The ability to generate multiple plans is central to using planning in real-life applications. Top-quality planners generate sets of such top-cost plans, allowing flexibility in determining equivalent ones. In terms of the order between actions in a plan, the literature only considers two extremes -- either all orders are important, making each plan unique, or all orders are unimportant, treating two plans differing only in the order of actions as equivalent. To allow flexibility in selecting important orders, we propose specifying a subset of actions the orders between which are important, interpolating between the top-quality and unordered top-quality planning problems. We explore the ways of adapting partial order reduction search pruning techniques to address this new computational problem and present experimental evaluations demonstrating the benefits of exploiting such techniques in this setting.

We propose a general semantics for strategic abilities of agents in asynchronous systems, with and without perfect information. Based on the semantics, we show some general complexity results for verification of strategic abilities in asynchronous interaction. More importantly, we develop a methodology for partial order reduction in verification of agents with imperfect information. We show that the reduction preserves an important subset of strategic properties, with as well as without the fairness assumption. We also demonstrate the effectiveness of the reduction on a number of benchmarks. Interestingly, the reduction does not work for strategic abilities under perfect information.

Pruning techniques based on partial order reduction and symmetry elimination have recently found increasing attention for optimal planning. Although these techniques appear to be rather different, they base their pruning decisions on similar ideas from a high level perspective. In this paper, we propose safe integrations of partial order reduction and symmetry elimination for cost-optimal classical planning. We show that previously proposed symmetry-based search algorithms can safely be applied with strong stubborn sets. In addition, we derive the notion of symmetrical strong stubborn sets as a more tightly integrated concept. Our experiments show the potential of our approaches.