On Hybrid Systems and the Modal µ-calculus
نویسنده
چکیده
We start from a basic and fruitful idea in current work on the formal analysis and veriication of hybrid and real-time systems: the uniform representation of both sorts of state dynamics { both continuous evolution within a control mode, and the eeect of discrete jumps between control modes { as abstract transition relations over a hybrid space X Q R n , where Q is a nite set of control modes. The resulting \machine" or transition system model is currently analyzed using the resources of concurrent and reactive systems theory and temporal logic veriication, abstracted from their original setting of nite state spaces and purely discrete transitions. One such resource is the propositional-calculus: a richly expressive formal logic of transition system models (of arbitrary cardinality), which subsumes virtually all temporal and modal logics. The key move here is to view the transition system models of hybrid automata not merely as some form of \discrete abstraction", but rather as a skeleton which can be eshed out by imbuing the state space with topological, metric tolerance or other structure. Drawing on the resources of modal logics, we give explicit symbolic representation to such structure in polymodal logics extending the modal-calculus. The result is a logical formalism in which we can directly and simply express continuity properties of transition relations and metric tolerance properties such as \being within distance " of a set. Moreover, the logics have sound and complete deductive proof systems, so assumptions of continuity or tolerance can be used as hypotheses in deductive veri-cation. By also viewing transition relations in their equivalent form as set-valued functions, and drawing on the resources of set-valued analysis and dynamical systems theory, we open the way to a richer formal analysis of robustness and stability for hybrid automata and related classes of systems.
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Personalia Date of birth: 27 December 1965. Place of birth: Lucca (Italy). Nationality: Italian. Civil state: married with Luisa Allara. Children: one step-daughter named Lavinia, and one daughter named Athena Livia. (in italian): Modelli di teorie dei Fondamenti della Matematica con proprietà di autoriferimento. The title means: Models of theories for the Foundations of Mathematics with proper...
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