Models of Computation

406 Pages·2017·1.797 MB·English

by  Roberto Bruni, Ugo Montanari

Texts in Theoretical Computer Science.
An EATCS Series
Roberto Bruni
Ugo Montanari
Models of
Computation
Texts in Theoretical Computer Science.
An EATCS Series
Series editors
Monika Henzinger, Faculty of Science, Universität Wien, Vienna, Austria
Juraj Hromkovič, Department of Computer Science, ETH Zentrum, Zürich,
Switzerland
Mogens Nielsen, Department of Computer Science, Aarhus Universitet, Aarhus,
Denmark
Grzegorz Rozenberg, Leiden Center of Advanced Computer Science, Leiden,
The Netherlands
Arto Salomaa, Turku Centre of Computer Science, Turku, Finland
More information about this series at http://www.springer.com/series/3214
Roberto Bruni Ugo Montanari
(cid:129)
Models of Computation
123
RobertoBruni UgoMontanari
Dipartimento di Informatica Dipartimento di Informatica
Universitàdi Pisa Universitàdi Pisa
Pisa Pisa
Italy Italy
ISSN 1862-4499
Textsin TheoreticalComputer Science. AnEATCSSeries
ISBN978-3-319-42898-7 ISBN978-3-319-42900-7 (eBook)
DOI 10.1007/978-3-319-42900-7
LibraryofCongressControlNumber:2017937525
©SpringerInternationalPublishingSwitzerland2017
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Mathematicalreasoningmayberegarded
ratherschematicallyastheexerciseofa
combinationoftwofacilities,whichwemay
callintuitionandingenuity.
AlanTuring1
1Thepurposeofordinallogics(fromSystemsofLogicBasedonOrdinals),Proceedingsofthe
LondonMathematicalSociety,series2,vol.45,no.1,161–228,1939.
Foreword
Basedonmorethanfifteenyearsofteaching,thisbookprovidesanexceptionally
usefuladditiontotheintroductoryliteratureonModelsofComputation.Itcovers
awealthofmaterialonimperative,functional,concurrentandprobabilisticcompu-
tation,theirmodelsandreasoningtechniques.Itdoessoinacarefullypedagogic
way,honedovertheyearswiththehelpofthestudentsatPisa.Supplementedwith
educative examples, explanations and problems (accompanied by solutions) and
includingacoverageofthetechniquesofprobabilisticandquantitativecomputation,
itprovidesthestudentwitharichbackgroundandsolidfoundationforfuturestudy
andresearch.
Ifqualityofteachingistobejudgedfromthequalityofstudents,thenteaching
inPisascoresveryhighlyindeed.Overseveralgenerationsbrilliantstudentsfrom
PisahavemadetheirmarkinComputerScienceinEuropeandtheUS.AllthoseI
knowhavecomeundertheinfluenceofUgoMontanariandmorerecentlythatofhis
colleagueRobertoBruni.Thebroaderaccessthisbookgivestotheirexpertiseand
teachingisverywelcome.
Onapersonalnoteitisapleasuretoacknowledgethefriendlycollaborationthat
UgoMontanarihashelpedfosterovermanyyears,fromthefirsttimeIvisitedPisa
forthePisaSummerSchoolin1978—myPhDthesiswasbornonthegrassyareaby
theCathedralandLeaningTower—throughtoUgoleadinganEUprojectinwhich
Iparticipated.OnthepossiblestartoftheUK’swithdrawalfromtheEUIlookback
withnostalgiatothosedaysofopennessandcooperation,nowfallenvictimtothe
selfishinterferenceofpoliticians.Thisbookinitsunifyingtreatmentofacriss-cross
ofworkcarriedoutinEuropeandtheUSisatestimonytothepowerofcollaboration
inresearchandeducation.
Cambridge GlynnWinskel
July2016
vii
Preface
Theoriginsofthisbookhavetheirrootsinmorethan15yearsofteachingacourse
onformalsemanticstoComputerSciencegraduatestudentsinPisa,originallycalled
Fondamentidell’Informatica:Semantica(FoundationsofComputerScience:Seman-
tics)andcoveringmodelsforimperative,functionalandconcurrentprogramming.
ItlaterevolvedintoTecnichediSpecificaeDimostrazione(TechniquesforSpecifi-
cationsandProofs)andfinallyintothecurrentlyrunningModelsofComputation,
whereadditionalmaterialonprobabilisticmodelsisincluded.
Theobjectiveofthisbook,aswellasoftheabovecourses,istopresentdifferent
modelsofcomputationandtheirbasicprogrammingparadigms,togetherwiththeir
mathematicaldescriptions,bothconcreteandabstract.Eachmodelisaccompaniedby
somerelevantformaltechniquesforreasoningonitandforprovingsomeproperties.
Tothisaim,wefollowarigorousapproachtothedefinitionofthesyntax,the
typing discipline and the semantics of the paradigms we present, i.e., the way in
whichwell-formedprogramsarewritten,ill-typedprogramsarediscardedandthe
meaningofwell-typedprogramsisunambiguouslydefined,respectively.Indoing
so,wefocusonbasicprooftechniquesanddonotaddressmoreadvancedtopicsin
detail,forwhichclassicalreferencestotheliteraturearegiveninstead.
