Mobility in Process Calculi and Natural Computing

223 Pages·2011·2.14 MB·English

by  Bogdan Aman

Natural Computing Series
SeriesEditors: G.Rozenberg
Th.Bäck A.E.Eiben J.N.Kok H.P.Spaink
LeidenCenterforNaturalComputing
AdvisoryBoard: S.Amari G.Brassard K.A.DeJong C.C.A.M.Gielen T.Head
L.Kari L.Landweber T.Martinetz Z.Michalewicz M.C.Mozer E.Oja
G. Pa˘un J. Reif H. Rubin A. Salomaa M. Schoenauer H.-P. Schwefel C. Torras
D.Whitley E.Winfree J.M.Zurada
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Bogdan Aman (cid:2) Gabriel Ciobanu
Mobility in
Process Calculi
and Natural
Computing
Dr.BogdanAman Prof.Dr.GabrielCiobanu
InstituteofComputerScience InstituteofComputerScience
RomanianAcademy RomanianAcademy
Ias¸i,Romania Ias¸i,Romania
and and
AlexandruIoanCuzaUniversity AlexandruIoanCuzaUniversity
Ias¸i,Romania Ias¸i,Romania
[email protected] [email protected]
SeriesEditors
G.Rozenberg(ManagingEditor) A.E.Eiben
[email protected] VrijeUniversiteitAmsterdam
TheNetherlands
Th.Bäck,J.N.Kok,H.P.Spaink
LeidenCenterforNaturalComputing
LeidenUniversity
TheNetherlands
ISSN1619-7127 NaturalComputingSeries
ISBN978-3-642-24866-5 e-ISBN978-3-642-24867-2
DOI10.1007/978-3-642-24867-2
SpringerHeidelbergDordrechtLondonNewYork
LibraryofCongressControlNumber:2011942072
ACMComputingClassification(1998):F.1,F.4,I.2,I.6,J.3
©Springer-VerlagBerlinHeidelberg2011
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Preface
The design of formal calculi in which the fundamental concepts underlying inter-
activesystemscanbedescribedandstudiedhasbeenacentralthemeoftheoretical
computer science over the last two decades. In this book we refer to the formal
descriptionofmobilityincomputersciencebyusingπ-calculus,ambientcalculus,
bioambients,branecalculiandsystemsofmobilemembranes.
In process algebra the moving entities are the links (π-calculus), the ambients
(ambient calculus and bio-ambients) and the branes (brane calculi). In membrane
systemsthemovementisprovidedbyrulesinspiredbyendocytosisandexocytosis.
Cellmovementisadynamicphenomenonthatisessentialtoavarietyofbiological
processes(e.g.,immuneresponse).
InChapter1:MobilityinProcessCalculiwerefertotheformaldescriptionof
mobilityinprocesscalculi[52].Whenexpressingmobility,weshouldmentionwhat
entities move and in what space they move. The π-calculus [121] is a formalism
where links are the moving entities, and they move in a virtual space of linked
processes (the network of web pages is a good example for this approach). This
optionispowerfulenoughtoexpressmovingprocessesbothinaphysicalspaceof
computinglocationsandinavirtualspaceoflinkedprocesses[121].Theπ-calculus
hasasimplesemanticsandatractablealgebraictheory[121];itisawidelyaccepted
model of interacting systems with dynamically evolving communication topology
and (channel) mobility. Its mobility increases the expressive power enabling the
descriptionofmanyhigh-levelconcurrentfeatures.
Timeddistributedπ-calculus(tDπ)[67]isarigorousframeworkfordescribing
distributedsystemswithtimeconstraints.Thetimersonchannelsdefinetimeoutsfor
communications,andtimersonthechanneltypesrestrictthechannels’availability.
