Timed Multiset Rewriting and the Verification of Time-Sensitive Distributed Systems
Time-Sensitive Distributed Systems (TSDS), such as applications using autonomous drones, achieve goals under possible environment interference (e.g., winds). Moreover, goals are often specified using explicit time constraints which 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 analysing TSDSes. We introduce two properties, realizability (some trace is good) and survivability (where, in addition, all admissible traces are good). A good trace is an infinite trace in which goals are perpetually satisfied. We propose a class of systems called progressive 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 both the realizability and the survivability problems 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 is in the \(\varDelta _2^p\) class of the polynomial hierarchy. Finally, we demonstrate that the rewriting logic system Maude can be used to automate time bounded verification of PTS.
Kanovich’s research was partially supported by EPSRC. Scedrov’s research was partially supported by ONR and by AFOSR MURI. Kanovich’s and Scedrov’s work on this paper was partially carried out within the framework of the Basic Research Program at the National Research University Higher School of Economics (HSE) and partially supported within the framework of a subsidy by the Russian Academic Excellence Project ‘5–100’. Talcott was partially supported by NSF grant CNS-1318848 and ONR grant N00014-15-1-2202. Nigam and Talcott were partially supported by Capes Science without Borders grant 88881.030357/2013-01. Nigam was partially supported by Capes and CNPq.
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