Metric temporal logic with durations

Metric Temporal Logic with Durations

We present a formal framework based on metric temporal logic (MTL) for specifying and verifying real-time systems with a continuous environment. Metric temporal logic is extended to allow speciication of properties about duration of system's states. We prove that every formula of the duration calculus (DC) can be translated into an equivalent MTL-R formula. Expressiveness of DC and MTL-R are co...

Metric Temporal Logic with Counting

Ability to count number of occurrences of events within a specified time interval is very useful in specification of resource bounded real time computation. In this paper, we study an extension of Metric Temporal Logic (MTL) with two different counting modalities called C and UT (until with threshold), which enhance the expressive power of MTL in orthogonal fashion. We confine ourselves only to...

Executing Metric Temporal Logic ?

Making Metric Temporal Logic Rational

We study an extension of MTL in pointwise time with rational expression guarded modality RatI(re) where re is a rational expression over subformulae. We study the decidability and expressiveness of this extension (MTL+φURatI,reφ+RatI,reφ), called RatMTL, as well as its fragment SfrMTL where only star-free rational expressions are allowed. Using the technique of temporal projections, we show tha...

Eliminating past operators in Metric Temporal Logic

We consider variants of Metric Temporal Logic (MTL) with the past operators S and SI . We show that these operators can be “eliminated” in the sense that for any formula in these logics containing the S and SI modalities, we can give a formula over an extended set of propositions which does not contain these past operators, and which is equivalent to the original formula modulo a projection ont...