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BPSolver’s Winning Solutions to ASP Competition Problems

BPSolver’s Winning Solutions to ASP Competition Problems. Neng-Fa Zhou The City University of New York zhou@sci.brooklyn.cuny.edu. Outline. Overview of the ASP competition B-Prolog’s features BPSolver’s winning solutions BPSolver’s hopeful solutions BPSolver’s losing solutions

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BPSolver’s Winning Solutions to ASP Competition Problems

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  1. BPSolver’s Winning Solutions to ASP Competition Problems Neng-Fa Zhou The City University of New York zhou@sci.brooklyn.cuny.edu Neng-Fa Zhou at TUWIEN

  2. Outline • Overview of the ASP competition • B-Prolog’s features • BPSolver’s winning solutions • BPSolver’s hopeful solutions • BPSolver’s losing solutions • Observations Neng-Fa Zhou at TUWIEN

  3. Overview of ASP Competition (Model & Solve) • Principles • To foster open comparison of ASP with any other declarative paradigm • To foster development of new language constructs • To foster development of new heuristics and/or algorithms Neng-Fa Zhou at TUWIEN

  4. Overview of ASP Competition (Model & Solve) • Participants • Aclasp (Gringo + Clasp + Gecode) • BPSolver (B-Prolog) • EZCSP (Gringo + Clasp + B-Prolog) • Fastdownward (PDDL) • IDP (grounder Gidl + MinisatID) • Potassco (Gringo + Clasp + Gecode) Neng-Fa Zhou at TUWIEN

  5. Overview of ASP Competition (Model & Solve) • Benchmarks (34) • P-problems (7) • NP-problems (19) • Beyond NP problems (2) • Optimization problems (6) Neng-Fa Zhou at TUWIEN

  6. Another View of the Results(Clasp Vs. B-Prolog) Neng-Fa Zhou at TUWIEN

  7. Outline • Overview of the ASP competition • B-Prolog’s features • BPSolver’s winning solutions • BPSolver’s hopeful solutions • BPSolver’s losing solutions • Observations Neng-Fa Zhou at TUWIEN

  8. B-Prolog =Prolog + Tabling + CLP(FD) • Prolog enhanced with • Array subscripts • Loop constructs • Tabling • Memorize and reuse intermediate results • Suitable for dynamic programming problems • CLP(FD) • Constraint Logic Programming over Finite Domains • Suitable for constraint satisfaction problems (NP-complete) Neng-Fa Zhou at TUWIEN

  9. Array Subscripts in B-Prolog • In arithmetic expressions • In arithmetic constraints • In calls to @= and @:= • In any other context, X[I1,…,In] is the same as X^[I1,…,In] S is X[1]+X[2]+X[3] X[1]+X[2] #= X[3] X[1,2] @= 100X[1,2] @:= 100 Neng-Fa Zhou at TUWIEN

  10. Loop Constructs in B-Prolog • foreach • foreach(E1inD1, . . ., EninDn, LVars, Goal) • Example: • foreach(A in [a,b], I in 1..2, writeln((A,I)) • List comprehension • [T : E1inD1, . . ., EninDn, LVars, Goal] • Examples: • L @= [(A,I): A in [a,b], I in 1..2]. • sum([A[I,J] : I in 1..N, J in 1..N]) #= N*N Neng-Fa Zhou at TUWIEN

  11. Tabling in B-Prolog • Eliminate infinite loops • Reduce redundant computations • :-table path/2. • path(X,Y):-edge(X,Y).path(X,Y):-edge(X,Z),path(Z,Y). • :-table fib/2.fib(0,1).fib(1,1).fib(N,F):- N>1, N1 is N-1,fib(N1,F1), N2 is N-2,fib(N2,F2), F is F1+F2. Neng-Fa Zhou at TUWIEN

  12. The Table-All Approach • Characteristics • All the arguments of a tabled subgoal are used in variant checking • All answers are tabled • Problems • The number of answers may be too large or even infinite for DP and ML problems • When computing aggregates, tabling noncontributing answers is a waste Neng-Fa Zhou at TUWIEN

  13. Mode-Directed Tabling in B-Prolog • Table mode declaration • C: Cardinality limit • Modes • + : input • - : output • min: minimized • max: maximized :-table p(M1,...,Mn):C. Neng-Fa Zhou at TUWIEN

