On the Complexity of Verification of Time-Sensitive Distributed Systems: Technical Report

Time-Sensitive Distributed Systems (TSDS), such as applications using autonomous drones, achieve goals under possible environment interference (e.g., winds). Goals are often specified using explicit time constraints, and, moreover, goals must be satisfied by the system perpetually. For example, drones carrying out the surveillance of some area must always have recent pictures, i.e., at most M time units old, of some strategic locations. This paper proposes a Multiset Rewriting language with explicit time for specifying and analyzing TSDSes. We introduce new properties, such as realizability (there exists a good trace), survivability (where, in addition, all admissible traces are good), recoverability (all compliant traces do not reach points-of-no-return), and reliability (system can always continue functioning using a good trace). A good trace is an infinite trace in which goals are perpetually satisfied. We propose a class of systems called Progressing Timed Systems (PTS), where intuitively only a finite number of actions can be carried out in a bounded time period. We prove that for this class of systems the problems of realizability, recoverability, reliability, and survivability are PSPACE-complete. Furthermore, if we impose a bound on time (as in bounded model-checking), we show that for PTS, realizability becomes NP-complete, while survivability and reliability problems are in the $\Delta_2^p$ class of the polynomial hierarchy.