  We explore different ways of implementing temporal constraints expressed in
an extension of Answer Set Programming (ASP) with language constructs from
dynamic logic. Foremost, we investigate how automata can be used for enforcing
such constraints. The idea is to transform a dynamic constraint into an
automaton expressed in terms of a logic program that enforces the satisfaction
of the original constraint. What makes this approach attractive is its
independence of time stamps and the potential to detect unsatisfiability. On
the one hand, we elaborate upon a transformation of dynamic formulas into
alternating automata that relies on meta-programming in ASP. This is the first
application of reification applied to theory expressions in gringo. On the
other hand, we propose two transformations of dynamic formulas into monadic
second-order formulas. These can then be used by off-the-shelf tools to
construct the corresponding automata. We contrast both approaches empirically
with the one of the temporal ASP solver telingo that directly maps dynamic
constraints to logic programs. Since this preliminary study is restricted to
dynamic formulas in integrity constraints, its implementations and (empirical)
results readily apply to conventional linear dynamic logic, too.
