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Denotational semantics of hybrid automata. (English) Zbl 1168.68417
Aceto, Luca (ed.) et al., Foundations of software science and computation structures. 9th international conference, FOSSACS 2006, held as part of the joint European conferences on theory and practice of software, ETAPS 2006, Vienna, Austria, March 25–31, 2006. Proceedings. Berlin: Springer (ISBN 3-540-33045-3/pbk). Lecture Notes in Computer Science 3921, 231-245 (2006).
Summary: We introduce a denotational semantics for non-linear hybrid automata, and relate it to the operational semantics given in terms of hybrid trajectories. The semantics is defined as least fixpoint of an operator on the continuous domain of functions of time that take values in the lattice of compact subsets of n-dimensional Euclidean space. The semantic function assigns to every point in time the set of states the automaton can visit at that time, starting from one of its initial states. Our main results are the correctness and computational adequacy of the denotational semantics with respect to the operational semantics and the fact that the denotational semantics is computable.
MSC:
68Q45Formal languages and automata
68Q55Semantics