We introduce and analyze new envy-based fairness concepts for agents with weights that quantify their entitlements in the allocation of indivisible items. propose two variants weighted envy-freeness up to one item (WEF1): strong , where envy can be eliminated by removing an from envied agent’s bundle, weak either (as version) or replicating bundle envying bundle. show additive valuations, is bo...

State of the art formal verification is based on methods and its goal proving given correctness properties. For example, a PSTM scheduler was modeled in CSP order to prove deadlock-freeness starvation-freeness. However, as this paper shows, using solely not sufficient. Therefore, we propose complete trustworthy software, which jointly uses model testing. As an first test previous transaction by...

Envy-freeness and Pareto Efficiency are two major goals in welfare economics. The existence of an allocation that satisfies both conditions has been studied for a long time. Whether items indivisible or divisible, it is impossible to achieve envy-freeness ex post even the case people items. In contrast, this work, we prove that, any cardinal utility functions (including complementary utilities ...