Generating None-Plans in Order to Find Plans 1

Transcription

1 Generating None-Plans in Order to Find Plans 1 Wojciech Penczek a joint work with Michał Knapik and Artur Niewiadomski Institute of Computer Sciences, PAS, Warsaw, and Siedlce University, Poland MINI PW, the 24th of November Best Paper Award at SEFM 15 Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 1/35

2 Outline 1 Introduction Related Work PlanICS TripICS Idea of None-plans Reductions Planning in PlanICS 2 3 Synthesis of None-Plans Applying None-Plans to Find Plans Experimental Results Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 2/35

3 Main Contributions Introduction Related Work PlanICS Idea of None-plans Reductions Planning in PlanICS New web service composition systems - PlanICS and TripICS, A new method for improving efficiency of algorithms solving hard problems, A new reduction method for planning, Application of the results in the tool PlanICS. Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 3/35

4 Related Work PlanICS Idea of None-plans Reductions Planning in PlanICS Related Work - Web Service Composition Systems Entish - IOPR, a two phase planning by an ontology, WSMO - ontology, IOPR, a formal goal, embedded rule languages WSMX - WSMO implementation, service registration, service discovery by matchmaking, service activation by adapters SUPER - composition based on WSMO ontology and AI algorithms PlanICS - a state-based approach, a two phase planning, a simple rule language, the abstract planners based on GA and SMT-solvers, the concrete planners based on GA, SA, GEO, and SMT-solvers, and their combinations. Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 4/35

5 Related Work PlanICS Idea of None-plans Reductions Planning in PlanICS Related Work - Reduction Methods Abstraction methods [Cousot, Cousot,...], Partial order reductions [Valmari, Peled, Godefroid,...], Symmetry reductions [Clarke, Emerson, Jha, Sistla,... ], CEGAR Counterexample Guided Abstraction [Clarke et al.], and others. Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 5/35

6 Related Work PlanICS Idea of None-plans Reductions Planning in PlanICS Web Service Composition Problem Which service types and instances to choose? Services of some type Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 6/35

7 Related Work PlanICS Idea of None-plans Reductions Planning in PlanICS Web Service Composition Problem PlanICS finds a solution! Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 6/35

8 PlanICS - Key Concepts Related Work PlanICS Idea of None-plans Reductions Planning in PlanICS User intention (query) Static knowledge (ontology) PlanICS Abstract Plan Concrete Dynamic knowledge (WS offers) The main goal: an arrangement of service executions satisfying a user intention Ontology - the types of services and objects A two phase composition process: abstract (on types) and concrete (on web services) Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 7/35

9 PlanICS - Key Concepts Related Work PlanICS Idea of None-plans Reductions Planning in PlanICS User intention (query) Static knowledge (ontology) PlanICS Abstract Plan Concrete Dynamic knowledge (WS offers) The main goal: an arrangement of service executions satisfying a user intention Ontology - the types of services and objects A two phase composition process: abstract (on types) and concrete (on web services) Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 7/35

10 PlanICS - Key Concepts Related Work PlanICS Idea of None-plans Reductions Planning in PlanICS User intention (query) Static knowledge (ontology) PlanICS Abstract Plan Concrete Dynamic knowledge (WS offers) The main goal: an arrangement of service executions satisfying a user intention Ontology - the types of services and objects A two phase composition process: abstract (on types) and concrete (on web services) Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 7/35

11 Related Work PlanICS Idea of None-plans Reductions Planning in PlanICS Architecture of PlanICS BPEL export module SMT Hybrid Abstract planner MultiSet Explorer SMT Hybrid Concrete planner Offer WSDL collector WS WS Web services GA GA WS WS WS Parser GUI controls all modules Ontology Service Register Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 8/35

12 Related Work PlanICS Idea of None-plans Reductions Planning in PlanICS Architecture of PlanICS BPEL export module SMT Hybrid Abstract planner MultiSet Explorer SMT Hybrid Concrete planner Offer WSDL collector WS WS Web services GA GA WS WS WS Parser GUI controls all modules Ontology Service Register Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 8/35

