient assisted living General game playing Torsten Schaub (KRR@UP) ASP in Practice 48 / 69

  79. Modeling by Example Traveling Salesperson What does ASP offer? Integration of KR, DB, and SAT techniques Succinct, elaboration-tolerant problem representations Rapid application development tool Easy handling of dynamic, knowledge intensive applications including: data, frame axioms, exceptions, defaults, closures, etc. Torsten Schaub (KRR@UP) ASP in Practice 49 / 69

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

Answer Set Solving in Practice Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de

Answer Set Solving in Practice Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de

Answer Set Solving in Practice Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de Potassco Slide Packages are licensed under a Creative Commons Attribution 3.0 Unported License. Torsten Schaub (KRR@UP) Answer Set Solving in

1.67k views • 134 slides
Answer Set Solving in Practice Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de

Answer Set Solving in Practice Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de

Answer Set Solving in Practice Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de Potassco Slide Packages are licensed under a Creative Commons Attribution 3.0 Unported License. Torsten Schaub (KRR@UP) Answer Set Solving in

1.75k views • 132 slides
Answer Set Solving in Practice Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de

Answer Set Solving in Practice Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de

Answer Set Solving in Practice Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de Potassco Slide Packages are licensed under a Creative Commons Attribution 3.0 Unported License. Torsten Schaub (KRR@UP) Answer Set Solving in

1.27k views • 113 slides
Answer Set Solving in Practice Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de

Answer Set Solving in Practice Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de

Answer Set Solving in Practice Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de Potassco Slide Packages are licensed under a Creative Commons Attribution 3.0 Unported License. Torsten Schaub (KRR@UP) Answer Set Solving in

1.98k views • 195 slides
Answer Set Solving in Practice Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de

Answer Set Solving in Practice Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de

Answer Set Solving in Practice Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de Potassco Slide Packages are licensed under a Creative Commons Attribution 3.0 Unported License. Torsten Schaub (KRR@UP) Answer Set Solving in

1.83k views • 168 slides
Answer Set Solving in Practice Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de

Answer Set Solving in Practice Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de

Answer Set Solving in Practice Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de Potassco Slide Packages are licensed under a Creative Commons Attribution 3.0 Unported License. Torsten Schaub (KRR@UP) Answer Set Solving in

1.66k views • 161 slides
Answer Set Solving in Practice Martin Gebser and Torsten Schaub University of Potsdam

Answer Set Solving in Practice Martin Gebser and Torsten Schaub University of Potsdam

Answer Set Solving in Practice Martin Gebser and Torsten Schaub University of Potsdam torsten@cs.uni-potsdam.de Potassco Slide Packages are licensed under a Creative Commons Attribution 3.0 Unported License. M. Gebser and T. Schaub (KRR@UP)

1.47k views • 113 slides
Outline Motivation Answer Set Programming is a well-known declarative problem solving approach.

Outline Motivation Answer Set Programming is a well-known declarative problem solving approach.

Motivation Motivation Outline Motivation Answer Set Programming is a well-known declarative problem solving approach. Answer Set Programs with Queries over Subprograms 1 Motivation Christoph Redl The Saturation Technique and its

259 views • 10 slides
Answer Set Programming, the Solving Paradigm for Knowledge Representation and Reasoning Martin

Answer Set Programming, the Solving Paradigm for Knowledge Representation and Reasoning Martin

Answer Set Programming, the Solving Paradigm for Knowledge Representation and Reasoning Martin Gebser Torsten Schaub University of Potsdam Martin Gebser (University of Potsdam) Answer Set Programming 1 / 33 Outline 1 Motivation 2

1.36k views • 105 slides
Physics 201 Test 2 practice Short Answer (4 points each) 1 What is the other half of the

Physics 201 Test 2 practice Short Answer (4 points each) 1 What is the other half of the

Physics 201 Test 2 practice Short Answer (4 points each) 1 What is the other half of the action/reaction pair associated with the normal force of a table supporting a book? 2 Give an algebraic expression for the net force acting on a skydiver

375 views • 3 slides
Table of Contents I Answer Set Programming ASP Solvers Example: Hamiltonian Cycles Choice Rules

Table of Contents I Answer Set Programming ASP Solvers Example: Hamiltonian Cycles Choice Rules

Table of Contents I Answer Set Programming ASP Solvers Example: Hamiltonian Cycles Choice Rules Solving Puzzles Yulia Kahl College of Charleston Artificial Intelligence 1 Reading Read Chapter 6, Answer-Set Programming Paradigm , in the

198 views • 15 slides
Winn Sales 15 May 2016 Peerceptiv Practice Issue Spotter Exam Assignment 2 Answer Key Plus

Winn Sales 15 May 2016 Peerceptiv Practice Issue Spotter Exam Assignment 2 Answer Key Plus

Winn Sales 15 May 2016 Peerceptiv Practice Issue Spotter Exam Assignment 2 Answer Key Plus Scoring Guidelines Farmer Sadie Smith normally planted 200 acres of soybeans every May and harvested them every September. In recent years, she has been

392 views • 3 slides
Practice to Pass- Compulsory Direct Questions Answer ALL questions 1. State three (3) elements of

Practice to Pass- Compulsory Direct Questions Answer ALL questions 1. State three (3) elements of

Practice to Pass- Compulsory Direct Questions Answer ALL questions 1. State three (3) elements of the external business environment and describe its impact on an organization of your choice briefly. ( 10 marks) 2. Describe the concept of motivation

