Rachid Hadjidj

CTL * model checking for time Petri nets

This paper aims at applying the CTL* model checking method to the time Petri net (TPN) model. We show here how to contract its generally infinite state space into a graph that captures all its CTL* properties. This graph, called atomic state class graph (ASCG), is finite if and only if, the model is bounded. Our approach is based on a partition refinement technique, similarly to what is proposed in [Berthomieu, Vernadat, State class constructions for branching analysis of time Petri nets, Lecture Notes in Computer Science, vol. 2619, 2003; Yoneda, Ryuba, CTL model checking of time Petri nets using geometric regions, IEICE Trans. Inf. Syst. E99-D(3) (1998)]. In such a technique, an intermediate abstraction (contraction) of the TPN state space is first built, then refined until CTL* properties are restored. Our approach improves the construction of the ASCG in two ways. The first way deals with speeding up the refinement process by using a much more compact intermediate contraction of the TPN state space than those used in [Berthomieu, Vernadat, State class constructions for branching analysis of time Petri nets, Lecture Notes in Computer Science, vol. 2619, 2003; Yoneda, Ryuba, CTL model checking of time Petri nets using geometric regions, IEICE Trans. Inf. Syst. E99-D(3) (1998)]. The second way deals with computing each ASCG node in O(n2) instead of O(n3), n being the number of transitions enabled at the node. Experimental results have shown that our improvements have a good impact on performances.

Improving state class constructions for CTL* model checking of time Petri nets

The state space explosion is still one of the most challenging problems in formal verification using enumerative techniques. The challenge is even greater for real time systems whose state spaces are generally infinite due to time density. To use enumerative techniques with these systems, their state spaces need to be contracted into finite structures that preserve properties of interest. We propose in this paper an efficient approach to construct a contraction of the time Petri net model state space, which preserves its CTL* properties.

On-the-fly TCTL model checking for time Petri nets

In this paper, we show how to efficiently model check a subset of TCTL properties for the Time Petri Net model (TPN model), using the state class method. The verification proceeds by augmenting the TPN model under analysis with a special TPN, called Alarm-clock, to allow the capture of relevant time events. A forward on-the-fly exploration is then applied on the resulting TPN state class space to verify a timed property. A relaxation operation on state classes is also introduced to further improve performances. Alarm-clock is the same for all properties, whereas the exploration technique is not. Three exploration techniques are presented to cover most interesting TCTL properties. We prove the decidability of our verification technique for bounded TPN models and compare it with the reachability algorithm implemented in the tool UPPAAL [G. Behrmann, J. Bengtsson, A. David, K.G. Larsen, P. Pettersson, W. Yi, Uppaal implementation secrets, in: Proc. of the 7th International Symposium on Formal Techniques in Real-Time and Fault-Tolerant Systems, 2002]. Finally, we give some experimental results to show the efficiency of our verification technique.

Efficient Reachability Analysis for Time Petri Nets

We propose in this paper some efficient approaches, based on the state class graph method, to construct abstractions for the Time Petri Net (TPN) model, suitable to verify its linear or reachability properties. Experimental results have shown that these abstractions are very appropriate as both time and size are considerably reduced. For some tested models, abstractions that preserve reachability properties can be as many as 2,051 times smaller and more than 592 times faster to compute. For abstractions, which are overapproximations (useful to prove that certain states are not reachable), gains can overpass 10,000 for both time and size.

Much compact Time Petri Net state class spaces useful to restore CTL* properties

This paper deals with the verification of CTL* properties of Time Petri Nets (TPN model). To verify such properties, we need to contract the generally infinite state space of the TPN model into a finite graph that preserves its CTL* properties. Such a graph can be constructed using a partition refinement technique, where an intermediate graph, representing a contraction of the TPN state space, is first built then refined until CTL* properties are restored. Comparing to other approaches, we propose to construct much compact intermediate graphs. Experimental results have shown that our contractions are very appropriate to boost the refinement procedure. We have been able to reduce computation times by factors reaching four and more in certain cases. Resulting graphs have also been reduced in size.

On-the-fly TCTL model checking for Time Petri Nets using state class graphs

This paper shows how to efficiently model check a subclass of TCTL properties for the TPN model, using the so called state class method. The idea is to put the TPN model under analysis in parallel with a special TPN to capture relevant time events to verify a timed property. The special TPN, we call alarm-clock, has two transitions, with special firing priorities, which can be set to fire at special moments. The verification of a timed property is based on a forward on-the-fly exploration technique, augmented with an abstraction by inclusion to further attenuate the state explosion problem. We prove the decidability of our verification technique for bounded TPN models and give some experimental results to show the effectiveness of our verification technique

Towards optimal CTL* model checking of time petri nets

Abstract This paper considers the Time Petri Net model (TPN model) and proposes a contraction of its generally infinite state space. This contraction preserves all CTL* properties of the model and produces finite graphs for bounded TPN models. When compared with other approaches ((Yoneda et al., 1998); (Berthomieu et al., 2003)), these graphs are smaller and much faster to compute. This paper shows also how to apply a fast computing bisimulation reduction rule to the obtained graphs so as to achieve or approach the optimal size with minor efforts.

Cluster validity index based on Jeffrey divergence

Cluster validity indexes are very important tools designed for two purposes: comparing the performance of clustering algorithms and determining the number of clusters that best fits the data. These indexes are in general constructed by combining a measure of compactness and a measure of separation. A classical measure of compactness is the variance. As for separation, the distance between cluster centers is used. However, such a distance does not always reflect the quality of the partition between clusters and sometimes gives misleading results. In this paper, we propose a new cluster validity index for which Jeffrey divergence is used to measure separation between clusters. Experimental results are conducted using different types of data and comparison with widely used cluster validity indexes demonstrates the outperformance of the proposed index.

Multispectral image denoising with optimized vector non-local mean filter

Nowadays, many applications rely on images of high quality to ensure good performance in conducting their tasks. However, noise goes against this objective as it is an unavoidable issue in most applications. Therefore, it is essential to develop techniques to attenuate the impact of noise, while maintaining the integrity of relevant information in images. We propose in this work to extend the application of the Non-Local Means filter (NLM) to the vector case and apply it for denoising multispectral images. The objective is to benefit from the additional information brought by multispectral imaging systems. The NLM filter exploits the redundancy of information in an image to remove noise. A restored pixel is a weighted average of all pixels in the image. In our contribution, we propose an optimization framework where we dynamically fine tune the NLM filter parameters and attenuate its computational complexity by considering only pixels which are most similar to each other in computing a restored pixel. Filter parameters are optimized using Steins Unbiased Risk Estimator (SURE) rather than using ad hoc means. Experiments have been conducted on multispectral images corrupted with additive white Gaussian noise. PSNR and similarity comparison with other approaches are provided to illustrate the efficiency of our approach in terms of both denoising performance and computation complexity.

Using inclusion abstraction to construct Atomic State Class Graphs for Time Petri Nets

We show in this paper how to contract the TPN state space into a graph that captures all its CTL* properties. This graph called Atomic State Class Graph (ASCG) is finite if and only if, the model is bounded. To achieve this objective, we use a refinement technique similarly to what is proposed in Berthomieu and Vernadat (2003) and Yoneda and Ryuba (1998). In such technique, an intermediate contraction of the TPN state space is first built then refined until CTL* properties are restored. Comparing with the approaches in Berthomieu and Vernadat (2003) and Yoneda and Ryuba (1998), we use inclusion abstraction during all phases of the construction process while reducing the complexity of computations. Our approach allows to construct smaller ASCGs in shorter times (more than five times faster in certain cases).