Classical planning asks for a sequence of operators reaching a given goal. While the most common case is to compute a plan, many scenarios require more than that. However, quantitative reasoning on the plan space remains mostly unexplored. A fundamental problem is to count plans, which relates to the conditional probability on the plan space. Indeed, qualitative and quantitative approaches are well-established in various other areas of automated reasoning. We present the first study to quantitative and qualitative reasoning on the plan space. In particular, we focus on polynomially bounded plans. On the theoretical side, we study its complexity, which gives rise to rich reasoning modes. Since counting is hard in general, we introduce the easier notion of facets, which enables understanding the significance of operators. On the practical side, we implement quantitative reasoning for planning. Thereby, we transform a planning task into a propositional formula and use knowledge compilation to count different plans. This framework scales well to large plan spaces, while enabling rich reasoning capabilities such as learning pruning functions and explainable planning.

In planning with object creation, actions might introduce new objects as part of their effect. While this makes the formalism more expressive, it also renders the plan existence problem undecidable. A natural next step is to ask whether simpler fragments and relaxations are still undecidable when powered with object creation. Probably the most popular fragment is delete-free planning, where actions can only add but never delete atoms. In this work, we show that delete-free planning with object creation is still undecidable. We do so by reducing the problem of deciding whether a given atom is reached by the chase procedure to the plan existence problem. Our result implies that heuristics based on the delete relaxation may not be immediately useful for the object creation setting. We then highlight which restrictions we can apply to make delete-free planning with object creation practical.

One key decision for heuristic search algorithms is how to balance exploration and exploitation. In classical planning, the two strongest approaches for this problem are to alternate between different heuristics and to enhance heuristics with novelty measures. The most well-known planner using alternation is LAMA, which cycles between different open-lists that are ordered using different heuristics. The strongest novelty-based algorithms use best-first width search (BFWS), which prefers states that contain previously unseen combinations of atoms. Considerable effort has been put into trying to combine these two approaches, but so far, no combination has been able to significantly improve over the individual planners. In this paper, we explore the simple idea of using BFWS as just another open-list for LAMA. Our results show that adding even the strongest BFWS version to LAMA is detrimental. However, combining only parts of each approach yields a new state-of-the-art agile planner.

In recent years, large language models (LLMs) have shown remarkable performance in many problems. However, they fail to plan reliably. Specialized attempts to improve their planning capabilities still produce incorrect plans and fail to generalize to larger tasks. Furthermore, LLMs designed for explicit "reasoning" fail to compete with automated planners while increasing computational costs, which reduces one of the advantages of using LLMs. In this paper, we show how to use LLMs to always generate correct plans, even for out-of-distribution tasks of increasing size. For a given planning domain, we ask an LLM to generate several domain-dependent heuristic functions in the form of Python code, evaluate them on a set of training tasks with a greedy best-first search, and choose the best one. The resulting LLM-generated heuristic functions solve substantially more unseen out-of-distribution test tasks than end-to-end LLM planning, particularly for non-reasoning LLMs. Moreover, they also solve many more tasks than state-of-the-art domain-independent heuristics for classical planning, and are competitive with the strongest learning algorithm for domain-dependent planning. These results are impressive given that our implementation is based on a Python planner and the baselines all build upon highly optimized C++ code. In some domains, the LLM-generated heuristics expand fewer states than the baselines, showing that they are not only efficiently computable but also more informative than the state-of-the-art heuristics. Overall, our results show that sampling a set of planning heuristic functions can significantly improve the planning capabilities of LLMs.

Classical planning problems are defined using some specification language, such as PDDL. The domain expert defines action schemas, objects, the initial state, and the goal. One key aspect of PDDL is that the set of objects cannot be modified during plan execution. While this is fine in many domains, sometimes it makes modeling more complicated. This may impact the performance of planners, and it requires the domain expert to bound the number of required objects beforehand, which can be a challenge. We introduce an extension to the classical planning formalism, where action effects can create and remove objects. This problem is semi-decidable, but it becomes decidable if we can bound the number of objects in any given state, even though the state space is still infinite. On the practical side, we extend the Powerlifted planning system to support this PDDL extension. Our results show that this extension improves the performance of Powerlifted while supporting more natural PDDL models.

In classical planning, the aim is to find a sequence of deterministic actions leading from the initial to a goal state. In this work, we consider the scenario where a party who knows the solution to a planning task, called the prover, wants to convince a second party, the verifier, that it has the solution without revealing any information about the solution itself. This is relevant in domains where privacy is important, for example when plans contain sensitive information or when the solution should not be revealed upfront. We achieve this by introducing a zero-knowledge protocol for plan existence. By restricting ourselves to tasks with polynomially-bounded plan length, we are able to construct a protocol that can be run efficiently by both the prover and verifier. The resulting protocol does not rely on any reduction, has a constant number of rounds, and runs in time polynomial in the size of the task.

Heuristics for lifted planning are not yet as informed as the best heuristics for ground planning. Recent work introduced the idea of using Datalog programs to compute the additive heuristic over lifted tasks. Based on this work, we show how to compute the more informed FF heuristic in a lifted manner. We extend the Datalog program with executable annotations that can also be used to define other delete-relaxation heuristics. In our experiments, we show that a planner using the lifted FF implementation produces state-of-the-art results for lifted planners. It also reduces the gap to state-of-the-art ground planners in domains where grounding is feasible.

Generalized planning aims at computing solutions that work for all instances of the same domain. In this paper, we show that several interesting planning domains possess compact generalized heuristics that can guide a greedy search in guaranteed polynomial time to the goal, and which work for any instance of the domain. These heuristics are weighted sums of state features that capture the number of objects satisfying a certain first-order logic property in any given state. These features have a meaningful interpretation and generalize naturally to the whole domain. Additionally, we present an approach based on mixed integer linear programming to compute such heuristics automatically from the observation of small training instances. We develop two variations of the approach that progressively refine the heuristic as new states are encountered. We illustrate the approach empirically on a number of standard domains, where we show that the generated heuristics will correctly generalize to all possible instances.

For a given state space and admissible heuristic function h there is always a tie-breaking strategy for which A* expands the minimum number of states [Dechter and Pearl, 1985]. We say that these strategies have optimal expansion. Although such a strategy always exists it may depend on the instance, and we currently do not know a tie-breaker that always guarantees optimal expansion. In this paper, we study tie-breaking strategies for A*. We analyze common strategies from the literature and prove that they do not have optimal expansion. We propose a novel tie-breaking strategy using cost adaptation that has always optimal expansion. We experimentally analyze the performance of A* using several tie-breaking strategies on domains from the IPC and zero-cost domains. Our best strategy solves significantly more instances than the standard method in the literature and more than the previous state-of-the-art strategy. Our analysis improves the understanding of how to develop effective tie-breaking strategies and our results also improve the state-of-the-art of tie-breaking strategies for A*.