as planning - cse.iitd.ernet.insak/courses/foav/planning-as-mc-slides.pdf · planning as model chec...

PlanningasModelChecking

MarcoPistore

DepartmentofInformaticsandTlc.UniversityofTrento-Italy

e-mail:[email protected]

1

The“Classical”PlanningProblem

•Domain=States(blockpositions)+Actions(moves)

•InitialState(“RedonTable”,“BlueonTable”,“GreenonBlue”)

•GoalState(“BlueonGreen”,“GreenonRed”,“RedonTable”)

•Plan(“MoveGreenonRed”,then“MoveBlueonGreen”)

PlanningProblem:Givenadomain(statesandactions),aninitialandgoalstate,theplanningproblemistheproblemtofindaplanofactionsthatleadsfromtheinitialstatetothegoal

2

The“Classical”PlanningProblem(cont.)

Abasicassumption...

3


Abasicassumption...nouncertainty...

4


Abasicassumption...nouncertainty...

5

PlanningunderUncertainty

Whathappensif...

6


Whathappensif...

The“Classical”PlanningAnswer:Planforthenominalcase!

7


Whathappensif...


BUT...

8


Whathappensif...


But:

•thissolutionisnotalwaysviable(planningunderuncertainty)

9


Whathappensif...


But:

•thissolutionisnotalwaysviable(planningunderuncertainty)

•thereisamuchbetterapproach(planningasmodelchecking)

10

Outline

•Whyplanningunderuncertainty?

•“Classical”planningasmodelchecking

•Planningwithtemporallyextendedgoals

•Conclusions

11

Outline




•Conclusions

12

PlanningunderUncertainty:Non-Determinism

Planforthenomicalcase?

Inmanydomains:

•actionshavenon-nominaloutcomesthatarehighlycritical.

13



Inmanydomains:


•thereareactionswithnonominaloutcome.

14



Inmanydomains:


•thereareactionswithnonominaloutcome.

Difficulties:

•aplanmayresultinmanydifferentexecutions.•theplannermustgenerateplansthathaveconditional

behaviours.•...

15

PlanningunderUncertainty:PartialObservability

Theassumptionofclassicalplanning:observationsnotneeded!

16



Butinseveralrealisticproblems,observationsareneeded.

17



Butinseveralrealisticproblems,observationsareneeded.

Difficulties:

•thestateofthesystemisonlypartiallyvisibleatrun-time.

•differentstatesareindistinguishableforthecontroller,namelyobservationsreturnsetsofstatesratherthansinglestates.

18

PlanningunderUncertainty:Extendedgoals

Theassumptionofclassicalplanning:goalsaresetsofstates!

19



Butinseveralrealisticproblems,goalsareconditionsontheentireexecutionpathofaplan!

20




•Goalsmayinvolvetemporalconditions(e.g.,airconditioner,safetyconditions)

•Goalsmayspecifyrequirementsofdifferentstrenghtthattakeintoaccountnondeterminismandpossiblefailures.

21




•Goalsmayinvolvetemporalconditions(e.g.,airconditioner,safetyconditions)

•Goalsmayspecifyrequirementsofdifferentstrenghtthattakeintoaccountnondeterminismandpossiblefailures.

Difficulties:

•Extendedgoalsaddafurthercomplexitytothealreadycomplicatedproblem.

22

PlanningunderUncertainty:DifferentDimensions

probabilistic

non-determ.

deterministic full obs.

partial obs.

no obs.

reachability goals

extended goals

23

WhyPlanningunderUncertainty?

DomainPlanner

Plan

Controller

SystemActions

Observations

Goal

24

BecauseitisUseful!RealCase(I)

3456789

AAB

SDBSDBSDBSDBSDBSDBSDB

OPERATOR

. . . . . .

