Monitoring for a decidable fragment of MTL-∫

Temporal logics targeting real-time systems are traditionally undecidable. Based on a restricted fragment of MTL-R, we propose a new approach for the runtime verification of hard real-time systems. The novelty of our technique is that it is based on incremental evaluation, allowing us to e↵ectively treat duration properties (which play a crucial role in real-time systems). We describe the two levels of operation of our approach: offline simplification by quantifier removal techniques; and online evaluation of a three-valued interpretation for formulas of our fragment. Our experiments show the applicability of this mechanism as well as the validity of the provided complexity results

Monitoring for a decidable fragment of MTLD

The 15th International Conference on Runtime Verification (RV'15). 22-25 September. Vienna, Austria.Temporal logics targeting real-time systems are traditionally undecidable. Based on a restricted fragment of MTLD, we propose a new approach for the runtime verification of hard real-time systems. The novelty of our technique is that it is based on incremental evaluation, allowing us to effectively treat duration properties (which play a crucial role in real-time systems). We describe the two levels of operation of our approach: offline simplification by quantifier removal techniques; and online evaluation of a three-valued interpretation for formulas of our fragment. Our experiments show the applicability of this mechanism as well as the validity of the provided complexity results

Crossing the Undecidability Border with Extensions of Propositional Neighborhood Logic over Natural Numbers

Propositional Neighborhood Logic (PNL) is an interval temporal logic featuring two modalities corresponding to the relations of right and left neighborhood between two intervals on a linear order (in terms of Allen's relations, meets and met by). Recently, it has been shown that PNL interpreted over several classes of linear orders, including natural numbers, is decidable (NEXPTIME-complete) and that some of its natural extensions preserve decidability. Most notably, this is the case with PNL over natural numbers extended with a limited form of metric constraints and with the future fragment of PNL extended with modal operators corresponding to Allen's relations begins, begun by, and before. This paper aims at demonstrating that PNL and its metric version MPNL, interpreted over natural numbers, are indeed very close to the border with undecidability, and even relatively weak extensions of them become undecidable. In particular, we show that (i) the addition of binders on integer variables ranging over interval lengths makes the resulting hybrid extension of MPNL undecidable, and (ii) a very weak first-order extension of the future fragment of PNL, obtained by replacing proposition letters by a restricted subclass of first-order formulae where only one variable is allowed, is undecidable (in contrast with the decidability of similar first-order extensions of point-based temporal logics)