13 Related Work PlanICS Idea of None-plans Reductions Planning in PlanICS Architecture of PlanICS BPEL export module SMT Hybrid Abstract planner MultiSet Explorer SMT Hybrid Concrete planner Offer WSDL collector WS WS Web services GA GA WS WS WS Parser GUI controls all modules Ontology Service Register Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 8/35

14 TripICS - Main Ideas Introduction Related Work PlanICS Idea of None-plans Reductions Planning in PlanICS TripICS - a real-life application of PlanICS to planning trips and travels around the world, TripICS - a specialization of the concrete planning viewed as a constrained optimization problem to the ontology containing services provided by hotels, airlines, railways, museums etc., TripICS finds an optimal plan satisfying the user s requirements by applying the concrete planners of PlanICS, Abstract planning of TripICS - semi-automatic, the user builds an abstract plan using a Graphical User Interface. Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 9/35

15 Related Work PlanICS Idea of None-plans Reductions Planning in PlanICS Architecture of TripICS SMT GUI Query builder Validation Plan presentation SCGEO GA IPH Concrete planner Offer collector Service Register JSON REST WSDL WS WS Web services WS SCSA WS WS Ontology Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 10/35

16 General System Description Related Work PlanICS Idea of None-plans Reductions Planning in PlanICS TripICS A user-friendly planning of visits to cities (places), travels, and entertainments, satisfying the user s requirements. User s Requirements Specification of cities, places, dates, means of travels, and quality requirements (level of prices, quality of hotels, etc.). Optimal Plan A plan of highest quality according to the given requirements. Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 11/35

17 Specifying Requirements Related Work PlanICS Idea of None-plans Reductions Planning in PlanICS Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 12/35

18 Related Work PlanICS Idea of None-plans Reductions Planning in PlanICS Plan Returned by TripICS Figure: The example plan Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 13/35

19 General idea intuition Related Work PlanICS Idea of None-plans Reductions Planning in PlanICS D a domain to search for a plan (difficult task!), D an abstract domain in which finding a plan is easier, a plan in D does not need to correspond to a plan in D, a none-plan in D corresponds to a none-plan in D, find (the) none-plans in D, prune D from (the) none-plans of D, search for (the) plans in D pruned. Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 14/35

20 Application to planning in PlanICS Related Work PlanICS Idea of None-plans Reductions Planning in PlanICS Given an ontology of object types and services (OWL-like language), Given a user query: (initial worlds, final worlds), A world a set of objects (each object has a type and attributes), A service: (in, inout, out, pre, post), where in, inout, out are sets of objects, pre a boolean formula over the object attributes of in and inout, post a boolean formula over the object attributes of inout and out. Task: Find all plans from some initial to some final world. This problem is NP-complete. Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 15/35

21 Service composition in PlanICS Related Work PlanICS Idea of None-plans Reductions Planning in PlanICS Initial world pre A preconditions on object attributes postconditions on object attributes post A pre B post B pre C Service A World 0 Service B World 1 Service C post C Final world Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 16/35

22 Service composition in PlanICS Related Work PlanICS Idea of None-plans Reductions Planning in PlanICS Initial world pre A preconditions on object attributes postconditions on object attributes post A pre B post B pre C Service A World 0 Service B World 1 Service C post C Final world Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 16/35

23 Simplifying the planning domain Idea simplify services and worlds: Related Work PlanICS Idea of None-plans Reductions Planning in PlanICS the simplified objects do not have attributes, a simplified world a multiset of objects, a simplified service (precondition, effect), precondition a multiset of objects (objects required), effect a multiset of objects (new objects added). Let B be a set of services, B the set of simplified services of B, The main Property of Abstraction: If B cannot be composed into a plan, then B cannot either. Goal: synthesize constraints of non-composability. Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 17/35

