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Hybrid systems are the result of merging the two most commonly used models for dynamical systems, namely continuous dynamical systems defined by differential equations and discrete-event systems defined by automata. One can view hybrid systems as constrained systems, where the constraints describe the possible process flows, invariants within states, and transitions on the one hand, and to characterize certain parts of the state space (e.g. the set of initial states, or the set of unsafe states) on the other hand. Therefore, it is advantageous to use constraint logic programming (CLP) as an approach to model hybrid systems. In this paper, we provide CLP implementations, that model hybrid systems comprising several concurrent hybrid automata, whose size is only straight proportional to the size of the given system description. Furthermore, we allow different levels of abstraction by making use of hierarchies as in UML statecharts. In consequence, the CLP model can be used for analyzing and testing the absence or existence of (un)wanted behaviors in hybrid systems. Thus in summary, we get a procedure for the formal verification of hybrid systems by model checking, employing logic programming with constraints.

Hybrid automata are used as standard means for the specification and analysis of dynamical systems. Several researches have approached them to formally specify reactive Multi-agent systems situated in a physical environment, where the agents react continuously to their environment. The specified systems, in turn, are formally checked with the help of existing hybrid automata verification tools. However, when dealing with multi-agent systems, two problems may be raised. The first problem is a state space problem raised due to the composition process, where the agents have to be parallel composed into an agent capturing all possible behaviors of the multi-agent system prior to the verification phase. The second problem concerns the expressiveness of verification tools when modeling and verifying certain behaviors. Therefore, this paper tackles these problems by showing how multi-agent systems, specified as hybrid automata, can be modeled and verified using constraint logic programming(CLP). In particular, a CLP framework is presented to show how the composition of multi-agent behaviors can be captured dynamically during the verification phase. This can relieve the state space complexity that may occur as a result of the composition process. Additionally, the expressiveness of the CLP model flexibly allows not only to model multi-agent systems, but also to check various properties by means of the reachability analysis. Experiments are promising to show the feasibility of our approach.

Specifying behaviors of multi-agent systems (MASs) is a demanding task, especially when applied in safety-critical systems. In the latter systems, the specification of behaviors has to be carried out carefully in order to avoid side effects that might cause unwanted or even disastrous behaviors. Thus, formal methods based on mathematical models of the system under design are helpful. They not only allow us to formally specify the system at different levels of abstraction, but also to verify the consistency of the specified systems before implementing them. The formal specification aims a precise and unambiguous description of the behavior of MASs, whereas the verification aims at proving the satisfaction of specified requirements. A behavior of an agent can be described as discrete changes of its states with respect to external or internal actions. Whenever an action occurs, the agent moves from one state to another one. Therefore, an efficient way to model this type of discrete behaviors is to use a kind of state transition diagrams such as finite automata. One remarkable advantage of such transition diagrams is that they lend themselves formal analysis techniques using model checking. The latter is an automatic verification technique which determines whether given properties are satisfied within a model underlying a particular system. In realistic physical environments, however, it is necessary to consider continuous behaviors in addition to discrete behaviors of MASs. Examples of those type of behaviors include the movement of a soccer agent to kick off or to go to the ball, the process of putting out the fire by a fire brigade agent in a rescue scenario, or any other behaviors that depend on any timed physical law. The traditional state transition diagrams are not sufficient to combine these types of behaviors. Hybrid automata offer an elegant method to capture such types of behaviors. Hybrid automata extend regular state transition diagrams with methods that deal with those continuous actions such that the state transition diagrams are used to model the discrete changes of behaviors, while differential equations are used to model the continuous changes. The semantics of hybrid automata make them accessible to formal verification by means of model checking. The main goal of this thesis is to approach hybrid automata for specifying and verifying behaviors of MASs. However, specifying and and verifying behaviors of MASs by means of hybrid automata raises several issues that should be considered. These issues include the complexity, modularity, and the expressiveness of MASs' models. This thesis addresses these issues and provides possible solutions to tackle them.