148 views • 3 slides
Lesson 10 - I can multiply 3 digits by 1 digit - reasoning and problem solving Starter- recap

Lesson 10 - I can multiply 3 digits by 1 digit - reasoning and problem solving Starter- recap

Lesson 10 - I can multiply 3 digits by 1 digit - reasoning and problem solving Starter- recap 657 X 3 = 6 5 7 x 3 Starter- answers 657 X 3 = 1971 6 5 7 x 3 1 9 7 1 1 1 2 P roblem Solving: Which calculation has an answer

507 views • 11 slides
Best Practice for Transformative Mitigation Projects Webinar 20 November 3:00 - 4:30 EST 2019

Best Practice for Transformative Mitigation Projects Webinar 20 November 3:00 - 4:30 EST 2019

Best Practice for Transformative Mitigation Projects Webinar 20 November 3:00 - 4:30 EST 2019 CDBG-DR Problem Solving Clinic 1 2019 CDBG-DR Problem Solving Clinic 1 Presenters HUD Jen Carpenter, Assistant Director of Policy, HUD DRSI

1.21k views • 47 slides
Solving Systems Solving Systems by Graphing by Solving Systems by Substitution Graphing

Solving Systems Solving Systems by Graphing by Solving Systems by Substitution Graphing

Slide 1 / 176 Slide 2 / 176 Algebra I System of Linear Equations 2015-11-02 www.njctl.org Slide 3 / 176 Slide 4 / 176 Table of Contents Click on the topic to go to that section Solving Systems Solving Systems by Graphing by Solving

596 views • 30 slides
Clean Energy Solutions Center and the International Energy Agency Modernizing Building Energy

Clean Energy Solutions Center and the International Energy Agency Modernizing Building Energy

Clean Energy Solutions Center and the International Energy Agency Modernizing Building Energy Codes to Secure our Global Energy Future August 20, 2013 Sean Esterly Moderator Didier Houssin International Energy Agency Yamina Saheb

416 views • 16 slides
The Configurable Sam Bayless, Holger Hoos, Kevin Leyton-Brown SAT Solver Challenge 2013

The Configurable Sam Bayless, Holger Hoos, Kevin Leyton-Brown SAT Solver Challenge 2013

3 C 1 o 0 n 2 fi e g g u n r e a b l l a l e h C S A r T e v S l o Frank Hutter, Adrian Balint , The Configurable Sam Bayless, Holger Hoos, Kevin Leyton-Brown SAT Solver Challenge 2013 08.03.2013 Page 2 The

512 views • 13 slides
Using Interval Constraint Propagation for Pseudo- Boolean Constraint Solving

Using Interval Constraint Propagation for Pseudo- Boolean Constraint Solving

Using Interval Constraint Propagation for Pseudo- Boolean Constraint Solving Albert-Ludwigs-Universitt Freiburg Karsten Scheibler, Bernd Becker Chair of Computer Architecture FMCAD 2014 PB Constraints PB Constraints: 2 x 1 + 4 x 2 + x 3

1.12k views • 23 slides
Answer Set Programming modulo Acyclicity Jori Bomanson 1 , Martin Gebser 1 , 2 , Tomi Janhunen 1

Answer Set Programming modulo Acyclicity Jori Bomanson 1 , Martin Gebser 1 , 2 , Tomi Janhunen 1

Answer Set Programming modulo Acyclicity Jori Bomanson 1 , Martin Gebser 1 , 2 , Tomi Janhunen 1 Benjamin Kaufmann 2 , and Torsten Schaub 2 , 3 1 ) Aalto University, Finland 2 ) University of Potsdam, Germany 3 ) INRIA Rennes, France Computational

476 views • 23 slides
Algorithm Configuration for Portfolio-based Parallel SAT-Solving Holger Hoos 1 , Kevin

Algorithm Configuration for Portfolio-based Parallel SAT-Solving Holger Hoos 1 , Kevin

Algorithm Configuration for Portfolio-based Parallel SAT-Solving Holger Hoos 1 , Kevin Leyton-Brown 1 , Torsten Schaub 2 , Marius Schneider 2 1 Department of Computer Science University of British Columbia Vancouver, BC, Canada 2 Institute of

511 views • 15 slides
Machine Learning for SAT Holger H. Hoos Department of Computer Science University of British

Machine Learning for SAT Holger H. Hoos Department of Computer Science University of British

Machine Learning for SAT Holger H. Hoos Department of Computer Science University of British Columbia Canada Dagstuhl Seminar on Theory and Practice of SAT Solving 2015/04/21 How can machine learning methods help to ... I build better SAT

689 views • 27 slides
Workforce Navigator Pilot Project GRANTEE CONVENING JANUARY 30, 2018 Systems Level Align

Workforce Navigator Pilot Project GRANTEE CONVENING JANUARY 30, 2018 Systems Level Align

English Language Learner Workforce Navigator Pilot Project GRANTEE CONVENING JANUARY 30, 2018 Systems Level Align educational opportunities to jobs in demand Shift relationships among partners Why career Change how workforce system

100 views • 9 slides
Algorithms for Dispersed Processing Josef Spillner, Alexander Schill

Algorithms for Dispersed Processing Josef Spillner, Alexander Schill

Department of Computer Science | Institute of Systems Architecture | Chair of Computer Networks Algorithms for Dispersed Processing Josef Spillner, Alexander Schill mailto:josef.spillner@tu-dresden.de xmpp:josef.spillner@jabber.org 1 st

440 views • 15 slides

More recommend