Bigraphical Languages and their Simulation

AbstractWe study bigraphs as a foundation for practical formal languages and the problem of simu-lating such bigraphical languages. The theory of bigraphs is a foundational, graphical model ofconcurrent systems focusing on mobility and connectivity. It is a meta-model in the sense thatit is parametrized over a signature and a set of reaction rules which determine the syntax anddynamic semantics, respectively. This allows for rather direct models and, together with a nat-ural yet formal graphical notation and an elegant theory of behavioral equivalence, this makesbigraphsanenticingfoundationforpracticalformallanguages. However,thetheoryofbigraphsisstillyoung. Whiledirectmodelsofmanyprocesscalculihavebeenconstructed,itisunclearhowsuitablebigraphsareformorepracticalformallanguages. Also,thegeneralityofbigraphscomesatapriceofcomplexityinthetheoryandsimulationofbigraphicalmodelsisnon-trivial. Akeyproblem is that of matching: deciding if and how a reaction rule applies to a bigraph. In thisdissertation, westudybigraphs and their simulation for two types of practicalformal languages:programminglanguagesandlanguagesforcellbiology.First, we study programming languages and binding bigraphs, a variant of bigraphs with afacilityformodelingthebindersfoundinmostprogramminglanguages. Buildingonanexistingtermlanguageandinductivecharacterizationofmatchingweconstructaprovablycorrectmatch-ing algorithm. We implement the term language and matching algorithm resulting in the BPLTool,afirsttoolforbindingbigraphs,whichprovidesfacilitiesformodeling,simulation,andvisu-alization. WethenemploybindingbigraphsandtheBPLTooltoformalizeasubsetofWS-BPEL,a commercial programming language for implementing business processes. We also propose andformalize an extension to WS-BPEL which supports mobile processes and process management.Whiledemonstratingthefeasibilityofusingbigraphsasafoundationforprogramminglanguages,our work reveals an inconvenience in the formulation of binding bigraphs, exposes the need forhigher-order reaction rules, data types and (practical) sortings, and demonstrates that the BPLToolistooinefficientforsimulatingsuchalanguage. Finally,asanaside,weidentifyacoresubsetof WS-BPEL and construct an idempotent transformation from WS-BPEL into the core subset,therebyshowingthataformalizationneedonlycoverthecoresubsettobecomplete.Next, we study languages for cell biology and stochastic bigraphs, an extension to bigraphsthat enables modeling and analysis of stochastic behavior which is useful in cell biology. Wegeneralizeanefficientandscalablestochasticsimulationalgorithmforthe -calculustobigraphs.For this purpose, we develop a number of theories for (stochastic) bigraphs: (i) a formulationof the theory that is amenable to implementation, (ii) embeddings, an alternative formulationof matches suitable for implementation, (iii) edit scripts, an alternative to reaction rules witha natural and fine-grained notion of modification, (iv) anchored matching, a localized matchingalgorithm,and(v)anotionandanalysisofcausalityatthelevelofrules. Parts(i)-(iii)havebeendevelopedinfullwhileparts(iv)-(v)areoutlinedindetail. Parts(i)-(iv)havebeenimplementedin a prototype. Finally, we develop a bigraphical language for protein-protein interaction withdynamiccompartments. Ourapproachdiffersfromsimilarpreviousworksinanumberofrespects.First,weelidethebigraphicalunderpinningstoobtainasimplerandmoreaccessiblepresentationin the style of process calculi. In particular, the development is incremental, adding only thecomplexity necessary for each feature. Second, we give a graphical notation which correspondsto a subset of bigraphs but is more suitable for the domain. Third, our approach includes anovel mechanism for handling connected components, which is necessary to model diffusion ofe.g.,protein-complexes. Ourworksuggeststhattworefinementsofstochasticbigraphswouldbeconvenient: connectedcomponentsshouldbeeasilyidentifiable,andmatchingshouldberestrictedtocertainlocalcontexts.i