A temporal model describes processes as a sequence of observable events characterised by distinguishable actions in time. Conformance checking allows these models to determine whether any sequence of temporally ordered and fully-observable events complies with their prescriptions. The latter aspect leads to Explainable and Trustworthy AI, as we can immediately assess the flaws in the recorded behaviours while suggesting any possible way to amend the wrongdoings. Recent findings on conformance checking and temporal learning lead to an interest in temporal models beyond the usual business process management community, thus including other domain areas such as Cyber Security, Industry 4.0, and e-Health. As current technologies for accessing this are purely formal and not ready for the real world returning large data volumes, the need to improve existing conformance checking and temporal model mining algorithms to make Explainable and Trustworthy AI more efficient and competitive is increasingly pressing. To effectively meet such demands, this paper offers KnoBAB, a novel business process management system for efficient Conformance Checking computations performed on top of a customised relational model. This architecture was implemented from scratch after following common practices in the design of relational database management systems. After defining our proposed temporal algebra for temporal queries (xtLTLf), we show that this can express existing temporal languages over finite and non-empty traces such as LTLf. This paper also proposes a parallelisation strategy for such queries, thus reducing conformance checking into an embarrassingly parallel problem leading to super-linear speed up. This paper also presents how a single xtLTLf operator (or even entire sub-expressions) might be efficiently implemented via different algorithms, thus paving the way to future algorithmic improvements. Finally, our benchmarks highlight that our proposed implementation of xtLTLf (KnoBAB) outperforms state-of-the-art conformance checking software running on LTLf logic.

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This paper extends our seminal paper on KnoBAB for efficient Conformance Checking computations performed on top of a customised relational model. After defining our proposed temporal algebra for temporal queries (xtLTLf ), we show that this can express existing temporal languages over finite and non-empty traces such as LTLf . This paper also proposes a parallelisation strategy for such queries thus reducing conformance checking into an embarrassingly parallel problem leading to super-linear speed up. This paper also presents how a single xtLTLf operator (or even entire sub-expressions) might be efficiently implemented via different algorithms thus paving the way to future algorithmic improvements. Finally, our benchmarks remark that our proposed implementation of xtLTLf (KnoBAB) outperforms state-of-the-art conformance checking software running on LTLf logic, be it data or dateless.

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