Decidable Veriication for Reducible Timed Automata Speciied in a First Order Logic with Time. Decidable Veriication for Reducible Timed Automata Speciied in a First Order Logic with Time

We consider the veriication problem for timed programs which requirements speciication is given in a rst order logic with explicit time (that is in a rather general setting), and program speciication is represented by a timed automaton. We formalize an observation concerning some practical systems of control which is related to their ""niteness". Algorithm of control often memorizes and uses only a ""nite" piece of its history. We prove that under some niteness properties of the speciication, the veriication problem becomes decidable. The niteness properties we introduce, "local refutability" and ""nite satissability", are undecidable. However, "local refutability" is often easy to verify. On the other hand, we give a suucient condition, namely reducibility, which assures the ""nite satissability" for timed automata, and we prove that the reducibility is decidable. The latter theorem is the most technical result of the paper. As a consequence, rather a large class of veriication problems is decidable. As an example belonging to this class we consider the Generalized Railroad Crossing Problem. .