Expressivity and Complexity of the Conjunctive Core of the SIGNAL Process Query Language

Timotheus Kampik, Cem Okulmus

Abstract: With the increased adoption of process mining, there is also a need for practical solutions that work at industry scales. In this context, process querying methods (PQMs) have emerged as an important tool for drawing inferences from event logs. Here, it can be expected that industry approaches differ from academic ones, due to practical engineering and business considerations. To understand what is at the core of industry-scale PQMs, a formal analysis of the underlying languages can provide a solid foundation. To this end, we formally analyse SIGNAL, an industry-scale language for querying business process event logs developed by a large enterprise software vendor. The formal analysis shows that the core capabilities of SIGNAL, which we refer to as the SIGNAL Conjunctive Core, are more expressive than relational algebra and thus not captured by standard relational databases. We provide an upper-bound on the expressiveness via a reduction to semi-positive Datalog, which also leads to an upper bound of P-hard for the data complexity of evaluating SIGNAL Conjunctive Core queries. The findings provide first insights into how (real-world) process query languages are fundamentally different from the more generally prevalent structured query languages for querying relational databases and provide a rigorous foundation for extending the existing capabilities of the industry-scale state-of-the-art of process data querying.