  HEX-programs are an extension of the Answer Set Programming (ASP) paradigm
incorporating external means of computation into the declarative programming
language through so-called external atoms. Their semantics is defined in terms
of minimal models of the Faber-Leone-Pfeifer (FLP) reduct. Developing native
solvers for HEX-programs based on an appropriate notion of unfounded sets has
been subject to recent research for reasons of efficiency. Although this has
lead to an improvement over naive minimality checking using the FLP reduct,
testing for foundedness remains a computationally expensive task. In this work
we improve on HEX-program evaluation in this respect by identifying a syntactic
class of programs, that can be efficiently recognized and allows to entirely
skip the foundedness check. Moreover, we develop criteria for decomposing a
program into components, such that the search for unfounded sets can be
restricted. Observing that our results apply to many HEX-program applications
provides analytic evidence for the significance and effectiveness of our
approach, which is complemented by a brief discussion of preliminary
experimental validation.
