Ursula Goltz

The non-sequential behaviour of Petri nets

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.

Refinement of actions and equivalence notions for concurrent systems

Abstract. 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.

Equivalence notions for concurrent systems and refinement of actions

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.

Refinement of actions in causality based models

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.

On Representing CCS Programs by Finite Petri Nets

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.

On the Relationship of CCS and Petri Nets

We give a partial order semantics to (pure) CCS via a translation into Petri nets and prove, that the interleaved behaviour of the resulting nets is equivalent to Milners semantics. We show that a large class of CCS programs can be represented by finite nets and that this is impossible for the whole CCS.

Timed sequence diagrams and tool-based analysis: a case study

We use UML timed Sequence Diagrams to specify the realtime behaviour of a communication protocol of audio/video components. The Sequence Diagrams build the requirements specification against which an implementation of the protocol developed by the Bang & Olufsen company is proven correct. To obtain a complete requirements specification, we have to mark the UML Sequence Diagrams as optional or mandatory behaviour. Then the Sequence Diagram interactions with their timing constraints and periods are transferred to a setting of timed automata. We use the Uppaal tool for verification. In particular, we show that the implementation of the protocol conforms to the Sequence Diagram specification concerning the correct data transfer on the bus.

Model-based pairwise testing for feature interaction coverage in software product line engineering

Testing software product lines (SPLs) is very challenging due to a high degree of variability leading to an enormous number of possible products. The vast majority of today’s testing approaches for SPLs validate products individually using different kinds of reuse techniques for testing. Because of their reusability and adaptability capabilities, model-based approaches are suitable to describe variability and are therefore frequently used for implementation and testing purposes of SPLs. Due to the enormous number of possible products, individual product testing becomes more and more infeasible. Pairwise testing offers one possibility to test a subset of all possible products. However, according to the best of our knowledge, there is no contribution discussing and rating this approach in the SPL context. In this contribution, we provide a mapping between feature models describing the common and variable parts of an SPL and a reusable test model in the form of statecharts. Thereby, we interrelate feature model-based coverage criteria and test model-based coverage criteria such as control and data flow coverage and are therefore able to discuss the potentials and limitations of pairwise testing. We pay particular attention to test requirements for feature interactions constituting a major challenge in SPL engineering. We give a concise definition of feature dependencies and feature interactions from a testing point of view, and we discuss adequacy criteria for SPL coverage under pairwise feature interaction testing and give a generalization to the T-wise case. The concept and implementation of our approach are evaluated by means of a case study from the automotive domain.

CSP-programs as nets with individual tokens

We define a subclass of predicate/transition-nets and show how to translate CSP-programs into such nets. We consider a subset of CSP for which Hennessy, Li and Plotkin have given an operational semantics in [HLP]. We show that the firing sequences of our net translation correspond to this operational semantics. Additionally, we also give a non-interleaving semantics to CSP by considering unfoldings and processes of the net translation.

Propositional Temporal Logics and Equivalences

We compare propositional temporal logics by comparing the equivalences that they induce on models. Linear time, branching time and partial order temporal logics are considered. The logics are interpreted on occurrence transition systems, generated by labelled prime event structures without autoconcurrency. The induced equivalences are also compared to directly defined equivalences, e.g., history preserving bisimulation, pomset bisimulation, pomset trace equivalence, and others. It is then shown which of the induced equivalences are and which are not preserved under action refinement.