Abstract
Metric temporal logic (MTL) is one of the most prominent specification formalisms for real-time systems. Over infinite timed words, full MTL is undecidable, but satisfiability for its safety fragment was proved decidable several years ago [18]. The problem is also known to be equivalent to a fair termination problem for a class of channel machines with insertion errors. However, the complexity has remained elusive, except for a non-elementary lower bound. Via another equivalent problem, namely termination for a class of rational relations, we show that satisfiability for safety MTL is not primitive recursive, yet is Ackermannian, i.e., among the simplest non-primitive recursive problems. This is surprising since decidability was originally established using Higman’s Lemma, suggesting a much higher non-multiply recursive complexity.
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Lazić, R., Ouaknine, J., Worrell, J. (2013). Zeno, Hercules and the Hydra: Downward Rational Termination Is Ackermannian. In: Chatterjee, K., Sgall, J. (eds) Mathematical Foundations of Computer Science 2013. MFCS 2013. Lecture Notes in Computer Science, vol 8087. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40313-2_57
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DOI: https://doi.org/10.1007/978-3-642-40313-2_57
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