Extending SymPA with Unsolvability Certificates Bachelor Thesis - PowerPoint PPT Presentation

Extending SymPA with Unsolvability Certificates Bachelor Thesis Claudia Grundke University of Basel Departement of Mathematics and Computer Science 18 September, 2020

Classical Planning A B start I G 1 G 2 C D Extending SymPA with Unsolvability Certificates 1 / 12

Classical Planning A B start I G 1 G 2 C D Extending SymPA with Unsolvability Certificates 1 / 12

Correctness How can we be sure that the planner gave the correct result? https://icon-icons.com/icon/Bug/115148 (09.09.2020) Extending SymPA with Unsolvability Certificates 2 / 12

Certifying Algorithms emit certificate alongside result certificate justifies result and can be verified independently Extending SymPA with Unsolvability Certificates 3 / 12

Certifying Algorithms emit certificate alongside result certificate justifies result and can be verified independently partially and fully certifying algorithms plan can serve as certificate Extending SymPA with Unsolvability Certificates 3 / 12

SymPA (´ Alvaro Torralba) Sym bolic P erimeter A bstractions forward and backward breadth first searches CD returns ”solvable” C D or ”unsolvable” Extending SymPA with Unsolvability Certificates 4 / 12

Certifying SymPA Sym bolic P erimeter A bstractions forward and backward breadth first searches returns plan or unsolvability certificate Extending SymPA with Unsolvability Certificates 5 / 12

Abstract Backward Search A B G open list: start G 1 G I closed list: - G 2 C D CD Extending SymPA with Unsolvability Certificates 6 / 12

Abstract Backward Search A B G open list: start G 1 CD I closed list: G G 2 C D CD Extending SymPA with Unsolvability Certificates 6 / 12

Abstract Backward Search A B G open list: start G 1 I I closed list: G , CD G 2 C D CD Extending SymPA with Unsolvability Certificates 6 / 12

Abstract Backward Search A B G open list: - start G 1 I closed list: G , CD , I G 2 C D CD Extending SymPA with Unsolvability Certificates 6 / 12

Forward Search dead ends A B open list: I G 1 start I closed list: - G 2 C D Extending SymPA with Unsolvability Certificates 7 / 12

Forward Search dead ends A B open list: C G 1 start I closed list: I G 2 C D Extending SymPA with Unsolvability Certificates 7 / 12

Forward Search dead ends A B open list: - G 1 start I closed list: I , C G 2 C D Extending SymPA with Unsolvability Certificates 7 / 12

Unsolvability Proof System (Salom´ e Eriksson) proofs serve as unsolvability certificates core concept: dead states Extending SymPA with Unsolvability Certificates 8 / 12

Unsolvability Proof System (Salom´ e Eriksson) proofs serve as unsolvability certificates core concept: dead states initial state or all goal states dead ⇒ task unsolvable Extending SymPA with Unsolvability Certificates 8 / 12

Forward Unsolvability Proof D is dead CL is dead all successors of CL either in CL itself or in D initial state is in CL a a a D = set of dead ends, CL = closed list Extending SymPA with Unsolvability Certificates 9 / 12

Forward Unsolvability Proof dead ends D is dead A B D contains no goal state D cannot be left CL is dead start G 1 I all successors of CL either in CL itself or in D G 2 C D initial state is in CL a open list: closed list:aaa a - I , C a D = set of dead ends, CL = closed list Extending SymPA with Unsolvability Certificates 9 / 12

Forward Unsolvability Proof dead ends D is dead A B D contains no goal state D cannot be left CL is dead start G 1 I CL contains no goal state all successors of CL either in CL itself or in D G 2 C D initial state is in CL a open list: closed list:aaa a - I , C a D = set of dead ends, CL = closed list Extending SymPA with Unsolvability Certificates 9 / 12

Forward Unsolvability Proof dead ends D is dead A B D contains no goal state D cannot be left CL is dead start G 1 I CL contains no goal state all successors of CL either in CL itself or in D G 2 C D initial state is in CL a open list: closed list:aaa a - I , C a D = set of dead ends, CL = closed list Extending SymPA with Unsolvability Certificates 9 / 12

Forward Unsolvability Proof D is dead D contains no goal state D cannot be left CL is dead CL contains no goal state all successors of CL either in CL itself or in D initial state is in CL a ⇒ initial state dead D = set of dead ends, CL = closed list Extending SymPA with Unsolvability Certificates 9 / 12

Forward Unsolvability Proof D is dead D contains no goal state D cannot be left CL is dead CL contains no goal state all successors of CL either in CL itself or in D initial state is in CL a ⇒ initial state dead ⇒ task unsolvable D = set of dead ends, CL = closed list Extending SymPA with Unsolvability Certificates 9 / 12

