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

Abstract

SUMMARYIn 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 NPMV g ) is length-decreasing self-reducible, then any function in NPMV (or NPMV g ) has a polynomial-time computable refinement. This result implies that there exists an NPMV (or NPMV g )-complete function which is not lengthdecreasing self-reducible unless P = NP.

Autoreducibility and Completeness for Partial Multivalued Functions

“…Even though our result does not directly lead to separations of complexity classes, the results of ours and Huh et al [6] show that the same point as Faliszewski and Ogihara's one applies for the classes NPMV and NPMV g . More concretely, the results imply that there exists a complete function for NPMV or NPMV g which is autoreducible but not length-decreasing self-reducible unless P = NP.…”

“…We first refer to the notions of functions and Turing transducers stated in [4] and [6]. Let X and Y be subsets of Σ * .…”

“…We now recall two many-one-like reductions: the metric many-one and the many-one reductions [6]. Intuitively, one can make only one query to the oracle in these reductions.…”