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BPSolver's Winning Solutions in ASP Competition: Insights from Neng-Fa Zhou

This presentation by Neng-Fa Zhou from The City University of New York delves into the successes of BPSolver in the ASP competition. It covers an overview of the competition's principles and participants, including Aclasp, EZCSP, and Potassco. Key features of B-Prolog, such as tabling and constraint logic programming, are discussed, along with BPSolver's winning, hopeful, and losing solutions. Observations on performance and comparative analysis with other systems like Clasp are also highlighted, giving a comprehensive view of advancements in Answer Set Programming.

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BPSolver's Winning Solutions in ASP Competition: Insights from Neng-Fa Zhou

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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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