Cartesian abstractions can flexibly approximate planning tasks to generate admissible heuristic functions. Constrained abstractions use state constraints, such as mutexes, to eliminate parts of the abstraction that cannot belong to solutions for the original problem. While this has been successfully applied to simple forms of abstraction, no previous work has explored how to do this for Cartesian abstractions. We introduce constrained Cartesian abstractions, which leverage state constraints in multiple ways: to prune spurious transitions and to simplify or even remove abstract states. Moreover, we also use disambiguation to better guide the counterexample-guided process used to generate the abstractions. Our experimental results show that the resulting constrained Cartesian abstractions induce more informed heuristics than their non-constrained counterpart.

In planning tasks, conditional effects model action outcomes that depend on the current state of the world. Conditional effects are a crucial modeling feature since compiling them away can cause an exponential growth in task size. However, only a few admissible heuristics support them. To add abstraction heuristics to this set, we show how to compute projections, Cartesian abstractions and merge-and-shrink abstractions for tasks with conditional effects. Our experiments show that these heuristics are competitive with, and often surpass, the state-of-the-art for conditional-effect tasks.

Counterexample-Guided Abstraction Refinement (CEGAR) is a prominent technique to generate Cartesian abstractions for guiding search in cost- optimal planning. The core idea is to iteratively refine the abstraction, finding a flaw of the current optimal abstract plan. All existing approaches find these flaws by executing the abstract plan using progression in the original state space. Instead, we propose to do backward refinements by using regression from the goals. This results in a new type of flaw, that can identify invalid plan suffixes. The resulting abstractions are less focused on the initial state, but more informative on average, significantly improving the performance of current CEGAR-based techniques. Furthermore, they can be combined with forward refinements in several bidirectional strategies that provide the benefits of both methods.

Counterexample-Guided Abstraction Refinement (CEGAR) is a prominent technique to generate Cartesian abstractions for guiding search in cost-optimal planning. The core idea is to iteratively refine the abstraction, by finding a flaw in the current optimal abstract plan. Previous works find only a single flaw, by executing the abstract plan in the concrete state space and stopping when such execution cannot be continued. We show, however, that many flaws can be identified on a single plan. To that end, we introduce sequence flaws, which execute the plan in a Cartesian relaxation of the task to characterize issues beyond the first flaw found along its execution. This greatly increases the flexibility of CEGAR regarding how to refine the abstraction. Our experiments show that a high number of sequence flaws exist in most abstract plans across existing benchmarks. We observe that the selected flaw has a high impact on the resulting heuristic, opening new research opportunities for better selection strategies.