24 (Abstract) Planning Domain (Abstract) Planning Domain P = (W H, F I, F G, Act): W H N n a set of abstract worlds (multisets), F I, F G W H initial, final worlds, Act a set of actions (simplified services), where n is the number of all types of the objects. For each act Act: pre(act) precondition of act, eff(act) effect of act. pre(act), eff(act) N n. Action act Act is enabled in ω W H iff pre(act) ω and the results of firing act: ω act ω + eff(act) Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 18/35

25 Plans Given P = (W H, F I, F G, Act), B Act π Π(ω, B, ω ) iff act π = ω 1 act 0 2 act n 1 act ω1... ω n n 1 ωn where ω 0 = ω, ω n ω, and {act 1,..., act n } B ω I F I ω F F G Π(ω I, B, ω F ) the plans over B Each plan starts from an initial world and its last world covers a final world. Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 19/35

26 Exemplary planning domain Vehicle Car Boat Amphibian Vehicles inheritance Actions: makevehicle: needs nothing, builds vehicle makecar: needs vehicle, builds car makeboat: needs vehicle, builds boat makeamphibian: needs boat and car, builds amphibian tinker: needs amphibian and car, builds two amphibians Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 20/35

27 Exemplary planning domain, ct d (1, 0, 0, 0) Vehicle (1, 1, 0, 0) (1, 0, 1, 0) Car Boat Amphibian (1, 1, 1, 1) Vehicles inheritance Order of the objects: (Vehicle, Car, Boat, Amphibian) makeamphibian: needs boat and car, builds amphibian pre(makeamphibian) = (1, 0, 1, 0) + (1, 1, 0, 0) = (2, 1, 1, 0) eff(makeamphibian) = (1, 1, 1, 1) Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 21/35

28 Exemplary planning domain, ct d (1, 0, 0, 0) Vehicle (1, 1, 0, 0) (1, 0, 1, 0) Car Boat Amphibian (1, 1, 1, 1) Vehicles inheritance Order of the objects: (Vehicle, Car, Boat, Amphibian) makeamphibian: needs boat and car, builds amphibian pre(makeamphibian) = (1, 0, 1, 0) + (1, 1, 0, 0) = (2, 1, 1, 0) eff(makeamphibian) = (1, 1, 1, 1) Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 21/35

29 Exemplary planning domain, ct d (1, 0, 0, 0) Vehicle (1, 1, 0, 0) (1, 0, 1, 0) Car Boat Amphibian (1, 1, 1, 1) Vehicles inheritance Order of the objects: (Vehicle, Car, Boat, Amphibian) makeamphibian: needs boat and car, builds amphibian pre(makeamphibian) = (1, 0, 1, 0) + (1, 1, 0, 0) = (2, 1, 1, 0) eff(makeamphibian) = (1, 1, 1, 1) Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 21/35

30 Exemplary planning domain, ct d (1, 0, 0, 0) Vehicle (1, 1, 0, 0) (1, 0, 1, 0) Car Boat Amphibian (1, 1, 1, 1) Vehicles inheritance Order of the objects: (Vehicle, Car, Boat, Amphibian) makeamphibian: needs boat and car, builds amphibian pre(makeamphibian) = (1, 0, 1, 0) + (1, 1, 0, 0) = (2, 1, 1, 0) eff(makeamphibian) = (1, 1, 1, 1) Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 21/35

31 Exemplary planning domain, ct d Car Vehicle Amphibian Boat Vehicles inheritance Actions: pre(makevehicle) = (0, 0, 0, 0) eff(makevehicle) = (1, 0, 0, 0) pre(makecar) = (1, 0, 0, 0) eff(makecar) = (1, 1, 0, 0) pre(makeboat) = (1, 0, 0, 0) eff(makeboat) = (1, 0, 1, 0) pre(makeamphibian) =(2, 1, 1, 0) eff(makeamphibian) = (1, 1, 1, 1) pre(tinker)=(2, 2, 1, 1) eff(tinker) = (2, 2, 2, 2) ω I = (0, 0, 0, 0) (one initial world) ω F = (0, 0, 0, 1) (one final world) Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 22/35

