Satisfiability checking for Mission-time LTL (MLTL)

Abstract

Mission-time Linear Temporal Logic (LTL), abbreviated as MLTL, is a bounded variant of Metric Temporal Logic (MTL) over naturals designed to generically specify requirements for mission-based system operation common to aircraft, spacecraft, vehicles, and robots. Despite the utility of MLTL as a specification logic, major gaps remain in analyzing MLTL, e.g., for specification debugging or model checking, centering on the absence of any complete MLTL satisfiability checker. In this paper, we explore both the theoretical and algorithmic problems of MLTL satisfiability checking. We prove that the MLTL satisfiability checking problem is NEXPTIME-complete and that satisfiability checking MLTL0, the variant of MLTL where all intervals start at 0, is PSPACE-complete. To explore the best algorithmic solution for MLTL satisifiability checking, we reduce this problem to LTL satisfiability checking, LTLf (LTL over finite traces) satisfiability checking, and model checking respectively, thus conducting translations for MLTL-to-LTL, MLTL-to-LTLf, and MLTL-to-SMV. Moreover, we propose a new SMT-based solution for MLTL satisfiability checking and create a translation for MLTL-to-SMT. Our extensive experimental evaluation shows that while the MLTL-to-SMV translation with NuXmv model checker performs best on the benchmarks whose interval ranges are small (than 100), the MLTL-to-SMT translation with the Z3 SMT solver offers the most scalable performance.