This paper considers a specific fragment of Linear Temporal Logic for Finite traces, DECLAREd, which, to the best of our knowledge, we prove for the first time to be a {polytime} fragment of LTLf. We derive this in terms of the following ancillary results: we propose a set of novel LTLf equivalence rules that, when applied to \LTLf specifications, lead to an equivalent specification which can be computed faster by any existing verified temporal artificial intelligence task. We also introduce the concept of temporal non-simultaneity, prescribing that two activities shall never satisfy the same atom, and temporal short-circuit, that occurs when a specification interpreted in LTL would accept an infinitely long trace while, on LTLf, it can be rewritten so to postulate the absence of certain activity labels. We test these considerations over formal synthesis (Lydia), SAT-Solvers (AALTAF) and formal verification (KnoBAB) tools, where formal verification can be also run on top of a relational database and can be therefore expressed in terms of relational query answering. We show that all these benefit from the aforementioned assumptions, as running their tasks over a rewritten equivalent specification will improve their running times.

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.