32 Classifying actions Introduction Synthesis of None-Plans Applying None-Plans to Find Plans Experimental Results V max - the largest number occurring in pre(act) for act Act. enact(a) = {act Act V max eff(act ) pre(act)}. act A all actions that can be enabled by firing actions from A Act, ω W H, i > 0 G ω 0 = {act Act pre(act) ω} the actions enabled in ω, G ω i+1 = enact(gω i ) the actions enabled in i th step H0 ω = Gω 0, Hi+1 ω = Gω i+1 \ Gω i the actions newly enabled in i th step. Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 23/35

33 Synthesis of None-Plans Applying None-Plans to Find Plans Experimental Results Classifying actions, ct d ω, ω W H kgoal(ω, ω ) = min({k N act G ω k V max eff(act) ω }) the minimal step at which greedily fired actions cover ω. Lemma A kgoal(ω, ω ) < iff Π(ω, Act, ω ), kgoal(ω, ω ) can be computed in time O( Act 2 n). Planning in P is easy. Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 24/35

34 Synthesis of None-Plans Applying None-Plans to Find Plans Experimental Results Classifying actions Lemma B Let A Act. If there is a plan over A, then A contains at least one element from H ω I i for all 0 i kgoal(ω I, ω F ). First easy reductions: block all sets of actions that do not satisfy Lemma B. More reductions: consider none-plans. Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 25/35

35 None-plans Introduction Synthesis of None-Plans Applying None-Plans to Find Plans Experimental Results A Act, ω, ω W H Z(ω, A, ω ) := {B A Π(ω, B, ω ) = } None-plan: a set of actions B which is not a support of any plan starting at ω and covering ω. I(ω) := {ω ω = 1 ω ω } unitary coordination vectors of ω e.g., I((2, 1, 1, 0)) = {(1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1, 0)} Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 26/35

36 Characterisation of none-plans Synthesis of None-Plans Applying None-Plans to Find Plans Experimental Results Theorem Z(ω, A, ω ) = ω I(ω ) ω ω act A eff(act) ω ( D(ω, A, act) 2 A\{act} ) where D(ω, A, act) = {B {act} B Z(ω, A \ {act}, pre(act))} Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 27/35

37 Synthesis of None-Plans Applying None-Plans to Find Plans Experimental Results Characterisation of none-plans, ct d Theorem Z(ω, A, ω ) = ω I(ω ) ω ω act A eff(act) ω ( D(ω, A, act) 2 A\{act} ) where D(ω, A, act) = {B {act} B Z(ω, A \ {act}, pre(act))} To find all B A that do not make a plan from ω to cover ω take a coordinate ω of ω that needs to be covered for each action act that could cover ω when fired ensure that either act cannot be enabled and take it or throw act away. Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 28/35

38 Synthesis of None-Plans Applying None-Plans to Find Plans Experimental Results Characterisation of none-plans, ct d Theorem Z(ω, A, ω ) = ω I(ω ) ω ω act A eff(act) ω ( D(ω, A, act) 2 A\{act} ) where D(ω, A, act) = {B {act} B Z(ω, A \ {act}, pre(act))} To find all B A that do not make a plan from ω to cover ω take a coordinate ω of ω that needs to be covered for each action act that could cover ω when fired ensure that either act cannot be enabled and take it or throw act away. Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 28/35

39 Synthesis of None-Plans Applying None-Plans to Find Plans Experimental Results Characterisation of none-plans, ct d Theorem Z(ω, A, ω ) = ω I(ω ) ω ω act A eff(act) ω ( D(ω, A, act) 2 A\{act} ) where D(ω, A, act) = {B {act} B Z(ω, A \ {act}, pre(act))} To find all B A that do not make a plan from ω to cover ω take a coordinate ω of ω that needs to be covered for each action act that could cover ω when fired ensure that either act cannot be enabled and take it or throw act away. Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 28/35

