Deciding FO-Rewritability of Ontology-Mediated Queries in Linear Temporal Logic

11 Our concern is the problem of determining the data complexity of answering an ontology-mediated 12 query (OMQ) given in linear temporal logic LTL over ( Z , < ) and deciding whether it is rewritable to an 13 FO ( < )-query, possibly with extra predicates. First, we observe that, in line with the circuit complexity 14 and FO-definability of regular languages, OMQ answering in AC 0 , ACC 0 and NC 1 coincides 15 with FO ( <, ≡ )-rewritability using unary predicates x ≡ 0 (mod n ), FO ( <, MOD )-rewritability, and 16 FO ( RPR )-rewritability using relational primitive recursion, respectively. We then show that deciding 17 FO ( < )-, FO ( <, ≡ )- and FO ( <, MOD )-rewritability of LTL OMQs is ExpSpace -complete, and that 18 these problems become PSpace -complete for OMQs with a linear Horn ontology and an atomic 19 query, and also a positive query in the cases of FO ( < )- and FO ( <, ≡ )-rewritability. Further, we 20 consider FO ( < )-rewritability of OMQs with a binary-clause ontology and identify OMQ classes, for 21 which deciding it is PSpace -, Π p 2 - and coNP -complete. 22