Thomas Chatain

AN INVERSE METHOD FOR PARAMETRIC TIMED AUTOMATA

We consider in this paper systems modeled by timed automata. The timing bounds involved in the action guards and location invariants of our timed automata are not constants, but parameters. Those parametric timed automata allow the modelling of various kinds of timed systems, e.g. communication protocols or asynchronous circuits. We will also assume that we are given an initial tuple π0 of values for the parameters, which corresponds to values for which the system is known to behave properly. Our goal is to compute a constraint K0 on the parameters, satisfied by π0, guaranteeing that, under any parameter valuation satisfying K0, the system behaves in the same manner: for any two parameter valuations satisfying K0, the behaviors of the timed automata are (time-abstract) equivalent, i.e., the traces of execution viewed as alternating sequences of actions and locations are identical. We present an algorithm InverseMethod that terminates in the case of acyclic models, and discuss how to extend it in the cyclic case. We also explain how to combine our method with classical synthesis methods which are based on the avoidance of a given set of bad states. A prototype implementation has been done, and various experiments are described.

Complete finite prefixes of symbolic unfoldings of safe time petri nets

Time Petri nets have proved their interest in modeling real-time concurrent systems. Their usual semantics is defined in term of firing sequences, which can be coded in a (symbolic and global) state graph, computable from a bounded net. An alternative is to consider a “partial order” semantics given in term of processes, which keep explicit the notions of causality and concurrency without computing arbitrary interleavings. In ordinary place/transition bounded nets, it has been shown for many years that the whole set of processes can be finitely represented by a prefix of what is called the “unfolding”. This paper defines such a prefix for safe time Petri nets. It is based on a symbolic unfolding of the net, using a notion of “partial state”.

Unfolding-based diagnosis of systems with an evolving topology

We propose a framework for model-based diagnosis of systems with mobility and variable topologies, modelled as graph transformation systems. Generally speaking, model-based diagnosis is aimed at constructing explanations of observed faulty behaviours on the basis of a given model of the system. Since the number of possible explanations may be huge we exploit the unfolding as a compact data structure to store them, along the lines of previous work dealing with Petri net models. Given a model of a system and an observation, the explanations can be constructed by unfolding the model constrained by the observation, and then removing incomplete explanations in a pruning phase. The theory is formalised in a general categorical setting: constraining the system by the observation corresponds to taking a product in the chosen category of graph grammars, so that the correctness of the procedure can be proved by using the fact that the unfolding is a right adjoint and thus it preserves products. The theory thus should be easily applicable to a wide class of system models, including graph grammars and Petri nets.

Efficient on-the-fly Algorithm for Checking Alternating Timed Simulation

In this paper we focus on property-preserving preorders between timed game automata and their application to control of partially observable systems. We define timed weak alternating simulation as a preorder between timed game automata, which preserves controllability. We define the rules of building a symbolic turn-based two-player game such that the existence of a winning strategy is equivalent to the simulation being satisfied. We also propose an on-the-fly algorithm for solving this game. This simulation checking method can be applied to the case of non-alternating or strong simulations as well. We illustrate our algorithm by a case study and report on results.

Symbolic unfoldings for networks of timed automata

In this paper we give a symbolic concurrent semantics for network of timed automata (NTA) in terms of extended symbolic nets. Extended symbolic nets are standard occurrence nets extended with read arcs and symbolic constraints on places and transitions. We prove that there is a complete finite prefix for any NTA that contains at least the information of the simulation graph of the NTA but keep explicit the notions of concurrency and causality of the network.

Symbolic Diagnosis of Partially Observable Concurrent Systems

Monitoring large distributed concurrent systems is a challenging task. In this paper we formulate (model-based) diagnosis by means of hidden state history reconstruction, from event (e.g. alarm) observations. We follow a so-called true concurrency approach: the model defines explicitly the causal and concurrency relations between the observable events, produced by the system under supervision on different points of observation. The problem is to compute on-the-fly the different partial order histories, which are the possible explanations of the observable events. In this paper we extend our first method based on Petri nets unfolding to high-level parameterized Petri nets. This allows the designer to model data aspects (even on infinite domains) and non deterministic actions. The observation of such an action gives only partial information and the supervisor has to introduce parameters to represent the hidden aspects of the reached state. This supposes that the possible values for the parameters are symbolically computed and refined during supervision. In practice, non deterministic actions can also be used as an approximation to deal with incomplete information about the system. In this case the refinement of the parameters during supervision improves the knowledge of the model.

Playing Games with Timed Games

In this paper we focus on property-preserving preorders between timed game automata and their application to control of partially observable systems. Following the example of timed simulation between timed automata, we define timed alternating simulation as a preorder between timed game automata, which preserves controllability. We define a method to reduce the timed alternating simulation problem to a safety game. We show how timed alternating simulation can be used to control efficiently a partially observable system. This method is illustrated by a generic case study.

Unfolding-Based Diagnosis of Systems with an Evolving Topology

We propose a framework for model-based diagnosis of systems with mobility and variable topologies, modelled as graph transformation systems. Generally speaking, model-based diagnosis is aimed at constructing explanations of observed faulty behaviours on the basis of a given model of the system. Since the number of possible explanations may be huge we exploit the unfolding as a compact data structure to store them, along the lines of previous work dealing with Petri net models. Given a model of a system and an observation, the explanations can be constructed by unfolding the model constrained by the observation, and then removing incomplete explanations in a pruning phase. The theory is formalised in a general categorical setting: constraining the system by the observation corresponds to taking a product in the chosen category of graph grammars, so that the correctness of the procedure can be proved by using the fact that the unfolding is a right adjoint and thus it preserves products. The theory thus should be easily applicable to a wide class of system models, including graph grammars and Petri nets.

Characterization of Reachable Attractors Using Petri Net Unfoldings

Attractors of network dynamics represent the long-term behaviours of the modelled system. Their characterization is therefore crucial for understanding the response and differentiation capabilities of a dynamical system. In the scope of qualitative models of interaction networks, the computation of attractors reachable from a given state of the network faces combinatorial issues due to the state space explosion.

Building Tight Occurrence Nets from Reveals Relations

Occurrence nets are a well known partial order model for the concurrent behavior of Petri nets. The causality and conflict relations between events, which are explicitly represented in occurrence nets, induce logical dependencies between event occurrences: the occurrence of an event e in a run implies that all its causal predecessors also occur, and that no event in conflict with e occurs. But these structural relations do not express all the logical dependencies between event occurrences in maximal runs: in particular, the occurrence of e in any maximal run may imply the occurrence of another event that is not a causal predecessor of e, in that run. The reveals relation has been introduced to express this dependency between two events. Here we generalize the reveals relation to express more general dependencies, involving more than two events, and we introduce ERL logic to express them as boolean formulas. Finally we answer the synthesis problem that arises: given an ERL formula phi, is there an occurrence net N such that phi describes exactly the dependencies between the events of N?