Raymond Devillers

Sequential and concurrent behaviour in Petri net theory

Abstract Two ways of describing the behaviour of concurrent systems have widely been suggested: arbitrary interleaving and partial orders. Sometimes the latter has been claimed superior because concurrency is represented in a ‘true’ way; on the other hand, some authors have claimed that the former is sufficient for all practical purposes. Petri net theory offers a framework in which both kinds of semantics can be defined formally and hence compared with each other. Occurence sequences correspond to interleaved behaviour while the notion of a process is used to capture partial-order semantics. This paper aims at obtaining formal results about the relationship between various classes of processes and occurence sequences in net theory. We shall compare an axiomatic approach to the definition of processes with an inductive approach which relates processes to occurence sequences (and generalisations thereof). We shall show that, in general, axiomatic process semantics is more powerful than inductive semantics using occurence sequences. However, we shall also show that the latter can be generalised, or the former be restricted, to yield various equivalence results. The structure of the relation between sequences and processes will also be explored, exhibiting two meaningful relations, one on the sequences and one on the processes, which correspond to each other bijectively. We shall apply and simplify the theory to the practically important case of nets which are of finite synchronisation and 1-safe.

The box calculus: a new causal algebra with multi-label communication

A new Petri net calculus called the calculus of Petri Boxes is described. It has been designed to allow reasoning about the structure of a net and about the relationship between nets, and to facilitate the compositional semantic translation of high level constructs such as blocks, variables and atomic actions into elementary Petri nets. The calculus is located ‘midway’ in such a translation.

Concurrent bisimulations in Petri nets

SummaryAfter various attempts, an equivalence relation is defined for labelled Petri nets, on the base of the concurrency semantics of net theory. This relation, called Fully Concurrent bisimulation and abbreviated FC-bisimulation, preserves the level of concurrency of visible operations and, under some conditions, allows to enforce injective labelling on them. Refinements of a visible operation are also defined and we show that, under some conditions, they preserve FC-bisimulation.

The Non-Optimality of the Monotonic Priority Assignmentsfor Hard Real-Time Offset Free Systems

In this paper, we study the problem of scheduling hard real-time periodic tasks with static priority pre-emptive algorithms. We consider tasks which are characterized by a period, a hard deadline, a computation time and an offset (the time of the first request), where the offsets may be chosen by the scheduling algorithm, hence the denomination offset free systems.We study the rate monotonic and the deadline monotonic priority assignments for this kind of system and we compare the offset free systems and the asynchronous systems in terms of priority assignment. Hence, we show that the rate and the deadline monotonic priority assignments are not optimal for offset free systems.

General Refinement and Recursion Operators for the Petri Box Calculus

New generalised definitions are given for the refinement and recursion operators in the calculus of Petri Boxes. It is shown that not only recursion, but also other operators such as sequence, choice and iteration can be viewed as based on refinement. Various structural properties of these operators can be deduced from a general property of (simultaneous) refinement. A partial order based denotational approach for recursion is presented, which yields a unique fixpoint even in unguarded cases. The construction is based on a judicious naming discipline for places and transitions and yields a closed form for the fixpoint.

Maximality preserving bisimulation

Abstract A new bisimulation notion is introduced for the specification of concurrent systems, which resists to a large class of action refinements, even in the presence of invisible actions. The work is presented in the context of labelled P/T nets, but it may be transported to other popular frameworks like prime event structures, process graphs, etc.

Concurrent and maximally concurrent evolution of nonsequential systems

Abstract The semantics expressed intuitively as ‘execute as much as possible in parallel’ is formally defined and analysed. The relation between such a maximally concurrent semantics and ‘normal’ concurrent semantics is developed. Necessary and sufficient criteria for the equivalence of these semantics are formulated. As an abstract model of nonsequential systems the COSY path expression formalism is used.

Liu and Layland's schedulability test revisited

In this paper, we study the problem of scheduling hard real-time periodic task sets on a single processor with the rate monotonic scheduler. We are concerned with the feasibility test given by Liu and Layland, based on the least upper bound of the utilization factor. We show that the result is incomplete and that the argument is incorrect. We complete and correct the result.

The box algebra = Petri nets + process expressions

The paper describes a Petri net as well as a structural operational semantics for an algebra of process expressions. It specifically addresses this problem for the box algebra, a model of concurrent computation which combines Petri nets and standard process algebras. The main result is that it is possible to obtain a framework where process expressions can be given two, entirely consistent, kinds of semantics: one based on Petri nets, the other on SOS rules. This consistency can also be extended to a partial order semantics.

Feasibility intervals for the deadline driven scheduler with arbitrary deadlines

In this paper, we extend the determination of feasibility intervals to task sets with arbitrary deadlines, both in the synchronous and the asynchronous case. Meanwhile we also improve the arguments and results generally found in the literature.