7 research outputs found
On the expressiveness of MTL variants over dense time
Abstract. The basic modal operator bounded until of Metric Temporal Logic (MTL) comes in several variants. In particular it can be strict (when it does not constrain the current instant) or not, and matching (when it requires its two arguments to eventually hold together) or not. This paper compares the relative expressiveness of the resulting MTL variants over dense time. We prove that the expressiveness is not affected by the variations when considering non-Zeno interpretations and arbitrary nesting of temporal operators. On the contrary, the expressiveness changes for flat (i.e., without nesting) formulas, or when Zeno interpretations are allowed.
Model-checking Timed Temporal Logics
AbstractIn this paper, we present several timed extensions of temporal logics, that can be used for model-checking real-time systems. We give different formalisms and the corresponding decidability/complexity results. We also give intuition to explain these results
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]
Generalizing Non-Punctuality for Timed Temporal Logic with Freeze Quantifiers
Metric Temporal Logic (MTL) and Timed Propositional Temporal Logic (TPTL) are
prominent real-time extensions of Linear Temporal Logic (LTL). In general, the
satisfiability checking problem for these extensions is undecidable when both
the future U and the past S modalities are used. In a classical result, the
satisfiability checking for MITL[U,S], a non punctual fragment of MTL[U,S], is
shown to be decidable with EXPSPACE complete complexity. Given that this notion
of non punctuality does not recover decidability in the case of TPTL[U,S], we
propose a generalization of non punctuality called \emph{non adjacency} for
TPTL[U,S], and focus on its 1-variable fragment, 1-TPTL[U,S]. While non
adjacent 1-TPTL[U,S] appears to be be a very small fragment, it is strictly
more expressive than MITL. As our main result, we show that the satisfiability
checking problem for non adjacent 1-TPTL[U,S] is decidable with EXPSPACE
complete complexity
On the expressiveness and monitoring of metric temporal logic
It is known that Metric Temporal Logic (MTL) is strictly less expressive than the Monadic First-Order Logic of Order and Metric (FO[<, +1]) when interpreted over timed words; this remains true even when the time domain is bounded a priori. In this work, we present an extension of MTL with the same expressive power as FO[<, +1] over bounded timed words (and also, trivially, over time-bounded signals). We then show that expressive completeness also holds in the general (time-unbounded) case if we allow the use of rational constants q ∈ Q in formulas. This extended version of MTL therefore yields a definitive real-time analogue of Kamp’s theorem. As an application, we propose a trace-length independent monitoring procedure for our extension of MTL, the first such procedure in a dense real-time setting