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In this paper, we investigate a relationship between the length-decreasing self-reducibility and the many-one-like reducibilities for partial multivalued functions. We show that if any parsimonious (manyone or metric many-one) complete function for NPMV (or NPMVg) is length-decreasing self-reducible, then any function in NPMV (or NPMVg) has a polynomial-time computable refinement. This result implies that there exists an NPMV (or NPMVg)-complete function which is not lengthdecreasing self-reducible unless P = NP. key words: partial multivalued function, length-decreasing self-reduction, many-one-like reduction

On the Length-Decreasing Self-Reducibility and the Many-One-Like Reducibilities for Partial Multivalued Functions