Timed Multiset Rewriting and the Verification of Time-Sensitive Distributed Systems

TL;DR

This paper introduces a multiset rewriting language with explicit time to specify and analyze time-sensitive distributed systems, proving complexity results and demonstrating automated verification with Maude.

Contribution

It defines realizability and survivability properties for TSDS, introduces progressive timed systems, and analyzes their verification complexity, including automation with Maude.

Findings

Realizability and survivability are PSPACE-complete for PTS.

Bounded realizability is NP-complete, survivability is in $ ext{Delta}_2^p$.

Maude can automate time-bounded verification of PTS.

Abstract

Time-Sensitive Distributed Systems (TSDS), such as applications using autonomous drones, achieve goals under possible environment interference (\eg, winds). Moreover, goals are often specified using explicit time constraints which must be satisfied by the system \emph{perpetually}. For example, drones carrying out the surveillance of some area must always have \emph{recent pictures}, \ie, 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, \emph{realizability} (some trace is good) and \emph{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 \emph{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 $\Delta_2^p$ class of the polynomial hierarchy. Finally, we demonstrate that the rewriting logic system Maude can be used to automate time bounded verification of PTS.