[2408.04486] The Complexity of Learning Temporal Properties
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Computer Science > Logic in Computer Science

arXiv:2408.04486 (cs)
[Submitted on 8 Aug 2024]

Title:The Complexity of Learning Temporal Properties

Authors:Benjamin Bordais, Daniel Neider, Rajarshi Roy
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Abstract:We consider the problem of learning temporal logic formulas from examples of system behavior. Learning temporal properties has crystallized as an effective mean to explain complex temporal behaviors. Several efficient algorithms have been designed for learning temporal formulas. However, the theoretical understanding of the complexity of the learning decision problems remains largely unexplored. To address this, we study the complexity of the passive learning problems of three prominent temporal logics, Linear Temporal Logic (LTL), Computation Tree Logic (CTL) and Alternating-time Temporal Logic (ATL) and several of their fragments. We show that learning formulas using an unbounded amount of occurrences of binary operators is NP-complete for all of these logics. On the other hand, when investigating the complexity of learning formulas with bounded amount of occurrences of binary operators, we exhibit discrepancies between the complexity of learning LTL, CTL and ATL formulas (with a varying number of agents).
Subjects: Logic in Computer Science (cs.LO)
Cite as: arXiv:2408.04486 [cs.LO]
  (or arXiv:2408.04486v1 [cs.LO] for this version)
  https://doi.org/10.48550/arXiv.2408.04486

Submission history

From: Benjamin Bordais [view email]
[v1] Thu, 8 Aug 2024 14:25:30 UTC (964 KB)
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