Our concern is the problem of determining the data complexity of answering an ontology-mediated query (OMQ) formulated in linear temporal logic LTL over (Z,<) and deciding whether it is rewritable to an FO(<)-query, possibly with some extra predicates. First, we observe that, in line with the circuit complexity and FO-definability of regular languages, OMQ answering in AC^0, ACC^0 and NC^1 coincides with FO(<,\equiv)-rewritability using unary predicates x \equiv 0 (mod n), FO(<,MOD)-rewritability, and FO(RPR)-rewritability using relational primitive recursion, respectively. We prove that, similarly to known PSPACE-completeness of recognising FO(<)-definability of regular languages, deciding FO(<,\equiv)- and FO(<,MOD)-definability is also \PSPACE-complete (unless ACC^0 = NC^1). We then use this result to show that deciding FO(<)-, FO(<,\equiv)- and FO(<,MOD)-rewritability of LTL OMQs is EXPSPACE-complete, and that these problems become PSPACE-complete for OMQs with a linear Horn ontology and an atomic query, and also a positive query in the cases of FO(<)- and FO(<,\equiv)-rewritability. Further, we consider FO(<)-rewritability of OMQs with a binary-clause ontology and identify OMQ classes, for which deciding it is PSPACE-, Pi_2^p- and coNP-complete.

翻译：首先,我们注意到,根据常规语言的电路复杂性和可定义性,OMQ在ACQ0、ACC0、0和NC ⁇ 1中的回答与使用直线时间逻辑LTL(Mond n)、FO( < MOD)-可替换性和FO(RPR)-可替换性的数据复杂性(OMQ)的问题,以及决定它是否适合FO( < ) 和FO( < equiv)-可替换性(OMQ)、F(FO( < )-可更新性)和FO(RPR)-可替换性的问题,我们首先注意到,根据常规语言的电路复杂性和可定义性,OMQQ(FO)(FO)和直线性(O-可更新性,我们然后使用这个结果来决定FO(MR)-MLQ(FO) 和直径(FO-LLLT)的稳定性问题。