  The last decade has seen a variety of Asset-Transfer systems designed for
decentralized environments. To address the problem of double-spending, these
systems inherently make strong model assumptions and spend a lot of resources.
In this paper, we take a non-orthodox approach to the double-spending problem
that might suit better realistic environments in which these systems are to be
deployed. We consider the decentralized trust setting, where each user may
independently choose who to trust by forming its local quorums. In this
setting, we define $k$-Spending Asset Transfer, a relaxed version of asset
transfer which bounds the number of times the same asset can be spent. We
establish a precise relationship between the decentralized trust assumptions
and $k$, the optimal spending number of the system.
