Aligning Metric Temporal Constraints and Event Logs via Numeric Planning

In business process (BP) execution, meeting deadlines and optimizing response time is essential to ensuring efficiency and compliance. Metric temporal constraints, which define precise timing requirements between BP activities, can be effectively modeled using Timed Declare, a declarative BP modeling language grounded in Metric Temporal Logic on finite traces (mtlf) that extends Declare with quantitative time restrictions. Within this framework, Timed Trace Alignment (TTA) refers to the problem of determining the optimal execution sequence of a BP model, expressed as a collection of Timed Declare constraints, that best reconstructs an observed log trace of the same BP to detect deviations and suggest corrective actions. In this paper, we propose a technique based on theoretic manipulations of 1-clock deterministic timed automata (1-DTAs) to formalize the TTA problem as a state-space search over these automata. Then, we show how our technique can be encoded as a numeric planning problem in Artificial Intelligence (AI), which enables computing optimal alignments. Experimental results show the feasibility and scalability of our technique.