You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Metric Temporal Logic (MTL) is a prominent specification formalism for real-time systems. In this paper, we show that the satisfiability problem for MTL over finite timed words is decidable, with non-primitive recursive complexity. We also consider the model-checking problem for MTL: whether all words accepted by a given Alur-Dill timed automaton satisfy a given MTL formula. We show that this problem is decidable over finite words. Over infinite words, we show that model checking the safety fragment of MTL--which includes invariance and time-bounded response properties--is also decidable. These results are quite surprising in that they contradict various claims to the contrary that have appeared in the literature.

Cited Abstract(s):
[1]: We introduce timed alternating tree automata as a natural extension of timed automata for the purpose of solving the model checking problem for timed computation tree logic (TCTL) following the automata-theoretic approach. This settles a problem posed by Henzinger, Kupferman, and Vardi
A class of timed alternating tree automata has been defined by Dickh " o fer and Wilke [1] in the context of model checking a real-time version of Computation Tree Logic, called TCTL @. The language-emptiness problem for these automata is undecidable in general. However, TCTL model checking reduces to a special case of language emptiness, which is shown in [1] to be decidable using Alur and Dill's clock regions construction. In contrast, bounded-dimension clock regions do not suffice in the present paper: we combine clock regions with the notion of well-quasi-orders.