  Powerful formalisms for abstract argumentation have been proposed, among them
abstract dialectical frameworks (ADFs) that allow for a succinct and flexible
specification of the relationship between arguments, and the GRAPPA framework
which allows argumentation scenarios to be represented as arbitrary
edge-labelled graphs. The complexity of ADFs and GRAPPA is located beyond NP
and ranges up to the third level of the polynomial hierarchy. The combined
complexity of Answer Set Programming (ASP) exactly matches this complexity when
programs are restricted to predicates of bounded arity. In this paper, we
exploit this coincidence and present novel efficient translations from ADFs and
GRAPPA to ASP. More specifically, we provide reductions for the five main ADF
semantics of admissible, complete, preferred, grounded, and stable
interpretations, and exemplify how these reductions need to be adapted for
GRAPPA for the admissible, complete and preferred semantics. Under
consideration in Theory and Practice of Logic Programming (TPLP).