SCHEDULER

PROCESS i

PROCESS n

Safety Logic

PROCESS 1

COMMANDS

MANUAL

PERIPHERAL CONTROLS

PERIPHERAL STATUS

DEVICESPHERIPHERAL

Sourcesofuncertainty:

•operator,traindynamics,faults(actionswithuncertaineffects)•localsensors,neighborscontrollers(partialobservability)

25

BecauseitisUseful!ARealCase(II)

Dir. Gas

Interfaccia Utente

ON/OFF

ALARM/RESET

ALTA PRESSIONE

FN

ON/OFF/RESET

REQUEST

OPERATION

TERMICA

Evapor

Condensatore

Dir. Gas

Alta

pre

ssio

ne

Con

trol

lo

Con

trol

lo V

alvo

la

Ven

tole

Tem

pera

tura

Ven

tole

Bassa Pressione

Comandi

Compressore

Termica

Compressore

Controllo led

Pressione tasti

Tem

pera

tura

term

oreg

olaz

ione

Flussostato

Condensatore

Bassa Pressione

Flussostato

Controller

Sourcesofuncertainty:

•operator,temperature,faults(actionswithuncertaineffects)•unaccessiblevariables(partialobservability)

26

Outline




•Conclusions

27

ModelChecking

ModelChecking:atechniquetovalidateaformalmodelofasystemagainstalogicalspecification.

temporal formula

finite−state model

p

q

G(p −> Fq)

ModelChecker

p

yes!

no!

counterexample

q

28

PlanningbyModelChecking

PlanningbyModelChecking:atechniquetosynthesizeaplanfromaformalmodelofadomainandalogicalspecificationofagoal.

planning domain

goal

α

β

no plan!

yes!

Planner

reach r

p

q rα

βχ

plan

α

29

ModelCheckingandPlanning(informal)

•Themodelcheckingproblem:givenamodelMofasystemandapropertyϕ,where...

–ModelMisrepresentedasaFSM.

–Propertyϕisatemporallogicformula.

checkwhetherthepropertyissatisfiedinthemodel:M|=ϕ

•Theplanningproblem:givenamodelMofasystemandagoalϕ,findaplanπthatachievesthegoal:Mπ|=ϕ

•Theplanningvalidationproblemisamodelcheckingproblem

30

PlanningunderUncertaintybyModelChecking

Keyingredients:

2Planningdomainsasnon-deterministicstate-transitionsystems

2Goalsasformulasintemporallogic

2Plangenerationby(BDD-based,symbolic)modelcheckingtechniques

Results:

2Well-founded:formalframework,completeandcorrectalgorithms

2General:planninginnondeterministicdomains,underpartialobservability,andfor(temporally)extendedgoals,...

2Practical:implementationintheModelBasedPlanner(MBP)-automaticplanningforproblemsoflargesize

31

TheFirstResults:PlanningforReachabilityGoals

•Domains:nondeterministicautomata

•Goal:setofdesiredfinalstates

•Plans:memory-lesspoliciesthatmapstatestoactions

•Solutions:

1.Weaksolutions:“optimisticplans”[ECP97]

2.Strongsolutions:“safeplans”[AIPS98]

3.Strongcyclicsolutions:“iterativetrial-and-errorstrategies”[AAAI98]

A.Cimatti,M.Pistore,M.Roveri,P.Traverso.

Weak,Strong,andStrongCyclicPlanningviaSymbolicModelChecking.ArtificialIntelligence,147(1–2),2003

32

AnExample

DoorUncontrollable

Sensorsare not perfect

33

AnExample

34

Reachabilitygoals

Strongsolutions:Plansthatareguaranteedtoreachthegoal•allexecutiontracesreachthegoal

35

Reachabilitygoals

Weaksolutions:Plansthatmayachievethegoal•atleastoneexecutiontracereachesthegoal

36

Reachabilitygoals

StrongCyclicsolutions:trial-and-errorstrategies

•goalisreachablefromallthestatesofexecutiontraces•solutionsthatareguaranteedtoreachthegoalunderthe

fairnessassumptionof“noinfinitebadluck”

37

Implementation:TheMBPplanner

•MBP:AModelBasedPlanner(http://sra.itc.it/tools/mbp/)

•MBPbuiltontopofastate-of-the-artsymbolicBDD-basedmodelchecker,NUSMV(http://sra.itc.it/tools/nusmv/)

•MBPhastheplanningalgorithmsforweak,strong,andstrongcyclic(localandglobal)planning

•MBPhasalgorithmsforconformantplanning,forplanningunderpartialobservability,andforplanningfortemporallyextendedgoals

38

BDD-basedSymbolicModelChecking:Intuitions

SymbolicModelChecking[McMillan’93]basedonBDDs[Bryant’86]:

2Exploresetsofstatesrepresentedsymbolicallyasbooleanformulas

2BooleanformulasasOrderedBinaryDecisionDiagrams(BDDs)

