47 research outputs found
Partially Punctual Metric Temporal Logic is Decidable
Metric Temporal Logic \mathsf{MTL}[\until_I,\since_I] is one of the most
studied real time logics. It exhibits considerable diversity in expressiveness
and decidability properties based on the permitted set of modalities and the
nature of time interval constraints . Henzinger et al., in their seminal
paper showed that the non-punctual fragment of called
is decidable. In this paper, we sharpen this decidability
result by showing that the partially punctual fragment of
(denoted ) is decidable over strictly monotonic finite point
wise time. In this fragment, we allow either punctual future modalities, or
punctual past modalities, but never both together. We give two satisfiability
preserving reductions from to the decidable logic
\mathsf{MTL}[\until_I]. The first reduction uses simple projections, while
the second reduction uses a novel technique of temporal projections with
oversampling. We study the trade-off between the two reductions: while the
second reduction allows the introduction of extra action points in the
underlying model, the equisatisfiable \mathsf{MTL}[\until_I] formula obtained
is exponentially succinct than the one obtained via the first reduction, where
no oversampling of the underlying model is needed. We also show that
is strictly more expressive than the fragments
\mathsf{MTL}[\until_I,\since] and \mathsf{MTL}[\until,\since_I]