concurrent state machinesclasses.engr.oregonstate.edu › eecs › winter2018 › cs447 › lectures...

ConcurrentStateMachines

CS447– WirelessEmbeddedSystems

Outline

• Overview• Side-by-sidesynchronous• Side-by-sideasynchronous• Sharedvariables• Cascadescomposition• Generalcomposition

January26,20181

Overview

• Statemachinesaregreatwaytomodelsystems

• Problem:forinterestingsystems,numberofstatesislarge

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Overview

• Time-honoredpracticeinengineering:complicatedsystemsdescribeascomposition ofsimplerones

Jargon:• Syntax– rulesofmodelnotation• Semantics–meaningofnotation(seethislater)

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Overview

E.g.,useanactormodelforanextendedstatemachine• Twoinputs• Twooutputs• “don’tcare”aboutinternals• Abstraction..

January26,20184

Overview

Twocompositiontechniques:

• Concurrentcomposition(today’slecture)

• Hierarchicalcomposition(nextlecture)

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Overview

Concurrentcomposition• Twoormorestatemachinesthatreactsimultaneously orindependently

• Synchronouscomposition – reactionsaresimultaneous• Asynchronouscomposition – reactionsareindependent

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Overview

Concurrentcomposition

• Beginw/simplestcase:side-by-sidecomposition

• Composedstatemachineseither:• Donotcommunicatedirectly• Communicateviasharedvariables• Communicateviaports(e.g.,serial)

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Outline


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Side-by-SideSynchronousComposition

• Inputsandoutputsaredisjoint• Statemachinesdonotcommunicate• A:inputi1,outputo1• B:inputi2,outputo2

• IfA,Bareextendedstatemachines,thenvariablesdisjointaswell

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• C:compositionoftwoactors• Twoinputs(i1,i2)• Twooutputs(o1,o2)

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Synchronouscomposition:• ReactionofCissimultaneousreactionofAandB

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Whatdoesthismachinedo?

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Cactslikeanoscillator:outputis“bababababa…”

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Remember: A, B are simultaneous


CanmachineCeverreachstate(s1,s4)?Whatabout(s2,s3)?

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SbS synchronousmachinesare:• Modular• Deterministic• Compositional

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Modular – compositionitselfcanbeusedasanatomiccomponent

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Deterministic– IfAandBarebothdeterministic,Cisaswell

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Compositional– propertyheldbycomponentsisalsopropertyofcomposition

• E.g.,determinismisacompositionalproperty

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NOTE:previousexamplecanbedrawnassinglestatemachine

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Outline


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Side-by-SideAsynchronousComposition

Asynchronouscomposition:• Components(A,B)reactindependently

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Semantics#1• ReactionofCisreactionofAor B (justone)• A,Bneverreactsimultaneously (theyareinterleaved)• ChoiceofAvs.Bisnondeterministic

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Semantics#2• ReactionofCisreactionofA,B orboth• Choiceisnondeterministic

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PreviousexampledmodeledasasynchronousSBS..

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red arrows mark nondeterminism


Undersemantics#1• Cin(s1,s3)• Creacts• Cmovesto(s1,s4),emitsb• OR:Cmovesto(s2,s3),emits∅

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Undersemantics#2• Cin(s1,s3)• Creacts• Couldalsomoveto(s2,s4)• Couldalsooutput∅b ORb∅

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Takehomepoint:asynchronouscompositioncanbetreacherous

• Youmustbeclearaboutsemantics• E.g.,AmustalwayscomebeforeB

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Outline


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SharedVariables

• Extendedstatemachineshavelocalvariables• Variablesread/writtenduringtransitions

Whencomposingstatemachines:• Helpfultoallowsharedvariablesamongmachines• Canbeusedtomodelinterruptsandthreads

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SharedVariables

E.g.,twoserversreceivingnetworkrequests

• Sharedvariable“pending”integerthatcountsjobs

• WhenrequestarrivestocompositionmachineC,oneoftwoserverschosennon-deterministically• Assumesasynchronouscompositionundersemantics#1• I.e.,mutualexclusion

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SharedVariables

E.g.,twoserversreceivingnetworkrequests

Whenrequestarrives:• Ifserveridle,proceedstoserverequest• Ifserverbusy:• Coincidentallyfinishservingcurrent,outputdone,proceedtonew

-OR-

• Incrementcountofpending• Continueservingcurrent

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SharedVariables

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SharedVariables

Exampleshowssubtletiesofconcurrentsystems(1)

• Interleavingsemantics(#1):accesstoshared“pending”aremodeledasatomic

• Thiscanbechallengingtodoinpractice

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SharedVariables


• Semantics#1seemsreasonable• Butcouldleadtoidlemachines…

E.g.,whatifmachineAisserving,Bisidle,requestarrives• ButAispickednondeterministically(=>pending++)• Bneverused…

InSemantics#1,thisispossible.

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SharedVariables


• Semantics#2alsoreasonable(“simultaneous”execution)

• Butrequiresupdating“pending”inanatomicmanner

• Thiscanbemorechallengingtoimplement..

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SharedVariables

Whataboutsharedvariablesinsynchronouscomposition?

• WritefromAbeforereadingfromB?• ReadfromBbeforewritingfromA?• Mustmorechallenging!

• Mustuseinterleavedsemantics(i.e.,scheduling)

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Outline


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CascadesComposition(akaSerialComposition)

• Twomachines(A,B)composedinseries:

• OutputofAisinputtoB

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• Consideronlysynchronouscomposition• Asynchronouscompositionwouldrequirebuffering

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• ReactionofCisreactionofAandB• Areactsfirst,thenB• Weassumethisoccursinstantly(inzerotime)• Tworeactions(A,B)aresimultaneousandinstantaneous

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Example(remember,transitionsaresimultaneous!)• WhendoesmachineC output“c”?

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Equivalent machine:


Anotherexample:modifytrafficlightmodeltoincludepedestrianlightaswell.

• Cascadescomposition:turnonREDlight=>turnon”walk”• Causal..

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Outline


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GeneralComposition

• Side-by-sideandcascadescompositionprovidebasicbuildingblocks.• Thesemodelscanbecombined:e.g.,

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GeneralComposition

• A1,A3areside-by-side(defineB)• B,A2arecascadescompositioninoppositeorder(feedback)• Question:whichmachineshouldreactfirst?

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