Augmenting the discrete timed automaton with other data structures

We describe a general automata-theoretic approach for analyzing the verification problems of discrete timed automata (i.e., timed automata with integer-valued clocks) augmented with various data structures. Formally, let C be a class of nondeterministic machines with reversal-bounded counters and possibly other data structures (e.g., a pushdown stack, a queue, a read-write work-tape, etc.). Let A be a discrete timed automaton and M be a machine in b. Denote by A ⊕ M the combined automaton, i.e., A augmented with M (in some precise sense to be defined). We show that if c has a decidable emptiness problem, then the (binary, forward, backward) reachability, safety, and invariance for A ⊕ M are solvable. We give examples of such c's and exhibit some new properties of discrete timed automata that can be verified. We also briefly consider reachability in discrete timed automata operating in parallel.