Weight Constraints as Nested Expressions
  We compare two recent extensions of the answer set (stable model) semantics
of logic programs. One of them, due to Lifschitz, Tang and Turner, allows the
bodies and heads of rules to contain nested expressions. The other, due to
Niemela and Simons, uses weight constraints. We show that there is a simple,
modular translation from the language of weight constraints into the language
of nested expressions that preserves the program's answer sets. Nested
expressions can be eliminated from the result of this translation in favor of
additional atoms. The translation makes it possible to compute answer sets for
some programs with weight constraints using satisfiability solvers, and to
prove the strong equivalence of programs with weight constraints using the
logic of here-and there.
