Conflict-Tolerant Real-Time Specifications in Metric Temporal Logic

A framework based on the notion of ``conflict-tolerance'' was proposed in [DG08, DGRS08] as a compositional methodology for developing and reasoning about systems that comprise multiple independent controllers. A central notion in this framework is that of a ``conflict-tolerant'' specification for a controller. In this work we propose a way of defining conflict-tolerant real-time specifications in Metric Interval Temporal Logic (MITL). We call our logic CT-MITL for Conflict-Tolerant MITL. We then give a clock optimal ``delay-then-extend'' construction for building a timed transition system for monitoring past-MITL formulas. We show how this monitoring transition system can be used to solve the associated verification and synthesis problems for CT-MITL.