Adding Dense-Timed Stack to Integer Reset Timed Automata

Integer reset timed automata (IRTA) are known to be a determinizable subclass of timed automata, but it is not known whether they are input-determined, i.e., the clock values are completely determined by an input timed word. We first define a syntactic subclass of IRTA called strict IRTA and show that strict IRTA is equivalent to IRTA. We show that the class of strict IRTA is indeed input-determined. Visibly pushdown automata is another input-determined class of automata with a stack that is also closed under boolean operations and admits a logical characterization. We propose dtIRVPA as a class of timed automata with a dense-timed stack. Similar to strict IRTA, we define strict dtIRVPA and show that strict dtIRVPA is input-determined where both – stack operations and the values of the integer reset clocks – are determined by the input word, and this helps us to get the monadic second-order (MSO) logical characterization of dtIRVPA. We prove the closure properties of dtIRVPA under union, intersection, complementation, and determinization. Further, we show that reachability of dtIRVPA is PSPACE-complete, i.e. the complexity is no more than that of timed automata.