40 Synthesis of None-Plans Applying None-Plans to Find Plans Experimental Results Characterisation of none-plans, ct d Theorem Z(ω, A, ω ) = ω I(ω ) ω ω act A eff(act) ω ( D(ω, A, act) 2 A\{act} ) where D(ω, A, act) = {B {act} B Z(ω, A \ {act}, pre(act))} To find all B A that do not make a plan from ω to cover ω take a coordinate ω of ω that needs to be covered for each action act that could cover ω when fired ensure that either act cannot be enabled and take it or throw act away. Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 28/35

41 Synthesis of None-Plans Applying None-Plans to Find Plans Experimental Results Characterisation of none-plans, ct d Theorem Z(ω, A, ω ) = ω I(ω ) ω ω act A eff(act) ω ( D(ω, A, act) 2 A\{act} ) where D(ω, A, act) = {B {act} B Z(ω, A \ {act}, pre(act))} To find all B A that do not make a plan from ω to cover ω take a coordinate ω of ω that needs to be covered for each action act that could cover ω when fired ensure that either act cannot be enabled and take it or throw act away. Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 28/35

42 Synthesis of None-Plans Applying None-Plans to Find Plans Experimental Results Characterisation of none-plans, ct d Theorem Z(ω, A, ω ) = ω I(ω ) ω ω act A eff(act) ω ( D(ω, A, act) 2 A\{act} ) where D(ω, A, act) = {B {act} B Z(ω, A \ {act}, pre(act))} To find all B A that do not make a plan from ω to cover ω take a coordinate ω of ω that needs to be covered for each action act that could cover ω when fired ensure that either act cannot be enabled and take it or throw act away. Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 28/35

43 None-plans: tree encoding Synthesis of None-Plans Applying None-Plans to Find Plans Experimental Results {makevehicle, makecar, makeboat} target: (2, 1, 1, 0) {makevehicle, makecar, makeboat} target: (1, 0, 0, 0) {makevehicle, makecar, makeboat} target: (0, 1, 0, 0) {makevehicle, makeboat} target: (1, 0, 0, 0)... makecar {makevehicle, makecar, makeboat} target: (0, 0, 1, 0) Z((0, 0, 0, 0), {makevehicle, makecar, makeboat}, (2, 1, 1, 0)) = Z((0, 0, 0, 0), {makevehicle, makecar, makeboat}, ω) = ω I((2,1,1,0)) D((0, 0, 0, 0), {makevehicle, makecar, makeboat}, makecar) 2 A\{makeCar}... Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 29/35

44 None-plans: tree encoding Synthesis of None-Plans Applying None-Plans to Find Plans Experimental Results {makevehicle, makecar, makeboat} target: (2, 1, 1, 0) {makevehicle, makecar, makeboat} target: (1, 0, 0, 0) {makevehicle, makecar, makeboat} target: (0, 1, 0, 0) {makevehicle, makeboat} target: (1, 0, 0, 0)... makecar {makevehicle, makecar, makeboat} target: (0, 0, 1, 0) Z((0, 0, 0, 0), {makevehicle, makecar, makeboat}, (2, 1, 1, 0)) = Z((0, 0, 0, 0), {makevehicle, makecar, makeboat}, ω) = ω I((2,1,1,0)) D((0, 0, 0, 0), {makevehicle, makecar, makeboat}, makecar) 2 A\{makeCar}... Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 29/35

45 None-plans: tree encoding Synthesis of None-Plans Applying None-Plans to Find Plans Experimental Results {makevehicle, makecar, makeboat} target: (2, 1, 1, 0) {makevehicle, makecar, makeboat} target: (1, 0, 0, 0) {makevehicle, makecar, makeboat} target: (0, 1, 0, 0) {makevehicle, makeboat} target: (1, 0, 0, 0)... makecar {makevehicle, makecar, makeboat} target: (0, 0, 1, 0) Z((0, 0, 0, 0), {makevehicle, makecar, makeboat}, (2, 1, 1, 0)) = Z((0, 0, 0, 0), {makevehicle, makecar, makeboat}, ω) = ω I((2,1,1,0)) D((0, 0, 0, 0), {makevehicle, makecar, makeboat}, makecar) 2 A\{makeCar}... Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 29/35

