Abstract
A notion of alternating timed automata is proposed. It is shown that such automata with only one clock have decidable emptiness problem over finite words. This gives a new class of timed languages that is closed under boolean operations and which has an effective presentation. We prove that the complexity of the emptiness problem for alternating timed automata with one clock is nonprimitive recursive. The proof gives also the same lower bound for the universality problem for nondeterministic timed automata with one clock. We investigate extension of the model with epsilon-transitions and prove that emptiness is undecidable. Over infinite words, we show undecidability of the universality problem.
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