Evaluation average time search 1.11s total number of tasks 352 certificate returned ”unsolvable” 104 2.74s generation valid certificates 83 33.80s verification Extending SymPA with Unsolvability Certificates 10 / 12

Remaining Errors D is dead D contains no goal state D cannot be left CL is dead CL contains no goal state all successors of CL either in CL itself or in D initial state is in CL a ⇒ initial state dead ⇒ task unsolvable D = set of dead ends, CL = closed list Extending SymPA with Unsolvability Certificates 11 / 12

Summary fully certifying version of SymPA verifiable unsolvability proofs Extending SymPA with Unsolvability Certificates 12 / 12

Questions? Comments? Discussion!

Goals intersect Dead Ends A B abstract forward search open list: I closed list: - start G 1 D bw : - I abstract backward search open list: G 1 , G 2 closed list: - G 2 C D D fw : - CD Extending SymPA with Unsolvability Certificates 13 / 12

Goals intersect Dead Ends A B abstract forward search open list: A , CD closed list: I start G 1 D bw : - I abstract backward search open list: G 1 , G 2 closed list: - G 2 C D D fw : - CD Extending SymPA with Unsolvability Certificates 13 / 12

Goals intersect Dead Ends A B abstract forward search open list: B , CD closed list: I , A start G 1 D bw : - I abstract backward search open list: G 1 , G 2 closed list: - G 2 C D D fw : - CD Extending SymPA with Unsolvability Certificates 13 / 12

Goals intersect Dead Ends A B abstract forward search open list: CD closed list: I , A , B start G 1 D bw : - I abstract backward search open list: G 1 , G 2 closed list: - G 2 C D D fw : - CD Extending SymPA with Unsolvability Certificates 13 / 12

Goals intersect Dead Ends A B abstract forward search open list: G 2 I , A , B , closed list: CD start G 1 I D bw : - abstract backward search open list: G 1 , G 2 G 2 C D closed list: - D fw : - CD Extending SymPA with Unsolvability Certificates 13 / 12

Goals intersect Dead Ends A B abstract forward search open list: - I , A , B , closed list: CD , G 2 start G 1 I D bw : - abstract backward search open list: G 1 , G 2 G 2 C D closed list: - D fw : - CD Extending SymPA with Unsolvability Certificates 13 / 12

Goals intersect Dead Ends A B abstract forward search open list: - I , A , B , closed list: CD , G 2 start G 1 I D bw : G 1 abstract backward search open list: G 1 , G 2 G 2 C D closed list: - D fw : - CD Extending SymPA with Unsolvability Certificates 13 / 12

Goals intersect Dead Ends A B abstract forward search open list: - I , A , B , closed list: CD , G 2 start G 1 I D bw : G 1 abstract backward search open list: G 2 G 2 C D closed list: - D fw : - CD Extending SymPA with Unsolvability Certificates 13 / 12

Goals intersect Dead Ends A B abstract forward search open list: - I , A , B , closed list: CD , G 2 start G 1 I D bw : G 1 abstract backward search open list: CD G 2 C D closed list: G 2 D fw : - CD Extending SymPA with Unsolvability Certificates 13 / 12

Goals intersect Dead Ends A B abstract forward search open list: - I , A , B , closed list: CD , G 2 start G 1 I D bw : G 1 abstract backward search open list: I G 2 C D closed list: G 2 , CD D fw : - CD Extending SymPA with Unsolvability Certificates 13 / 12

Goals intersect Dead Ends A B abstract forward search open list: - I , A , B , closed list: CD , G 2 start G 1 I D bw : G 1 abstract backward search open list: - G 2 C D closed list: G 2 , CD , I D fw : - CD Extending SymPA with Unsolvability Certificates 13 / 12

Goals intersect Dead Ends A B abstract forward search open list: - I , A , B , closed list: CD , G 2 start G 1 I D bw : G 1 abstract backward search open list: - G 2 C D closed list: G 2 , CD , I D fw : A , B , G 1 CD Extending SymPA with Unsolvability Certificates 13 / 12

Goals intersect Dead Ends D bw G 1 D fw Extending SymPA with Unsolvability Certificates 14 / 12

main loop : search until current search infeasible or its open list empty current search infeasible? yes no generate new abstract search found solution? goto main loop yes no return ”unsolvable” current search abstract? yes no add unreachable states to dead ends of other direction return ”solvable” goto main loop Extending SymPA with Unsolvability Certificates 15 / 12