Olivier Roux

TCTL Model Checking of Time Petri Nets

We consider Time Petri Nets (TPN) for which a firing time interval is associated with each transition. State space abstractions for TPN preserving various classes of properties (LTL, CTL and CTL*) can be computed, in terms of so called state classes. Some methods were proposed to check quantitative timed properties but are not suitable for effective verification of properties of real-life systems. In this article, we consider subscript TCTL for TPN (TPN-TCTL) for which temporal operators are extended with a time interval, specifying a time constraint on the firing sequences. We prove the decidability of TPN-TCTL on bounded TPN and give its theoretical complexity. We propose a zone-based state space abstraction that preserves marking reachability and traces of the TPN. As for Timed Automata (TA), the abstraction may use an over-approximation operator on zones to enforce the termination. A coarser (and efficient) abstraction is then provided and proved exact w.r.t. marking reachability and traces (LTL properties). Finally, we consider a subset of TPN-TCTL properties (TPN-TCTLS) for which it is possible to propose efficient on-the-fly model-checking algorithms. Our approach consists in computing and exploring the zone-based state space abstraction. On a practical point of view, the method is integrated in Romeo [Gardey et al. (2005, Proceedings of 17th International Conference on CAV’05, Vol. 3576 of Lecture Notes in Computer Science, 418–423)], a tool for TPN edition and analysis. In addition to the old features it is now possible to effectively verify a subset of TCTL directly on TPN.

Safety Control Synthesis for Time Petri Nets

We study some control synthesis problems on an extension of time Petri nets that model a plant and its environment. The time Petri net control model both represents controllable and uncontrollable events, the problem is then to design a function (controller) such that a given property is fulfilled. We focus our analysis on safety properties expressed on the markings of the net and we propose a symbolic method to decide the existence of a controller that ensures these properties. Unlike existing methods on time Petri nets, that assume the net is bounded, the method is applicable for any time Petri nets. A consequence is that it is possible to decide the existence of a controller that k-bounds the plant. A method is then proposed to build a state-based controller and problems raised by the implementation (Zenoness, sampling) of the control function on the plant are discussed

Time Arc Petri Nets and Their Analysis

We propose to extend time arc Petri nets by associating with each transition a strong or a weak firing semantics. The proposed model includes the semantics of existing time Petri nets where time intervals are associated with places, transitions and arcs in their weak and strong semantics. We show afterwards that state space abstraction techniques for constructing zone graphs can be adapted to the proposed model. For the theory of time Petri nets this result gives the decidability of k-boundedness, markingreachability and language emptiness problems for the proposed model and all its sub-classes.

Discrete Parameters in Petri Nets (Informal Presentation)

With the aim of significantly increasing the modeling capability of Petri nets, we suggest models that involve parameters to represent the weights of arcs, or the number of tokens in places. We call these Petri nets parameterised nets or PPNs. Indeed, the introduction of parameters in models aims to improve genericity. nIt therefore allows the designer to leave unspecified aspects, nsuch as those related to the modeling of the environment. This increase in modeling power usually results in greater complexity in the analysis and verification of the model. Here, we consider the property of coverability of markings. Two general questions arise: Is there a parameter value for which the property is satisfied? and Does the property hold for all possible values of the parameters?. We first study the decidability of these issues, nwhich we show to be undecidable in the general case. Therefore, we also define subclasses of parameterised networks, based on restriction of the use of parameters, depending on whether the parameters are used on places, input or output arcs of transitions or combinations of them. Those subclasses have therefore a dual interest. From a modeling point of view, restrict the use of parameters to tokens, outputs or inputs can be seen as respectively processes or synchronisation of a given number of processes. From a theoretical point of view, it is interesting to introduce those subclasses of PPN in a concern of completeness of the study. We study the relations between those subclasses and prove that, for some subclasses, certain problems become decidable, making these subclasses more usable in practice.

Kinetic Theory Modeling and Efficient Numerical Simulation of Gene Regulatory Networks Based on Qualitative Descriptions

Using mathematical modeling to address large scale problems in the world of biological regulatory networks has become increasingly necessary given the sheer quantity of data made available by improved technology. In the most general sense, modeling approaches can be thought of as being either quantitative or qualitative. Quantitative methods such as ordinary differential equations or the chemical master equation are widespread in the literature; when the model is well developed, the detail therein can be incredibly informative. However, they require an in depth knowledge of the reaction kinetics and generally fail as the problem size grows. The alternative approach, qualitative models, does not possess the same amount of detail but captures the essential dynamics of the system. Gene regulation, as a sub-genre of biological regulatory networks, is characterized by large numbers of interconnected species whose influences depend on passing some threshold, thus, largely sigmoidal behaviors. The application of qualitative methods to these systems can be highly advantageous to the modeler. As just mentioned realistic models in gene regulation are immense and highly interconnected, such that the simply enumeration of the possible states of the resulting system creates a combinatorial explosion. There are some questions for which one must access the underlying probability distribution associated with the Markov transitions of the qualitative model, as for example a qualitative and intuitive analysis of the system as a whole. The most pervasive methods have historically been simulation-based. Here, we propose a method to solve the system by treating the Markov equations of a Process Hitting model with numerical techniques. Proper Generalized Decomposition (PGD) can be used to overcome the curse of dimensionality, providing fast and accurate solutions to an otherwise intractable problem. Moreover PGD allows considering unknown parameters as a model extra-coordinate to obtain a parametric solution.

Device driver synthesis for embedded systems

Currently the development of embedded software managing hardware devices that fulfills industrial constraints (safety, real time constraints) is a very complex task. To allow an increased reusability between projects, generic device drivers have been developed in order to be used in a wide range of applications. Usually the level of gener-icity of such drivers require a lot of configuration code, which is often generated. However, a generic driver requires a lot of configuration and need more computing power and more memory needs than a specific driver. This paper presents a more efficient methodology to solve this issue based on a formal modeling of the device and the application. Starting from this modeling, we use well-known game theory techniques to solve the driver model synthesis problem. The resulting model is then translated into the actual driver embedded code with respect to an implementation model. By isolating the model of the device, we allow more reusability and interoperability between devices for a given application, while generating an application-specific driver.

Oreste : a Reliable Reactive Real-Time Language

The behavior during execution of an Oreste program is driven by the application. To perform reliability, this behavior has to be always defined. The failure of an Oreste’s software component execution is either explicitly recovered, either implicitly propagated to the caller of the component. This is performed by a multi-tasking extension of programming by contract, organized panic and/or resumption proposed for the Eiffel sequential language by B. Meyer.