IEEEStateofMindProblemStatement

FiniteStateMachines(FSMs)canbeusedtomodelsystemswhoseoutputdependsonthecurrentstateanditsinputs.Thestatescanrepresentmanydifferentsystemsliketheon/offstateoftrafficlightsatanintersection,thevalvestateofthrustersonaspacecraft,theclick/keycombinationsenteredbyauserforakeyboardshortcut,orthesend/receivestepsinacommunicationprotocol.

AnFSMisdefinedbyasetofstates,inputs,andoutputs.Thestatesrepresentaknownconfigurationofthesystemataspecifictime.Transitioningtoanewstatedependsonthecurrentstateandtheinputsprovided.Thiswillinturnalsoproduceanassociatedoutputforthesystem.

OneoftheusesofFSMsistodesignandanalyzelogiccircuitswithmemorieslikeflip-flops.Yourtaskistowriteaprogramtovisualizethetimingdiagramrelatingtheinputsandoutputswhileprintingthecurrentstatenumbertohelpanalyzethecircuit.

Forthepurposeoftheprogram,youcanassumethatthereareNstateswithMinputs.StatesarelabeledwithnumberedsubscriptsintherangeS toS .Theinputsareeachlabeledwithasingleuppercasecharacterintherange'A'to'J',inclusive.Youmayassumethatnoletterorstatenumberisskipped.EachstatehasPuniquelydefinedtransitionstootherstates(thetransitionsareuniqueinthesensethatnosetofinputswilltriggermorethan1transition).Atransitionisonlytakenwhentheinputconditionsaresatisfied.TransitionsareevaluatedatthebeginningofeachoftheTdiscretetimesteps.

InputFormat

InputbeginswithalinecontainingNandM,where1≤N<100and1<M<10.

ThenthereareNlines,eachdescribingtheoutputofthesystemandthetransitionsfromthisstate.ThefirstlinecontainsadescriptionofstateS ,thesecondlinedescribesS ,etc.Theselinesallhavethefollowingformat:

StateOutputPVariableExpression /Dest VariableExpression /Dest ...VariableExpression /Dest

where

StateOutputiseithera0or1,representingthevaluethatisoutputwhenthesystemisinthisstate

Pisthenumberoftransitionsfromthisstate

VariableExpression isacomma-delimitedlistofVariable=Valuetokens.Foratransitionitobeactivated,alloftheinputvariablesgivenintheVariableExpression musthavethevalueslistedinthisexpression

Dest ,1<=i<=P,isadestinationstatenumber,intherange[0..N),fortransitioni

Followingthedescriptionofthestates,isalinecontainingtwointegers,TandI,whereTgivesthenumberoftimesteps(1<=T<1000),andIgivesthenumberoftheinitialstate(0<=I<N).

TheinputendswithM*TlinesthatprovidetheinputsforallMvariablesineachoftheTtimesteps.ThefirstMvaluesprovideinputsfortheMvariablesduringthefirsttimestep,thesecondMvaluesprovideinputsfortheMvariablesduringthesecondtimestep,andsoon.

Thetransitionsshouldbeinterpretedasfollows.AssumethatweareinastateS .Assumefurtherthattherearefourinputs,andthecurrentinputprovidedforthecurrenttimestepis(1,0,1,0).Wemaptheseinputsto

0 N-1

0 1

1 1 2 2 P P

ii

i

j

thevariables,startingwithletter'A',soA=1,B=0,C=1,andD=0.WewouldthenlookfortransitionsdefinedonthelinecorrespondingtostateS .Sincetransitionsmustbeunique,onlyoneofthefollowingVariableExpressionscouldappearinthelistofexpressions: A=1 , B=0 , C=1 , D=0 , A=1,B=0 , A=1,C=1 ,A=1,D=0 , A=1,B=0,C=1 ,etc.Ifsuchatransitionisthei transitionspecified,thenewstatewouldbeDest .Iftherearenomatches,thesystemremainsinthecurrentstate.

OutputFormat

Theoutputconsistsofawaveform.Thewaveformisrepresentedbyunderscores,‘_’,forthenumber0,andasterisks,‘*’,forthenumber1.

Amaximumof16ticksareprintedtogether,whereeachtimetickis3characterswide.Thelinenumbersarelabeledwiththesignalnamesasshownintheexample.

Asshownintheexamplebelow,onthefirstlineofthegroupingisthetext Tick#X where X isreplacedbythenumberofthefirsttickinthegrouping.

Nextcomewaveformsforeachofthevariables,inalphabeticalorder,oneperline.Ontheselinesthevariablenameisoutput,followedbyfivespaces,andthenthewaveform.

Thenthewaveformofthesystemoutputisdisplayed.Thislinebeginswiththeword OUT ,followedby3spaces,andthenthewaveform.

Finally,onthelastlinethenumericvalueofthesystemoutputisdisplayed.ThislinebeginswiththewordSTATE .Thenumericvaluesofsystemoutputshouldalwaysbealignedwiththethirdcolumnoftherespectivetick.

Ifnotalltickshavebeendisplayed,thenablanklineshouldbeoutput,followedbythenextgroupofticksinthesameformat.

SampleInput

2312A=1,B=1,C=1/1A=1,B=0/001A=0/0200000001010011100101110111000001010011100101110111000001010011

SampleOutput

Tick#1A____________************____________************B______******______******______******______******C___***___***___***___***___***___***___***___***

j

th i

OUT*********************___*********************___STATE0000000100000001

Tick#17A____________B______******C___***___***OUT************STATE0000

Explanation

ThesampleinputexecutesaparitycheckFSM.ThereareN=2stateswithM=3inputs.Sincethereare3inputs,theseinputsarelabeled A , B ,and C .

State0,S ,outputsthevalue 1 (logichigh).Therearetwotransitionsoriginatingfromthisstate.ThefirsttransitiongoestoS wheninput A=1, B=1,and C=1.ThesecondtransitiongoestoS wheninput A=1and B=0(that’saself-looptothesamestate). C cantakeanyvalueinthesecondtransition.

S outputsthevalue 0 (logiclow).Thereisonlyonetransitionoriginatingfromthisstatedefinedintheinput.ThistransitiongoestoS when A=0.

Notethatalthoughnotdefined,thereareimplicittransitionstosatisfytheothercasesthatarenotexplicitlydescribedintheinput.Theimplicittransitionsareallself-loopstothesamestate.

Priortotickt=1,weareintheinitialstate,S .Theinputissetto A=0, B=0,and C=0,thereforewetaketheimplicitself-looptransitionandstayinS andoutputthevalueassociatedwiththestate,i.e. 1 .

Whenwestarttickst=2throught=7,wearestillinS .Ineachofthesecases,wetaketheimplicitlooptothesamestateandnothingchangesintheoutput.

Intickt=8,theinputs, A=1, B=1,and C=1,triggerthetransitiontostateS .Thischangestheoutputofourlogiccircuittoa 0 .

Intickt=9,theinput, A=0,triggerthetransitiontostateS .Thischangestheoutputofourlogiccircuittoa 1 .

Thesamepatternofinputsisrepeatedafewmoretimes.Tick17beginsonanewlinebecausewelimittheoutputto16ticksperline.

01 0

10

00

0

1

0