Starts with a brief review of the history and the application areas considered in the literature. The author then proceeds with introductory modeling examples, behavioral and structural properties, three methods of analysis, subclasses of Petri nets and their analysis. In particular, one section is devoted to marked graphs, the concurrent system model most amenable to analysis. Introductory discussions on stochastic nets with their application to performance modeling, and on high-level nets with their application to logic programming, are provided. Also included are recent results on reachability criteria. Suggestions are provided for further reading on many subject areas of Petri nets. >

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Petri nets: Properties, analysis and applications

Aspect] is a simple and practical aspect-oriented extension to Java With just a few new constructs, AspectJ provides support for modular implementation of a range of crosscutting concerns. In AspectJ's dynamic join point model, join points are well-defined points in the execution of the program; pointcuts are collections of join points; advice are special method-like constructs that can be attached to pointcuts; and aspects are modular units of crosscutting implementation, comprising pointcuts, advice, and ordinary Java member declarations. AspectJ code is compiled into standard Java bytecode. Simple extensions to existing Java development environments make it possible to browse the crosscutting structure of aspects in the same kind of way as one browses the inheritance structure of classes. Several examples show that AspectJ is powerful, and that programs written using it are easy to understand.

An overview of AspectJ

[서평]「Component Software」 - Beyond Object-Oriented Programming -

Process algebra is the study of distributed or parallel syst em by algebraic means. Originating in computer science, process algebra has been extended in re ce t years to encompass not just discrete-event systems, but also continuously evolving ph enomena, resulting in so-called hybrid process algebras. A hybrid process algebra can be used for th e specification, simulation, control and verification of embedded systems in combination with the ir environment, and for any dynamic system in general. As the vehicle of our exposition, we use th e hybrid process algebra χ (Chi). The syntax and semantics of χ are discussed, and it is explained how equational reasoning simplifies tool implementations for simulation and verification. A bot tle filling line example is introduced to illustrate system analysis by means of equational reasonin g.

Process algebra

In comparative concurrency semantics, one usually distinguishes between linear time and branching time semantic equivalences. Milner's notion of observatin equivalence is often mentioned as the standard example of a branching time equivalence. In this paper we investigate whether observation equivalence really does respect the branching structure of processes, and find that in the presence of the unobservable action t of CCS this is not the case.Therefore, the notion of branching bisimulation equivalence is introduced which strongly preserves the branching structure of processes, in the sense that it preserves computations together with the potentials in all intermediate states that are passed through, even if silent moves are involved. On closed CCS-terms branching bisimulation congruence can be completely axiomatized by the single axion scheme: a.(t.(y+z)+y)=a.(y+z) (where a ranges over all actions) and the usual loaws for strong congruence.We also establish that for sequential processes observation equivalence is not preserved under refinement of actions, whereas branching bisimulation is.For a large class of processes, it turns out that branching bisimulation and observation equivalence are the same. As far as we know, all protocols that have been verified in the setting of observation equivalence happen to fit in this class, and hence are also valid in the stronger setting of branching bisimulation equivalence.

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Branching time and abstraction in bisimulation semantics

The idea of representing non-sequential processes as partially ordered sets (occurrence nets) is applied to place/transition nets (Petri nets), based on the well known notion of process for condition/event-systems. For occurrence nets some theorems relating K -density, cut finiteness, and discreteness are proved. With these theorems the result that a place/transition net is bounded if and only if its processes are K -dense is obtained.

The non-sequential behaviour of Petri nets

We study an operator for refinement of actions to be used in the design of concurrent systems. Actions on a given level of abstraction are replaced by more complicated processes on a lower level. This is done in such a way that the behaviour of the refined system may be inferred compositionally from the behaviour of the original system and from the behaviour of the processes substituted for actions. We recall that interleaving models of concurrent systems are not suited for defining such an operator in its general form. Instead, we define this operator on several causality based, event oriented models, taking into account the distinction between deadlock and successful termination. Then we investigate the interplay of action refinement with abstraction in terms of equivalence notions for concurrent systems, considering both linear time and branching time approaches. We show that besides the interleaving equivalences, also the equivalences based on steps are not preserved under refinement of actions. We prove that linear time partial order semantics are invariant under refinement. Finally we consider various bisimulation equivalences based on partial orders and show that the finest two of them are preserved under refinement whereas the others are not. Termination sensitive versions of these equivalences are even congruences for action refinement.

Refinement of actions and equivalence notions for concurrent systems

We investigate equivalence notions for concurrent systems. We consider ”linear time” approaches where the system behaviour is characterised as the set of possible runs as well as ”branching time” approaches where the conflict structure of systems is taken into account. We show that the usual interleaving equivalences, and also the equivalences based on steps (multisets of concurrently executed actions) are not preserved by refinement of atomic actions. We prove that ”linear time” partial order semantics, where causality in runs is explicit, is invariant under refinement. Finally, we consider various bisimulation equivalences based on partial orders and show that the strongest one of them is preserved by refinement whereas the others are not.

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Equivalence notions for concurrent systems and refinement of actions

We consider an operator for refinement of actions to be used in the design of concurrent systems. Actions on a given level of abstraction are replaced by more complicated processes on a lower level. This is done in such a way that the behaviour of the refined system may be inferred compositionally from the behaviour of the original system and from the behaviour of the processes substituted for actions. We define this refinement operation for causality based models like event structures and Petri nets. For Petri nets, we relate it to other approaches for refining transitions.

Refinement of actions in causality based models

A non-interleaving semantics for a subset of CCS using finite place/transition-systems is presented. Straightforward constructions on nets for CCS operations are given. When restricting the language appropriately (no restriction and relabelling, only guarded choice), these operations yield a net semantics with a clear distinction of concurrency and nondeterminism. It is shown that the usual interleaving semantics is retrievable from the net semantics. Partial order semantics and equivalence notions for labelled P/T-systems are discussed. This shows how the intuitive causal dependencies in a CCS program are represented via the net semantics.

Ursula Goltz

Papers

The non-sequential behaviour of Petri nets

Refinement of actions and equivalence notions for concurrent systems

Equivalence notions for concurrent systems and refinement of actions

Refinement of actions in causality based models

On Representing CCS Programs by Finite Petri Nets