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Under what conditions can query answering in OWL EL be done in PTIME?

Conjunctive query answering in OWL EL can be done in EXPTIME, and is PTIME-complete if the property hierarchy can be translated into a polynomially-sized nondeterministic finite automaton (https://www.w3.org/TR/owl2-profiles/#Computational_Properties). So, under what conditions can the property hierarchy be translated into a polynomially-sized nondeterministic finite automaton?

user10264746
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  • you should read the work from D. Calvanese and C. Lutz I guess. Not sure if this question is useful for StackOverflow. It would also be good if you give a reference to the paper with the statement in your question which makes it easier to follow. – UninformedUser Jan 18 '19 at 08:52
  • Thanks. Is there another venue for which this question would be more appropriate? – user10264746 Jan 18 '19 at 16:54
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    the role hierarchy must be *regular* and for polynomial size NFA it must be a so-called *simple* role hierarchy. This means further restriction of the syntax of regular role hierarchies to avoid the exponential blow up. See section 4.4 in [Decidability of SHIQ with complex role inclusion axioms.](http://www.cs.man.ac.uk/~ezolin/dl/bib/Decidability_of_SHIQ_with_complex_role_inclusion_axioms_(AI_2004).pdf) for the restrictions of a simple role hierarchy – UninformedUser Jan 19 '19 at 12:02

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