46 None-plans: tree encoding Synthesis of None-Plans Applying None-Plans to Find Plans Experimental Results {makevehicle, makecar, makeboat} target: (2, 1, 1, 0) {makevehicle, makecar, makeboat} target: (1, 0, 0, 0) {makevehicle, makecar, makeboat} target: (0, 1, 0, 0) {makevehicle, makeboat} target: (1, 0, 0, 0)... makecar {makevehicle, makecar, makeboat} target: (0, 0, 1, 0) Z((0, 0, 0, 0), {makevehicle, makecar, makeboat}, (2, 1, 1, 0)) = Z((0, 0, 0, 0), {makevehicle, makecar, makeboat}, ω) = ω I((2,1,1,0)) D((0, 0, 0, 0), {makevehicle, makecar, makeboat}, makecar) 2 A\{makeCar}... Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 29/35

47 None-plans: the full tree unfolding Synthesis of None-Plans Applying None-Plans to Find Plans Experimental Results acts: makevehicle, makecar, makeboat, makeamphibian trgt: (0, 0, 0, 1) acts: makevehicle, makecar, makeboat, makeamphibian trgt: (0, 0, 0, 1) makeamphibian acts: makevehicle, makecar, makeboat trgt: (2, 1, 1, 0) acts: makevehicle, makecar, makeboat trgt: (1, 0, 0, 0) acts: makevehicle, makecar, makeboat trgt: (0, 1, 0, 0) acts: makevehicle, makecar, makeboat trgt: (0, 0, 1, 0) makevehicle makecar makeboat makecar makeboat acts: makecar, makeboat trgt: (0, 0, 0, 0) acts: makevehicle, makeboat trgt: (1, 0, 0, 0) acts: makevehicle, makecar trgt: (1, 0, 0, 0) acts: makevehicle, makeboat trgt: (1, 0, 0, 0) acts: makevehicle, makecar trgt: (1, 0, 0, 0) acts: makevehicle, makeboat trgt: (1, 0, 0, 0) acts: makevehicle, makecar trgt: (1, 0, 0, 0) makevehicle makeboat makevehicle makecar acts: makeboat trgt: (0, 0, 0, 0) acts: makevehicle trgt: (1, 0, 0, 0) acts: makecar trgt: (0, 0, 0, 0) acts: makevehicle trgt: (1, 0, 0, 0) acts: makevehicle trgt: (1, 0, 0, 0) makevehicle acts: trgt: (0, 0, 0, 0) One can stop unfolding at depth k to underapproximate the none-plan space. Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 30/35

48 Synthesis of None-Plans Applying None-Plans to Find Plans Experimental Results Back to the original domain The SMT-formulae: AP encoding of the original domain plan space (courtesy of PlanICS), CL blocking sets following from Lemma B, N OP k encoding of the none-plan space unfolding up to k N {ω} A new encoding in the original domain plan space: ÃP k = AP CL N OP k A longer formula: easier or more difficult for an SMT-solver? Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 31/35

49 Synthesis of None-Plans Applying None-Plans to Find Plans Experimental Results Experimental results Setup: random ontologies produced by Ontology Generator two experiments/ontology: First single plan synthesis Total all plan synthesis Results for reduction: First usually substantial speedup at some depth Total always substantial speedup at some depth Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 32/35

50 Experimental results, ct d Synthesis of None-Plans Applying None-Plans to Find Plans Experimental Results NoRedTime BestRedTime NoRedTime 100% 100 % 50 % 0 % timeout of Total First Total benchmark id NoRedTime time without reduction BestRedTime best time with reduction Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 33/35

51 Conclusions Introduction Synthesis of None-Plans Applying None-Plans to Find Plans Experimental Results A new web composition system PlanICS - A new method for improving efficiency of algorithms solving hard problems, A new reduction method for planning, Application of the results in the tool PlanICS: quite impressive improvement in some cases. Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 34/35

52 Synthesis of None-Plans Applying None-Plans to Find Plans Experimental Results Thank you! Wojciech Penczek & the PlanICS team Generating None-Plans in Order to Find Plans 35/35