Efficient Necessary-and-Sufficient Conditions for Pareto-Point Achievability

Characterize efficiently checkable necessary and sufficient conditions under which Pareto-optimal points for probabilistic programs with nondeterminism are precisely achievable by determinizations rather than merely almost achievable.

Background

The framework characterizes almost-achievable trade-offs, meaning points that can be approached arbitrarily closely by mixed determinizations, and provides exact synthesis only under sufficient conditions such as suitable Scott-closedness and the existence of optimal determinizations for scalarized objectives.

The paper identifies the gap between almost achievability and exact achievability as a central limitation of its synthesis approach. The unresolved problem is to obtain conditions that are both necessary and sufficient and can be checked efficiently, thereby deciding when Pareto-optimal points are realized exactly.