Aftertheintroductorymaterial(PartI),wherewefixsomenotationandpresent
somebasicconceptssuchastermsignatures,proofsystemswithaxiomsandinference
rules,Hornclauses,unificationandgoal-drivenderivations,thebookisdividedinto
four main parts (Parts II-V), according to the different styles of the models we
consider:
IMP: imperativemodels,whereweapplyvariousincarnationsofwell-founded
inductionandintroducel-notationandconceptslikestructuralrecursion,
program equivalence, compositionality, completeness and correctness,
andalsocompletepartialorders,continuousfunctions,andfixpointthe-
ory;
HOFL: higher-orderfunctionalmodels,wherewestudytheroleoftypesystems,
themainconceptsfromdomaintheoryandthedistinctionbetweenlazy
andeagerevaluation;
ix
x Preface
CCS,p: concurrent,nondeterministicandinteractivemodels,where,startingfrom
operationalsemanticsbasedonlabelledtransitionsystems,weintroduce
thenotionsofbisimulationequivalencesandobservationalcongruences,
andoverviewsomeapproachestonamemobility,andtemporalandmodal
logicsystemspecifications;
PEPA: probabilistic/stochasticmodels,whereweexploitthetheoryofMarkov
chains and of probabilistic reactive and generative systems to address
quantitativeanalysisof,possiblyconcurrent,systems.
Eachoftheabovemodelscanbestudiedseparatelyfromtheothers,butprevious
partsintroduceabodyofnotionsandtechniquesthatarealsoappliedandextended
inlaterparts.
PartsIandIIcovertheessential,classictopicsofacourseonformalsemantics.
PartIIIintroducessomebasicmaterialonprocessalgebraicmodelsandtemporal
and modal logic for the specification and verification of concurrent and mobile
systems.CCSispresentedingooddetail,whilethetheoryoftemporalandmodal
logic,aswellasthep-calculus,arejustoverviewed.ThematerialinPartIIIcanbe
usedinconjunctionwithothertextbooks,e.g.,onmodelcheckingorthep-calculus,
in the context of a more advanced course on the formal modelling of distributed
systems.
PartIVoutlinesthemodellingofprobabilisticandstochasticsystemsandtheir
quantitativeanalysiswithtoolslikePEPA.Itprovidesthebasisforamoreadvanced
courseonquantitativeanalysisofsequentialandinterleavingsystems.
Thediagramthathighlightsthemaindependenciesisrepresentedbelow:
Imperative Functional
Chapter 3 Chapter 7
induction
and
Chapter 4 structural Chapter 8
recursion
Chapter 5 Chapter 9
Chapter 6 Chapter 10
CPO and
fixpoint
lambda
notation
Concurrent CChhaapptteerr 1111 LTS and Probabilistic CChhaapptteerr 1114
bisimulation
CChhaapptteerr 1122 CChhaapptteerr 1125
HM logic
CChhaapptteerr 1133 CChhaapptteerr 1136
Thediagramcontainsarectangularboxforeachchapter/partandaround-cornered
box for each subject: a line with a filled-circle end joins a subject to the chapter
whereitisintroduced,whilealinewithanarrowendlinksasubjecttoachapteror
partwhereitisused.Inshort:
Preface xi
Inductionandrecursion: variousprinciplesofinductionandtheconceptofstruc-
tural recursion are introduced in Chapter 4 and used
extensivelyinallsubsequentchapters.
CPOandfixpoint: thenotionsofcompletepartialorderandfixpointcompu-
tationarefirstpresentedinChapter5.Theyprovidethe
basisfordefiningthedenotationalsemanticsofIMPand
HOFL.InthecaseofHOFL,ageneraltheoryofproduct
andfunctionaldomainsisalsointroduced(Chapter8).
Thenotionoffixpointisalsousedtodefineaparticular
formofequivalenceforconcurrentandprobabilisticsys-
tems,calledbisimilarity,andtodefinethesemanticsof
modallogicformulas.
Lambdanotation: l-notationisausefulsyntaxformanaginganonymous
functions.ItisintroducedinChapter6andusedexten-
sivelyinPartIII.
LTSandbisimulation: LabelledtransitionsystemsareintroducedinChapter11
todefinetheoperationalsemanticsofCCSintermsofthe
interactionsperformed.Theyarethenextendedtodeal
withnamemobilityinChapter13andwithprobabilities
inPartV.Abisimulationisarelationoverthestatesofan
LTSthatisclosedundertheexecutionoftransitions.The
abovementionedbisimilarityisthecoarsestbisimulation
relation. Various forms of bisimulation are studied in
PartsIVandV.
HM-logic: Hennessy-Milnerlogicisthelogiccounterpartofbisimi-
larity:twostatesarebisimilarifandonlyiftheysatisfy
the same set of HM-logic formulas. In the context of
probabilisticsystems,theapproachisextendedtoLarsen-
SkoulogicinChapter15.
Eachchapterofthebookconcludeswithalistofexercisesthatspanoverthemain
techniquesintroducedinthatchapter.Solutionstoselectedexercisesarecollectedat
theendofthebook.
Pisa, RobertoBruni
February2016 UgoMontanari