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arXiv · 2312.11403

Learning Temporal Properties is NP-hard

Benjamin Bordais·Daniel Neider·Rajarshi Roy
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Abstract

We investigate the complexity of LTL learning, which consists in deciding given a finite set of positive ultimately periodic words, a finite set of negative ultimately periodic words, and a bound B given in unary, if there is an LTL-formula of size less than or equal to B that all positive words satisfy and that all negative violate. We prove that this decision problem is NP-hard. We then use this result to show that CTL learning is also NP-hard. CTL learning is similar to LTL learning except that words are replaced by finite Kripke structures and we look for the existence of CTL formulae.

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Benjamin Bordais, Daniel Neider, Rajarshi Roy. 2023-12-18. Learning Temporal Properties is NP-hard. https://arxiv.org/abs/2312.11403

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