Metric Interval Temporal Logic ( $$\textsf {MITL} $$ ) is a popular formalism for specifying properties of reactive systems with timing constraints. Existing approaches to using $$\textsf {MITL} $$ in verification tasks, however, have notable drawbacks: they either support only limited fragments of the logic (the future only fragment $$\textsf {MITL} [\textsf{Fut}]$$ ) or allow for only incomplete verification. This paper introduces $$\textsc {MightyPPL} $$ , a new tool for translating formulae in Metric Interval Temporal Logic with Past and Pnueli modalities ( $$\textsf {MITPPL} $$ ) over the pointwise semantics into timed automata, enabling satisfiability and model checking of this expressive specification logic over both finite and infinite timed words. $$\textsc {MightyPPL} $$ optimises performance via specialised constructions for simple cases, a novel symbolic transition encoding, and a symmetry reduction technique that yields an exponential improvement in reachable discrete states. The tool generates language-equivalent automata compatible with back-ends such as Uppaal, TChecker, and LTSmin. Our evaluation demonstrates that $$\textsc {MightyPPL} $$ significantly outperforms the state-of-the-art tool $$\textsc {MightyL} $$ on future-only fragments and across various benchmarks.

We demonstrate a surprising and first-of-its-kind expressive equivalence between decidable metric and freeze logics over timed words in pointwise semantics. Our main result states that Metric Interval Temporal Logic with future, past and Pnueli modalities, MITPPL, and full unilateral timed propositional temporal logic with both future and past temporal modalities, UPTL, have identical expressiveness. One of the highlights of this paper, which allows for this equivalence, is to prove that UPTL formulas admit monadic decomposition. Our result also implies that several decidable logics for real-time specifications, such as one-variable UPTL, unilateral MITPPL, and Q2MLO, are all expressively equivalent, and the reductions between them are effective. Hence, our result unifies the fragmented expressiveness boundary of timed temporal logics. As corollaries, we resolve the open question of the decidability for full UPTL, and the variable or clock hierarchy problem for the future fragment of UPTL.

We study the expressiveness of the pointwise interpretations (i.e. over timed words) of some predicate and temporal logics with metric and counting features. We show that counting in the unit interval (0,1) is strictly weaker than counting in (0,b) with arbitrary b≥0; moreover, allowing the latter to be included in temporal logics leads to expressive completeness for the metric predicate logic Q2MLO, recovering the corresponding result for the continuous interpretations (i.e. over signals). Exploiting this connection, we show that in contrast to the continuous case, adding ‘punctual’ predicates into Q2MLO is still insufficient for the full expressive power of the Monadic First-Order Logic of Order and Metric (FO[<,+1]); as a remedy, we propose a generalisation of the recently proposed Pnueli automata modalities and show that the resulting metric temporal logic is expressively complete for FO[<,+1]. On the practical side, we propose a compositional construction from metric interval temporal logic with counting or similar extensions to timed automata, which is more amenable to implementation based on existing tools that support on-the-fly model checking.

Binary instrumentation and rewriting frameworks provide a powerful way of implementing custom analysis and transformation techniques for applications ranging from performance profiling to security monitoring. However, using these frameworks to write even simple analyses and transformations is non-trivial. Developers often need to write framework-specific boilerplate code and work with low-level and complex programming details. This not only results in hundreds (or thousands) of lines of code, but also leaves significant room for error. To address this, we introduce Cinnamon, a domain-specific language designed to write programs for binary profiling and monitoring. Cinnamon's abstractions allow the programmer to focus on implementing their technique in a platform-independent way, without worrying about complex lower-level details. Programmers can use these abstractions to perform analysis and instrumentation at different locations and granularity levels in the binary. The flexibility of Cinnamon also enables its programs to be mapped to static, dynamic or hybrid analysis and instrumentation approaches. As a proof of concept, we target Cinnamon to three different binary frameworks by implementing a custom Cinnamon to C/C++ compiler and integrating the generated code within these frameworks. We further demonstrate the ability of Cinnamon to express a range of profiling and monitoring tools through different use-cases.

It is well known that (timed) ω-regular properties such as 'p holds at every even position' and 'p occurs at least three times within the next 10 time units' cannot be expressed in Metric Interval Temporal Logic (MITL) and Event Clock Logic (ECL). A standard remedy to this deficiency is to extend these with modalities defined in terms of automata. In this paper, we show that the logics EMITL0, ∞ (adding non-deterministic finite automata modalities into the fragment of MITL with only lower- and upper-bound constraints) and EECL (adding automata modalities into ECL) are already as expressive as EMITL (full MITL with automata modalities). In particular, the satisfiability and model-checking problems for EMITL0, ∞ and EECL are PSPACE-complete, whereas the same problems for EMITL are EXPSPACE-complete. We also provide a simple translation from EMITL0, ∞ to diagonal-free timed automata, which enables practical satisfiability and model checking based on off-the-shelf tools.

We study the satisfiability and model-checking problems for timed hyperproperties specified with HyperMTL, a timed extension of HyperLTL. Depending on whether interleaving of events in different traces is allowed, two possible semantics can be defined for timed hyperproperties: asynchronous and synchronous. While the satisfiability problem can be decided similarly to HyperLTL regardless of the choice of semantics, we show that the model-checking problem, unless the specification is alternation-free, is undecidable even when very restricted timing constraints are allowed. On the positive side, we show that model checking HyperMTL with quantifier alternations is possible under certain conditions in the synchronous semantics, or when there is a fixed bound on the length of the time domain.

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 $q \in \mathbb{Q}$ 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.

Metric Interval Temporal Logic (MITL) is an extension of the classical Linear Time Logic (LTL) that can be used to characterise real-time properties of computer systems. While the practical interest of MITL is undeniable, there is still today a remarkable lack of tool support for this logic. In this short paper, we report on our on-going work effort to complete the theoretical knowledge about MITL. We also report on our recently introduced tool MightyL, which translates MITL formulae into timed automata, enabling efficient model-checking of this logic. Finally, we sketch the future directions of our current line of research, which will be to extend MightyL to support reactive synthesis of MITL properties.

It has been argued that the most suitable semantic model for real-time formalisms is the non-negative real line (signals), i.e. the continuous semantics, which naturally captures the continuous evolution of system states. Existing tools like UPPAAL are, however, based on omega-sequences with timestamps (timed words), i.e. the pointwise semantics. Furthermore, the support for logic formalisms is very limited in these tools. In this article, we amend these issues by a compositional translation from Metric Temporal Interval Logic (MITL) to signal automata. Combined with an emptiness-preserving encoding of signal automata into timed automata, we obtain a practical automata-based approach to MITL model-checking over signals. We implement the translation in our tool MightyL and report on case studies using LTSmin as the back-end.