Charles Lakos

From Coloured Petri Nets to Object Petri Nets

This paper seeks to establish within a formal framework how Coloured Petri Nets can be enhanced to produce Object Petri Nets. It does so by defining a number of intermediate Petri Net formalisms and identifying the features introduced at each step of the development. Object Petri Nets support a complete integration of object-oriented concepts into Petri Nets, including inheritance and the associated polymorphism and dynamic binding. In particular, Object Petri Nets have a single class hierarchy which includes both token types and subnet types. Interaction between subnets can be either synchronous or asynchronous depending on whether the subnet is defined as a super place or a super transition. The single class hierarchy readily supports multiple levels of activity in the net and the generation and removal of tokens has been defined so that all subcomponents are simultaneously generated or removed, thus simplifying memory management. Despite this descriptive power, Object Petri Nets can be transformed into behaviourally equivalent Coloured Petri Nets, thus providing a basis for adapting existing analysis techniques.

Object oriented modelling with object petri nets

This paper informally introduces Object Petri Nets (OPNs) with a number of examples. OPNs support a thorough integration of object-oriented concepts into Petri Nets, including inheritance and the associated polymorphism and dynamic binding. They have a single class hierarchy which includes both token types and subnet types, thereby allowing multiple levels of activity in the net. The paper discusses some theoretical issues pertinent to the analysis of OPNs, and compares the provisions of OPNs with those of other Concurrent Object-Oriented Programming Languages. The paper then considers a case study of using OPNs to model a cooperative editor for hierarchical diagrams. This extended example demonstrates the applicability of OPNs to the modelling of non-trivial concurrent systems. The methodology for deriving a Petri Net model is to adapt an object-oriented design methodology: the Object Model is prepared in Rumbaughs OMT notation; the Dynamic Model is then prepared in the form of lifecycles, following the Shlaer-Mellor methodology; and finally these models are mapped into an OPN model. This approach has the advantage of guiding the development with well-accepted methodologies, and demonstrates the generality and flexibility of the OPN formalism.

A General Systematic Approach to Arc Extensions for Coloured Petri Nets

This paper proposes an approach to arc extensions in CP-nets which is claimed to be both general and systematic. It is general because the enabling rules cater for true concurrency as well as an interleaving semantics and because it encompasses the other proposals for arc extensions that have been made recently in the Petri Net literature, often in the context of the requirements of specific application domains. It is systematic because it proposes a set of fundamental arcs in the context of a general complementary place construction and then considers how these arcs can be combined in arbitrary ways. Because of the utility of some of these compound arcs and the minimal overhead in implementing them, it is argued that CP-net tools should provide explicit support for them.

On the Abstraction of Coloured Petri Nets

This paper considers the appropriate properties for abstract net components in the Coloured Petri Net formalism. In doing so, it attempts to maintain the duality between places and transitions which is so foundational to Petri Net theory. It also defines what it means to execute the net at an abstract level.

Composing abstractions of coloured Petri nets

An earlier paper considered appropriate properties for abstract net components (or nodes) in the Coloured Petri Net formalism. This paper augments that earlier work in three main areas -- it proposes general canonical forms for such node refinements, it identifies two other forms of refinement which will be used in concert with node refinement, and it considers the compositionality of these refinements. All of them maintain behavioural compatibility between refined and abstract nets, which is captured by the notion of a system morphism.

Modelling layered protocols in LOOPN

LOOPN is a language and simulator for specifying systems in terms of coloured timed Petri nets. It includes object-oriented features such as subtyping, inheritance and polymorphism which allow for the convenient modularisation of complex specifications. This paper briefly describes LOOPN and considers its application to the modelling of layered network protocols.<<ETX>>

Modular analysis of systems composed of semiautonomous subsystems

This paper reviews a proposal for the modular analysis of Petri nets and its applicability to factory automation systems. It presents new algorithms to harness this modular analysis in the determination of reachable states with specified partial markings, to determine possible deadlocks, both global and local, and also liveness. These algorithms have been implemented in a prototype tool which has then been used to solve a problem in factory automation which, even for relatively simple configurations, can lead to state spaces beyond the capabilities of many analysis tools.

A petri net view of mobility

Mobile systems explore the interplay between locality and connectivity. A subsystem may have a connection to a remote subsystem and use this for communication. Alternatively, it may be necessary or desirable to move the subsystem close to the other in order to communicate. This paper presents a Petri Net formalisation of mobile systems so as to harness the intuitive graphical representation of Petri Nets and the long history of associated analysis techniques. The proposed formalism starts with modular Petri Nets, where a net is divided into modules which can interact via place and transition fusion. The first change is that the flat module structure is replaced by fully nested modules, called locations. The nesting of locations provides a notion of locality while their fusion context determines their connectivity. The transitions constituting a location are constrained so that we can determine when a location is occupied by a subsystem, and when the subsystem shifts from one location to another. The colourless version of the formalism is conceptually simpler, while the coloured version caters for more dynamic configurations and helps identify isolated subsystems for which garbage collection may be appropriate.

The Consistent Use of Names and Polymorphism in the Definition of Object Petri Nets

This paper seeks to present a more elegant and general definition of Object Petri Nets than previously. It is more general since it supports transition fusion as well as place fusion. It is more elegant because it captures all the notions of place substitution, transition substitution, place fusion, and transition fusion under the single notion of binding. This is achieved by explicitly supporting names in the formalism, in line with the π-calculus which recognises that names are pervasive and should be explicitly included in a formalism in order to model object mobility. The definition in this paper is also more consistent in its use of polymorphism and embodies a more obvious duality between states and changes of state. Object Petri Nets represent a complete integration of object-oriented concepts into Petri Nets. They have a single class hierarchy which includes both token types and subnet types, and which readily supports modelling systems with multiple levels of activity. Interaction between subnets can be synchronous or asynchronous depending on whether the subnet is defined as a super place or a super transition. While not presented in this paper, Object Petri Nets can be transformed into behaviourally equivalent Coloured Petri Nets, thus providing a basis for adapting existing analysis techniques.

Modular state space exploration for timed petri nets

This paper extends modular state space construction for concurrent systems to cater for timed systems. It identifies different forms of timed state space and presents algorithms for computing them. These include uniprocessor algorithms inspired by conservative and optimistic approaches to discrete event simulation, and also a distributed algorithm. The paper discusses implementation issues and performance results for a simple case study.