  14. Example: Shortest Path Problem • sp(X,Y,P,W) • P is a shortest path between X and Y with minimal weight W. :-table sp(+,+,-,min). sp(X,Y,[(X,Y)],W) :- edge(X,Y,W). sp(X,Y,[(X,Z)|Path],W) :- edge(X,Z,W1), sp(Z,Y,Path,W2), W is W1+W2. Neng-Fa Zhou at TUWIEN

  15. CLP(FD) in B-Prolog • A rich set of built-in constraints • Unification and arithmetic constraints (#=, #\=, #>, #>=, #<, #=<) • Global constraints • A glass-box approach to the implementation • All propagators are described in Action Rules (TPLP’06) • Action Rules is open to the user for describing problem-specific propagators • A rich set of labeling options Neng-Fa Zhou at TUWIEN

  16. Global Constraints in B-Prolog • all_different(L) & all_distinct(L) • post_neqs(L) • circuit(L) • count(V,L,RelOp,N) • exactly(N,L,V) • atleast(N,L,V) • atmost(N,L,V) • cumulative(Starts,Durations,Resources,Limit) • serialized(Starts,Durations) • diffn(L) • element(I,L,V) • path_from_to(From,To,L)& path_from_to(From,To,L,Lab) Neng-Fa Zhou at TUWIEN

  17. Outline • Overview of the ASP competition • B-Prolog’s features • BPSolver’s winning solutions • BPSolver’s hopeful solutions • BPSolver’s losing solutions • Observations Neng-Fa Zhou at TUWIEN

  18. BPSolver’s Winning Solutions Neng-Fa Zhou at TUWIEN

  19. Winning Solutions in Prolog • Grammar-Based Information Extraction • Parsing • Labyrinth • State space search • Tomography • Set covering Neng-Fa Zhou at TUWIEN

  20. Winning Solutions With Tabling • Reachability • Hydraulic Planning • Hydraulic Leaking • Airport Pickup • Hanoi Tower Neng-Fa Zhou at TUWIEN

  21. Reachability :-table reach/1. reach(X):- start(X). reach(Y):- reach(X), edge(X,Y). Neng-Fa Zhou at TUWIEN

  22. Hydraulic Planning :-table pressurize(+,-,min). pressurize(Node,Plan,Len):- full(Node),!, Plan=[],Len=0. pressurize(Node,[Valve|Plan],Len):- link(AnotherNode,Node,Valve), \+ stuck(Valve), pressurize(AnotherNode,Plan,Len1), Len is Len1+1. Neng-Fa Zhou at TUWIEN

  23. Hydraulic Leaking :-table pressurize(+,-,min). pressurize(Node,Plan,(Leaks,Len)):- full(Node),!, Plan=[],Leaks=0,Len=0. pressurize(Node,[Valve|Plan],(Leaks,Len)):- link(AnotherNode,Node,Valve), \+ stuck(Valve), pressurize(AnotherNode,Plan,(Leaks1,Len1)), Len is Len1+1, (leaking(Valve)-> Leaks is Leaks1+1 ; Leaks is Leaks1 ). Neng-Fa Zhou at TUWIEN

  24. Airport Pickup • Passengers at Airport #1 want to move to Airport #2 and vice versa • A certain number of vehicles are available • Some of the locations are gas stations CITY MAP Neng-Fa Zhou at TUWIEN

  25. Solution to Airport Pickup :-table move_vehicle(+,+,+,+,max,-). move_vehicle(X,X,_Cap,GasLevel,Objective,Steps):- Objective=(GasLevel,0),Steps=[]. move_vehicle(X,Y,Cap,GasLevel,Objective,[drive(Z)|Steps]):- (driveway(X,Z,GasNeeded);driveway(Z,X,GasNeeded)), GasLevel>=GasNeeded, GasLevel1 is GasLevel-GasNeeded, move_vehicle(Z,Y,Cap,GasLevel1,Objective1,Steps), Objective1=(AfterGasLevel,MLen), MLen1 is MLen-1, Objective=(AfterGasLevel,MLen1). move_vehicle(X,Y,Cap,GasLevel,Objective,[refuel|Steps]):- gasstation(X), GasLevel<Cap, move_vehicle(X,Y,Cap,Cap,Objective1,Steps), Objective1=(AfterGasLevel,MLen), MLen1 is MLen-1, Objective=(AfterGasLevel,MLen1). Neng-Fa Zhou at TUWIEN

