  Runtime monitoring is one of the central tasks in the area of operational
decision support for business process management. In particular, it helps
process executors to check on-the-fly whether a running process instance
satisfies business constraints of interest, providing an immediate feedback
when deviations occur. We study runtime monitoring of properties expressed in
LTL on finite traces (LTLf), and in its extension LDLf. LDLf is a powerful
logic that captures all monadic second order logic on finite traces, and that
is obtained by combining regular expressions with LTLf, adopting the syntax of
propositional dynamic logic (PDL). Interestingly, in spite of its greater
expressivity, \LDLf has exactly the same computational complexity of LTLf.
  We show that LDLf is able to declaratively express, in the logic itself, not
only the constraints to be monitored, but also the de-facto standard RV-LTL
monitors. On the one hand, this enables us to directly employ the standard
characterization of LDLf based on finite-state automata to monitor constraints
in a fine-grained way. On the other hand, it provides the basis for
declaratively expressing sophisticated metaconstraints that predicate on the
monitoring state of other constraints, and to check them by relying on standard
logical services instead of ad-hoc algorithms.
  In addition, we devise a direct translation of LDLf formulae into
nondeterministic finite-state automata, avoiding to detour to Buchi automata or
alternating automata. We then report on how this approach has been effectively
implemented using Java to manipulate LDLf formulae and their corresponding
monitors, and the well-known ProM process mining suite as underlying
operational decision support infrastructure.