2OBDDsrepresentstheassignmentssatisfying(andfalsifying)abooleanformula

2Operationsoversetsofstates(e.g.union,intersection)asbooleanoperations(e.g.conjunction,disjunction)implementedastransformationsoverBDDs

01

Loaded

0

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11

Locked1

10

0

Loaded

01

01

01

Loaded

0Locked

1

0 1

Loaded and not Locked Loaded or Locked Not Locked Loaded

39

PlannigasSymbolicModelChecking:Intuitions

Locked1

10

0

01

Loaded

0Locked

1

0 1

01

Loaded

0Locked

1

1 0

lockunload

unlocklock

unlock34 1

5

loadadjust

2

40

MoreResultsonPlanningforReachabilityGoals

•StrongSolutionswithPartialObservability:uncertaintyinobservations[Bertoli&Cimatti&Roveri&TraversoIJCAI01]

•PlanningforTemporallyExtendedGoals[Pistore&TraversoIJCAI01-AAAI02]

•Optimistic,Pessimistic&StrongCyclicplanninginUMOP[Jensen&VelosoJAIR00]

•Adversarialweak,strong,andstrongcyclicsolutions:environmentevents[Jensen,Veloso,BowlingECP01]

•SetBranchBDDbasedsearchenvironmentevents[Jensen&VelosoAIPS03]

41

Outline




•Conclusions

42

MotivationsforExtendedGoals

Themainmotivationsforintroducingextendedgoalsare:

•safeplanning:

–safetyconditions(“avoiddangerousstates”)complementthemaingoal.

•planningforreactivesystems:

–infiniteplanthatreactstoeventsintheenvironment(maildelivery,elevatorsystem,...).

•non-determinism:

–needtoexpress(reachability/maintainability)goalsofdifferentstrength(preferences).

43

Anexample

storelab

dep

Goal“reachdepandavoidlab”:

44

Anexample

storelab

dep


•“Doreachdepanddoavoidlab”isunsatisfiable

45

Anexample

storelab

dep


•“Doreachdepanddoavoidlab”isunsatisfiable•“Doreachdepandtrytoavoidlab”issatisfiablebyplan→

46

Anexample

storelab

dep


•“Doreachdepanddoavoidlab”isunsatisfiable•“Doreachdepandtrytoavoidlab”issatisfiablebyplan→

•“Trytoreachdepanddoavoidlab”issatisfiablebyplan→

47

Planningforextendedgoals

Objectives:

•Planninginnon-deterministicdomainsforextendedgoals

•Dealinginpracticewithnon-determinismandcomplexgoalsindomainsoflargesize

Problems:

•Howcanweexpressextendedgoals?

•Whichkindofplansmustbegenerated?

•Planningalgorithm?

•Howcantheplanningalgorithmdealinpracticewithdomainsoflargesize?

48

The“PlanningbyModelChecking”approach

2ExtendedgoalsasformulasintheCTLtemporallogic:temporalconditionson“allpossiblestates”andon“somestates”resultingfromactionexecutions.

2Plansencodingconditional,iterative,andhistorydependentbehaviours,strictlymoreexpressivethanmemory-lesspolicies

2PlanningalgorithmsbasedonBDD-basedSymbolicModelCheckingtechniques,designedtodealwithlargestatespaces

2ImplementationintheModelBasedPlanner(MBP),aplannerbasedonthestate-of-theartsymbolicmodelcheckerNuSMV

2Experimentalresultsshowthattheplanningalgorithmworksinpractice

49

ExtendedGoalsareCTLformulas

CTL:g::=b|g∧g|g∨g|AFg|EFg|AGg|EGg|

A(gUg)|E(gUg)|A(gWg)|E(gWg)

Intuition:CTLcombines

•temporaloperators:F(eventually),G(always),U(until)...

FGU

•pathquantifiers:A(forallevolutions),E(forsomeevolution)

AE

50

ReachabilityGoalsinCTL

GivenaplaningdomainΣ(astatetransitionsystem),andagoalφ(aCTLformula),findaplanπsuchthatΣπ|=φ

1.WeakSolutions:φisEFp-plansthatmayreachthegoal

2.StrongSolutions:φisAFp-plansguaranteedtoreachthegoal

3.StrongCyclicsolutions:φisA(EFpWp)-iterativetrial-and-errorstrategieswhoseexecutionsalwayshaveapossibilityofterminatingand,whentheydo,theyareguaranteedtoreachthegoal.

