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Generalized Mutant Subsumption

: Mutant Subsumption is an ordering relation between the mutants of a base program, which ranks mutants according to inclusion relationships between their differentiator sets. The differentiator set of a mutant with respect to a base program is the set of inputs for which execution of the base program and the mutant produce different outcomes. In this paper we propose to reﬁne the deﬁnition of mutant subsumption by pondering, in turn: what do we consider to be the outcome of a program’s execution? under what condition do we consider that two outcomes are comparable? and under what condition do we consider that two comparable outcomes are identical? We ﬁnd that the way we answer these questions determines what it means to kill a mutant, how subsumption is deﬁned, how mutants are ordered by subsumption, and what set of mutants is minimal.