Wheneverthetimerofeitherachannelorachanneltypeexpires,thecorresponding
channelisdiscarded,andrespectivelythechanneltypeislost.tDπcombinestempo-
ralconstraintswithtypesandlocationsinordertogivethepossibilityofmodelling
located and timed interactions between distributed processes with time-restricted
resourceaccess.
v
vi Preface
Another formalism able to express mobility is theambient calculus [42]; it de-
scribescomputationcarriedoutonmobiledevices(i.e.networkshavingadynamic
topology), and mobile computation (i.e. executable code able to move around the
network).Theprimitiveconceptofthecalculusistheambientdefinedasabounded
placeinwhichcomputationcanoccur.Ambientscanbenestedinsideotherambi-
ents. Each ambient has a name used to control access to it. Computation is repre-
sentedasthemovementofambients:theycanbemovedasawhole,changingtheir
locationbyconsumingcertaincapabilities:in,out,open.
Mobileambientswithtimers(tMA)[9,10,15]representaconservativeextension
oftheambientcalculus.Inspiredby[41],weintroducetypesforambientsintMA.
The type system associates to each ambient a set of types in order to control its
communication by allowing only well-typed messages. For instance, if a process
insideanambientsendsamessageofatypewhichisnotincludedinthetypesystem
oftheambient,thentheprocessfails.IntMAtheprocessmaycontinueitsexecution
afterthetimerofthecorrespondingoutputcommunicationexpires.
Thebiologicalinspirationispredominantinthecaseofbranecalculi[40].The
operations of the two basic brane calculi, namely pino, exo, phago (for the PEP
fragment)andmate,bud,drip(fortheMBDfragment)aredirectlyinspiredbythe
biologic processes of endocytosis, exocytosisand mitosis. Since some proteins are
embeddedincellmembranes,andcanactonbothsidesofthemembranesimultane-
ously,branecalculiusebothsidesofthemembrane,emphasizingthatcomputation
happensalsoonthemembranesurface.
Ontheotherhand,inChapter2:MobilityinMembraneComputing,westudy
mobilityintheframeworkof naturalcomputing.Naturalcomputingrefers toboth
computationalmodelsinspiredbynatureandbiologicalprocesses.Whencomplex
natural phenomena are analyzed in terms of computational processes, our under-
standingofbothnatureandcomputationisenhanced.Naturalcomputingislooking
forconcepts,principlesandmechanismsunderlyingnaturalsystems.
Membrane computing is part of natural computing, being a rule-based formal-
ism inspired by biological cells [128]. Mobile membranes represent a formalism
describingthemovementofmembranesinsideaspatialstructurebyapplyingspe-
cificrulesfromagivenset.Wedefineseveralsystemsofmobilemembranes:simple,
enhancedandmutualmobilemembranes,aswellasmutualmobilemembraneswith
objectsonsurface.Whenmembranesystemsareconsideredascomputingdevices,
two main research directions are considered: the computational power in compar-
ison with the classical notion of Turing computability, and the efficiency in algo-
rithmically solving hard problems (e.g., NP-problems) in polynomial time. In this
chapter we present mobile systems which are both powerful (mostly equivalent to
Turingmachines)andefficient(membranesystemalgorithmsprovideefficientso-
lutionstoNP-completeproblemsthroughthegenerationofanexponentialspacein
polynomialtime).
Reachability is the problem of deciding whether a system may reach a given
configurationduringitsexecution.Thisisoneofthemostcriticalpropertiesinthe
verificationofsystems;mostofthesafetypropertiesofcomputingsystemscanbe
Preface vii
reduced to the problem of checking whether a system may reach an “unintended
state”.Weinvestigatetheproblemofreachingacertainconfigurationinsystemsof
mobile membranes with replication rules, starting from a given configuration. We
provethatreachabilityinsystemsofmobilemembranescanbedecidedbyreducing
ittothereachabilityproblemofaversionofpureandpublicambientcalculusfrom
whichtheopencapabilityhasbeenremoved.
