A Sufficient Condition for Strong Equivalence Under the Well-Founded Semantics

We consider the problem of strong equivalence [1] under the infinite-valued semantics [2] (which is a purely model-theoretic version of the well-founded semantics). We demonstrate that two programs are now strongly equivalent if and only if they are logically equivalent under the infinite-valued logic of [2]. In particular, we show that for propositional programs strong equivalence is decidable but coNP-complete. Our results have a direct practical implication for the well-founded semantics since, as we demonstrate, if two programs are strongly equivalent under the infinite-valued semantics, then they are also strongly equivalent under the well-founded semantics.