  26. Hanoi Tower (4-Pegs) A B C D A B C D Two snapshots from the sequence by the Frame-Stewart algorithm Neng-Fa Zhou at TUWIEN

  27. Problem Reduction • If the largest disk is in its final position, remove it. A B C D A B C D Neng-Fa Zhou at TUWIEN

  28. Create an Intermediate State • Subproblems Sub-prob-1 A B C D A B C D Sub-prob-2 A B C D A B C D Neng-Fa Zhou at TUWIEN

  29. The Solution(4-Peg Hanoi Tower) :-table plan4(+,+,+,-,min). plan4(N,_CState,_GState,Plan,Len):-N=:=0,!,Plan=[],Len=0. plan4(N,CState,GState,Plan,Len):- reduce_prob(N,CState,GState,CState1,GState1),!, N1 is N-1, plan4(N1,CState1,GState1,Plan,Len). plan4(N,CState,GState,Plan,Len):- partition_disks(N,CState,GState,ItState,Mid,Peg), remove_larger_disks(CState,Mid,CState1), plan4(Mid,CState1,ItState,Plan1,Len1), % sub-prob1 remove_smaller_or_equal_disks(CState,Mid,CState2), remove_smaller_or_equal_disks(GState,Mid,GState2), N1 is N-Mid, plan3(N1,CState2,GState2,Peg,Plan2,Len2), % sub-prob2 remove_larger_disks(GState,Mid,GState1), plan4(Mid,ItState,GState1,Plan3,Len3), % sub-prob3 append(Plan1,Plan2,Plan3,Plan), Len is Len1+Len2+Len3. Neng-Fa Zhou at TUWIEN

  30. Winning Solutions in CLP(FD) • Tangram • Magic Square Sets (all_different) • Weight-Assignment Tree (element) • Knight Tour (circuit) • Disjunctive Scheduling (post_disjunctive_tasks) • Maximal Clique Neng-Fa Zhou at TUWIEN

  31. Magic Square Sets semi(Board,N,Magic):- foreach(I in 1..N, sum([Board[I,J] : J in 1..N])#=Magic), foreach(J in 1..N, sum([Board[I,J] : I in 1..N])#=Magic). normal(Board,N,Magic):- sum([Board[I,I] : I in 1..N]) #= Magic, sum([Board[I,N-I+1] : I in 1..N]) #= Magic. Neng-Fa Zhou at TUWIEN

  32. Outline • Overview of the ASP competition • B-Prolog’s features • BPSolver’s winning solutions • BPSolver’s hopeful solutions • BPSolver’s losing solutions • Observations Neng-Fa Zhou at TUWIEN

  33. BPSolver’s Hopeful Solutions • Graph Coloring (Ranking = 5) • Sokoban Optimization (Ranking = 4) Neng-Fa Zhou at TUWIEN

  34. Graph Coloring • Model-1 (neq) • For each two neighbors i and j, CiCj • Model-2 (all_distinct) • For each complete subgraph (clique) {i1,i2,…,ik}, all_distinct([Ci1, Ci2,…, Cik]) • post_neqs(Neqs) in B-Prolog • Model-3 (Model-2 + symmetry breaking) • Allen Van Gelder: Another look at graph coloring via propositional satisfiability Neng-Fa Zhou at TUWIEN

  35. Graph Coloring in B-Prolog Go:- create_vars(Vars), generate_neqs(Vars,Neqs), post_neqs(Neqs,Cliques), % new built-in largest_clique(Cliques,LClique), (labeling(LClique)-> labeling_ffc(Vars),!;fail), output(Vars). Neng-Fa Zhou at TUWIEN

  36. Performance Comparison(Model-2 Vs. Model-3) Neng-Fa Zhou at TUWIEN

  37. BPSolver’s Solution to Sokoban Neng-Fa Zhou at TUWIEN

  38. The Competition Results Neng-Fa Zhou at TUWIEN

  39. BPSolver’s Losing Solutions(Score) • Partner Units (0) • Reverse Folding (0) • Solitaire (0) • Strategic Companies (0) • Company Controls Optimize (0) • Stable Marriage (5) • Maze Generation (49) Neng-Fa Zhou at TUWIEN

  40. Observations Neng-Fa Zhou at TUWIEN

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