InChapter3:Encodingsweestablishseverallinksbetweenprocesscalculiand
membranecomputinginordertobeabletousetechniquesfromoneareaintheother
one.Thedifferencebetweenthesetworesearchareasisthefactthatprocessalge-
bras provide a tool for the high-level description of interactions, communications,
andsynchronizationsbetweenacollectionofindependentagentsorprocesses,pro-
viding also algebraic laws that allow process descriptions to be manipulated and
analyzed,andpermitformalreasoningaboutequivalencesbetweenprocesses(e.g.,
using bisimulation), while membrane computing uses techniques from languages,
automata, complexity, and dynamical systems. We consider our encodings as the
first efforts towards bridging the gap between process calculi and mobile mem-
branes.
In order to study the expressive power oftDπwe use a method of embeddings
among languages introduced in [148]. The method is based on a tuple composed
of a set of process expressions P, a partial operation over P (in process cal-
culiwechoosetheparallelcompositionoperator)andanobservationalequivalence.
To compare two formalisms by looking at their sets of syntactic expressions (lan-
guages) L and L , we are required to identify the corresponding algebraic lan-
1 2
guages (P;|;(cid:2)) respectively (P(cid:3);|(cid:3);(cid:2)(cid:3)). We adapt this method and use it to
showthattDπismoreexpressivethantheunderliningDπ.
Although both the π-calculus and the calculus of mobile ambients are Turing-
complete [42, 121] and they have almost the same field of application (mobile
computations),itiswidelybelieved(see[77])thattheπ-calculusdoesnotdirectly
model phenomena such as the distribution of processes within different localities,
theirmigrations,ortheirfailures.Wepresentatranslationofmobileambientsinto
theasynchronousπ-calculus:inordertoimitatethespatialstructureofmobileam-
bientsweimposesomeveryrigidrestrictionsonthestructuralcongruencerulesof
theπ-calculus.Akeyideaoftheencodingisbasedontheseparationofthespatial
structureofmobileambientsfromtheiroperationalsemantics.
Membranesystems[127,128]andmobileambients[42]havesimilarstructures
and common concepts. Both have a hierarchical structure representing locations,
and are used to model various aspects of biological systems. Mobile ambients are
suitabletorepresentthemovementofambientsthroughambientsandthecommuni-
cationwhichtakesplaceinsidetheboundariesofambients.Membranesystemsare
suitabletorepresentthemovementofobjectsandmembranesthroughmembranes.
Weconsiderthesenewcomputingmodelsusedindescribingvariousbiologicalphe-
nomena [40, 65], and encode the ambients into membrane systems [12, 19]. We
presentsuchanencoding,andprovideanoperationalcorrespondencebetweenthe
viii Preface
safeambientsandtheirencodings,aswellasvariousrelatedpropertiesofthemem-
branesystems[14].
Someworkhasbeendonetryingtorelatemembranesystemsandbranecalculi
[35, 37, 47, 105, 106]. Inspired by brane calculi, a model of membrane systems
havingobjectsattachedtomembraneshasbeenintroducedin[45].In[31],aclass
ofmembranesystemscontainingbothfreefloatingobjectsandobjectsattachedto
membranes has been proposed. We are continuing this research line, and simulate
afragmentofbranecalculibyusingsystemsofmutualmembraneswithobjectson
surface.BydefininganencodingofthePEPfragmentofbranecalculiintosystems
ofmutualmembraneswithobjectsonsurface,weshowthatthedifferencebetween
thetwomodelsisnotsignificant.
ArelationcanbeestablishedbetweenmobilemembranesandcolouredPetrinets
byprovidinganencodingofthefirstformalismintothesecondone.Byconsidering
the endocytic pathway for low-density lipoproteindegradation, we show how mo-
bilemembranescanbeusedtomodelsuchabiologicalphenomenon,whilecoloured
Petrinetscanbeusedtoanalyzeandverifyautomaticallysomebehaviouralprop-
ertiesofthepathway.SomeconnectionsbetweenmembranesystemsandPetrinets
are presented for the first time in [78] and [137]. In [101, 102], a direct structural
relationshipbetweenthesetwoformalismsisestablishedbydefininganewclassof
PetrinetscalledPetrinetswithlocalities.ThisnewclassofPetrinetshasbeenused
toshowhowmaximalevolutionsfrommembranesystemsarefaithfullyreflectedin
themaximallyconcurrentstepsequencesemanticsoftheircorrespondingPetrinets
withlocalities.