51

MaintainabilityGoalsinCTL

GivenaplaningdomainΣ(astatetransitionsystem),andagoalφ(aCTLformula),findaplanπsuchthatΣπ|=φ

1.WeakMaintain:φisEGp-plansthatmaymaintainthegoal

2.StrongMaintain:φisAGp-plansguaranteedtomaintainthegoal

3.StrongCyclicMaintain:φisAGEFp-“maintainthepossibilityofreachingp”

52

ExamplesofCTLgoals

DoreachdepanddoavoidlabAFdep∧AG¬lab

DoreachdepandtrytoavoidlabAFdep∧EG¬lab

TrytoreachdepanddoavoidlabEFdep∧AG¬lab

53

Plansforextendedgoals:anexample

lab store

dep

•Thelabisadangerousroom—itmayharmtherobot

•Thegoalis“Continuously,trytoreachdepanddoreachstore”

•CTLgoal:AG(EFdep∧AFstore)

54


store

dep

lab

Goal“Continuously,tryreachdepanddoreachstore”

•Satisfying“tryreachdep”(EFdep),...

55


storelab

dep


•Satisfying“doreachstore”(AFstore),......

56


store

dep

labstorelab

dep

?57


lab

dep

store


•Satisfying“tryreachdep”...

•Satisfying“doreachstore”...

58


Context 1Context 2

ExecutionContextsarenecessaryforthedifferentintentionsoftheexecutor:

•Context1:“tryreachdep”

•Context2:“doreachstore”

59

Plans

Aplanisdefinedintermsofanactionfunctionact:S×C⇀A,andacontextfunctionsense:S×C×S⇀C

statecontextactionnextstatenextcontext

swcontext1go-rightswcontext2

swcontext1go-rightdepcontext1/2

swcontext2go-upstorecontext1

...............

Context 1Context 2

store

storestore lablab

depdep sw

ne

sw

ne

60

Plans

APlanforadomainDisatuple〈C,c0,act,sense〉,where:

•Cisasetofexecutioncontexts,•c0istheinitialexecutioncontext,•act:S×C⇀Aistheactingfunction,•sense:S×C×S⇀Cisthesensingfunction.

Theidea:

•act(s,c)returnstheactiontobeexecutedbytheplan,•sense(s,c,s

′)associatestoeachreachedstates

′thenew

executioncontexts.

61

PlanExecution

•AtransitionofplanπinDisatuple(s,c)a

→(s′,c

′)suchthat:

–sa

→s′,

–a=act(s,c),and

–c′=sense(s,c,s

′).

•Arunofplanπfromstates0isaninfinitesequence(s0,c0)

a0

→(s1,c1)a1

→(s2,c2)a2

→(s3,c3)···

•TheexecutionstructureΣpofplanπhas:

–states(s,c)

–transitions(s,c)→(s′,c

′)

•Planthatsatisfiesagoal:Planπsatisfiesgoalgfrominitialstates0,writtenπ,s0|=g,if(s0,c0)|=ΣπgaccordingtothestandardsemanticsofCTL.

⇒planvalidationasmodelchecking:Σπ|=g

62

PlanningAlgorithm

functionsymbolic-plan(g):Plan

aut:=build-aut(g)

assoc:=build-assoc(aut)

plan:=extract-plan(aut,assoc)

returnplan

1.build-autconstructsanautomatonthatcontrolsthesymbolicsearch(statesarecontexts)

2.build-assocassociatesasetofstatesintheplanningdomaintoeachstateinthecontrolautomaton.

3.extract-planconstructsaplanfromthestatesassociatedtothecontexts.

63

Phase1:buildthecontrolautomaton

Whenwebuildthecontrolautomatonforthegivengoal:

•thecontrolstatesarethecontextsoftheplanthatisbeingbuilt

•thetransitionsrepresentthepossibleevolutionsofthecontextswhenactionsareexecuted.

