Expressiveness of Metric modalities for continuous time

Expressiveness of Metric Modalities for Continuous Time

We prove a conjecture by A. Pnueli and strengthen it showing a sequence of “counting modalities” none of which is expressible in the temporal logic generated by the previous modalities, over the real line, or over the positive reals. Moreover, there is no finite temporal logic that can express all of them over the real line, so that no finite metric temporal logic is expressively complete.

On the Metric Complexity of Continuous-time Systems

In this paper, metric complexities of certain classes of continuous-time systems are studied, using the time-domain sampling approach and the concepts of Kolmogorov, Gel’fand and sampling n-widths for certain classes of Sobolev space. A sampling theorem is obtained which extends Shannon’s sampling theorem to systems with possibly non-band-limited spectra. The theorem demonstrates that continuou...

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 sig...

Monitoring Dense-Time, Continuous-Semantics, Metric Temporal Logic

Integrating Discrete- and Continuous-Time Metric Temporal Logics Through Sampling

Real-time systems usually encompass parts that are best described by a continuous-time model, such as physical processes under control, together with other components that are more naturally formalized by a discrete-time model, such as digital computing modules. Describing such systems in a unified framework based on metric temporal logic requires to integrate formulas which are interpreted ove...