Alternating timed automata on infinite words are considered. The main result is a characterization of acceptance conditions for which the emptiness problem for these automata is decidable. This result implies new decidability results for fragments of timed temporal logics. It is also shown that, unlike for MITL, the characterisation remains the same even if no punctual constraints are allowed.

• 03B25 - Decidability of theories and sets of sentences
• 03B44 - Temporal logic
• 03D05 - Automata and formal grammars in connection with logical questions
• 68Q60 - Specification and verification (program logics, model checking, etc.)