64


TwocontextsareneededforgoalAG(EFdep∧AFstore):

•onecorrespondingEFdep

•onecorrespondingAFstore

65


store

store

InordertosatisfycontextAFstore,findanactionsuchthat:

•ifstoreholds,then:

–contextEFdepissatisfiableforALLtheoutcomes

•ifstoredoesnotholdthen:

–contextAFstoreissatisfiableforALLtheoutcomes

66


dep

SOMEALL−OTHER

dep

InordertosatisfycontextEFdep,findanactionsuchthat:

•ifdepholds,then:

–contextAFstoreissatisfiableforALLtheoutcomes

•ifdepdoesnotholdthen:

–contextEFdepissatisfiableforSOMEoftheoutcomes–contextAFstoreissatisfiableforALLtheotheroutcomes

67


dep

store

SOMEALL−OTHER

store dep

68

Phase2:search

Inthesearchphasethealgorithmassociatestoeachcontextthesetofstatesthatadmitaplanforthecontext.

•Initially,allthedomainstatesareassociatedtoeachcontext

•Theassociationisiterativelyrefined:

–Acontextischosen

–Thecorrespondingstatesarecomputed,basedonthecurrentassociation

–Theassociationforthecontextisupdated

•Thesearchterminateswhenafixpointisreached

69

Phase2:search

~dep

dep

~store

store

SOMEALL−OTHER

70

Phase2:search

~dep

dep

SOMEALL−OTHER

71

Phase2:search

~store

store

72

Phase2:search

~dep

dep

SOMEALL−OTHER

73

Step3:planextraction

•Findsuitableactionsforthestatesassociatedtothecontexts.

•Alltheinformationnecessarytoextracttheplanhasbeenalreadycomputedinthesearchphase.

•Reachabilityanalysisallowsforsimplerplans.

74

Step3:planextraction

~dep

dep

~store

store

SOMEALL−OTHER

go−south go−south

go−eastgo−northgo−north

go−west

75

Propertiesofthealgorithm

•Thealgorithmalwaysterminates.

•Thealgorithmiscorrectandcomplete:

–wheneverplansexist,thealgorithmfindsone;

–wheneverthereisnoplan,thealgorithmreturnsfail.

•Thecriticalstepforperformanceis“symbolicsearch”.

•ThealgorithmforextendedgoalsisimplementedinMBP

76

PlanningforCTLgoals:ExperimentalEvaluation

Aims:

•Testthescalabilityoftheapproach(domainsize,nondeterminism,goalcomplexity)

•ComparisonwithSimplan[Kabanzaet.al.](LTLgoals,explicitstate,handcodedstrategies)

•Comparisonwithspecialpurposestrong(cyclic)MBP

Results:

•Deterministiccase:SimPlanhandcodedstrategieswin•Nondeterministiccase:

–MBPperformancesdonotdegradewithnondeterminism–MBPoutperformsSimPlanevenwithhandcodedstrategies–Planningforextendedgoalscomparablewithspecialpurpose

strong(cyclic)algorithms

77

PlanningforCTLgoals:conclusions

•Goalswithtemporalconditionsonthewholeexecutionpath

•Goalsthattakeintoaccountnondeterminism(“forall”,“forsome”actionoutcomes)

•ImplementationintheMBPplanner(http://sra.itc.it/tools/mbp/)

•Experimentalevaluationshowsthattheapproachispractical

78

PlanningforCTLgoals:Conclusions

•Goalswithtemporalconditionsonthewholeexecutionpath

•Goalsthattakeintoaccountnondeterminism(“forall”,“forsome”actionoutcomes)

•ImplementationintheMBPplanner(http://sra.itc.it/tools/mbp/)

•Experimentalevaluationshowsthattheapproachispractical

...BUT...

79

LimitsofCTLgoals

RD

U A

S

Alarm!

Alarm!

SwitchToD

TrytoreachtheDirectposition,and...ifyouFail,DoreachtheAlarmposition

80

LimitsofCTLgoals

RD

U A

S

Alarm!

Alarm!

SwitchToD


Problem(1)...EFD–doesnotcaptureintentionality!!

81

LimitsofCTLgoals

RD

U A

S

Alarm!

Alarm!

SwitchToD


Problem(2)...CTLformulasdonotcapturepreferencesandfailurehandling!!

82

EaGLe:anExtendedGoalLanguage

EaGLeisanewExtendedGoalLanguagethat:

•canexpresstheintentionalaspectsnotcapturedinCTLandLTL(e.g.,“doeverythingpossibletoreachp”);

•candealwithfailureofgoalsandwithfailurerecovery(e.g.,“trytoachieveagoaland,ifyoufail,tryadifferentgoal”).