The book is devoted to researchers. However, since it contains examples and
exercises,itcanbeusedasacoursesupport.Thedependenciesofitschaptersand
sectionsarerepresentedbythefollowinggraph
1.1 1.5 2.2 2.1
1.2 3.2 1.3 3.4 2.3
3.1 1.4 3.3 2.4 2.5 2.6 3.5
Thebookisdesignedprimarilyforcomputerscientistsworkinginconcurrency
(process calculi, Petri nets), in biologically inspired formalisms (brane calculi,
membrane systems), and also for the mathematically inclined scientists interested
in formalizing moving agents and biological phenomena. As far as we know, the
bookisthefirstmonographthattreatsmobilityasitscentraltopic.
Ias¸i,2011 BogdanAman
GabrielCiobanu
Acknowledgements
MobilitywasdescribedandstudiedformallyincomputersciencebyRobinMilner.
RobinMilnerintroducedandstudiedmobilityinhisπ-calculus,atheoreticalframe-
workforconcurrentsystemsderivedfromhiscalculusofcommunicatingsystems.
WeexpressourgratitudetoRobinMilnernotonlyasapioneerofstudyingmobil-
ityincomputerscienceandhisremarkablecontributions(TuringAward1991),but
alsoasasupervisorandamentorofoneoftheauthors(GabrielCiobanu)duringhis
academicyearspentatUniversityofEdinburgh(1991–1992).
MobilityasaprimitiveoperationwasusedbyLucaCardelliinhisambientcalcu-
lusandvariousbranecalculi.Mobilemembranesdescribethemovementofmem-
branesinmembranecomputing,abranchofnaturalcomputingaimingtobridgefor-
mallanguagesandbiology;membranecomputingwasinitiatedbyGheorghePa˘un
andithasdevelopedquicklyduringthelastdecade.
Wearealsogratefulto:
• ourcolleagues:OanaAgrigoroaiei,OanaAndrei,CosminBonchis¸,LauraCorna˘-
cel,DanielDumitriu,MihaiGontineac,DorinHuzum,CornelIzbas¸a,Ca˘linJu-
ravle, Dorel Lucanu, Gabriel Moruz, Florentin Olariu, Dorin Paraschiv, Dana
Petcu,CristianPrisacariu,AndreasResios,MihaiRotaru,Da˘nu¸tRusu,Gheorghe
S¸tefa˘nescu,BogdanTanasa˘,DanielaZaharie,
• our(international)collaborators:HughAnderson,DanielaBesozzi,RahulDesai,
Maciej Koutny, Shankara Narayanan Krishna, Akash Kumar, Gheorghe Pa˘un,
MarioJ.Pe´rez-Jime´nez,VladimirZakharov,GuoWenyuan,
• all who helped us to advance in our research approach, including anonymous
reviewerandeditors.Apartoftheresearchreportedinthisbookwascarriedout
overthelastfiveyearswiththeirvaluablehelp.
ManythankstoRonanNugentandhisteamat Springerfortheirniceandkind
collaborationinwritingthisbook,improvingitslayout,andpolishingitsEnglish.
WewouldliketothanktheRomanianNationalAuthorityforScientificResearch,
theNationalResearchCouncil(CNCS)andotherpublicauthoritiesforfundingour
research projects; many results presented in this book have been obtained during
theseprojects.
Lastbutnotleast,thewarmestthanksgotoourfamiliesfortheirimportantsup-
port.
ix