83

SyntaxofEaGLe

•reachability(basic)goals:DoReachp,TryReachp

•maintenance(basic)goals:DoMaintainp,TryMaintainp

•conjunction:gAndg′

•failure:gFailg′

•controloperators:gTheng′,Repeatg

84

DoReach

Goal“DoReachp”:

•requiresaplanthatguaranteestoreachpdespitenondeterminism

•failsifnosuchplanexists.

p

p

p

p

p

p

p

p

p

pp

success

failure

85

TryReach

Goal“TryReachp”:

•requiresaplanthatdoesitsbesttoreachp;

•failswhenthereisnopossibilitytoreachp.

p

pp

p

p

p

pp

p

p

p

86

Fail

Goal“g1Failg2”:

•dealswithfailure/recoveryandwithpreferencesamonggoals.

•Theplantriestosatisfygoalg1;wheneverafailureoccurs,goalg2isconsideredinstead.

•Example:DoReachpFailDoReachqvsTryReachpFailDoReachq

p

pq

q

q

q q qqq

p

p

87

TheRailwaysSwitchExample

RD

U A

S

Alarm!

Alarm!

SwitchToD

TryReachDFailDoReachA

R DUA

88

And/Then/Repeat

Goal“g1Andg2”:

•requirestosatisfyg1andg2inparallel.

Goal“g1Theng2”:

•requirestosatisfyg1andthentosatisfyg2.

Goal“Repeatg”:

•requirestosatisfyginacyclicway.

89

Asimpleexample

lab

store dep

office

Sensors arenot perfect

Uncontrollabledoor

Continuously,pickanobjectfromthestoreandtrytodeliverittotheoffice;ifyoufail,deliverittothedep.Donotenterthelab.

90

Apossibleplan

lab

store dep

office


Uncontrollabledoor

init:/*inthestore*/

pickobject

/*trytoreachtheoffice*/

goeast;gosouth

if(room=office)then

dropobject

/*gobacktothestore*/

gowest;gonorth;gotoinit

else

/*reachthedep*/

gowest;gowest;dropobject

/*gobacktothestore*/

goeast;gotoinit

91

TheEaGleGoal

lab

store dep

office


Uncontrollabledoor

Repeat(DoReach(store∧objpicked)

And(TryReach(office∧objdelivered)

FailDoReach(dep∧objdelivered)))

AndDoMaintain¬lab

92

TheEaGleControlAutomaton

dep

office

store lab

lab

lab

lab

dep

office

store

DoMaintainDoReach

TryReach

DoReach

93

PlanningwithEaGle

•Oncethecontrolautomatonhasbeenbuilt,thesamealgorithmusedforCTLgoalscanbeapplied.

•Thealgorithmisterminating,correct,andcomplete.

•ThealgorithmhasbeenimplementedinMBP.

•TheperformanceissimilartotheoneforCTLgoals...

•...butthequalityofthegeneratedplansismuchhigher.

94

Outline




•Conclusions

95

PlanningasModelChecking

goal

planning domain

q

r

α

βPMC

rαq

βα

χp

plan

96

Relatedwork

•TheMDP-planningapproach(e.g.,GPT[Bonet&Geffner])(includingMDP-planningbasedonADDs[Hoeyetal.])

•TheSAT-planningapproach([Rintanen],[Giunchiglia])

•Interleavingplanningandexecution([Koenig&Simmons])

•UMOP[Jensen&Veloso],basedonSymbolicModelChecking

•Plannersbasedonothermodelcheckingtechniques:

–Simplan[Kabanza]–ModelCheckingwithtimedautomata[Goldmanetal.]

•Automatatheoreticapproachtosynthesis

97

DirectionsforFutureResearch

null

reachability

GOALS

full partial

OBSERVABILITY

maintainability

.....................

MDP + MBP

TIME & RESOURCESEXECUTION

CONTROLLER SYNTHESIS

98

ThankstomanypeopleatTrento,butespeciallyto...

•PiergiorgioBertoli

•AlessandroCimatti

•MarcoRoveri

•PaoloTraverso

99

as planning - cse.iitd.ernet.insak/courses/foav/planning-as-mc-slides.pdf · planning as model chec...

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