Finding and Exploiting LTL Trajectory Constraints in Heuristic Search

We suggest the use of linear temporal logic (LTL) for expressing declarative information about optimal solutions of search problems. We describe a general framework that associates LTLf formulas with search nodes in a heuristic search algorithm. Compared to previous approaches that integrate specific kinds of path information like landmarks into heuristic search, the approach is general, easy to prove correct and easy to integrate with other kinds of path information

Towards Certified Unsolvability in Classical Planning

While it is easy to verify that an action sequence is a solution for a classical planning task, there is no such verification capability if a task is reported unsolvable. We are therefore interested in certifi- cates that allow an independent verification of the absence of solutions. We identify promising concepts for certificates that can be generated by a wide range of planning approaches. We present a first proposal of unsolvability certificates and sketch ideas how the underlying concepts can be used as part of a more flexible unsolvability proof system

Unsolvability Certificates for Classical Planning

The plans that planning systems generate for solvable planning tasks are routinely verified by independent validation tools. For unsolvable planning tasks, no such validation capabilities currently exist. We describe a family of certificates of unsolvability for classical planning tasks that can be efficiently verified and are sufficiently general for a wide range of planning approaches including heuristic search with delete relaxation, critical-path, pattern database and linear merge-and-shrink heuristics, symbolic search with binary decision diagrams, and the Trapper algorithm for detecting dead ends. We also augmented a classical planning system with the ability to emit certificates of unsolvability and implemented a planner-independent certificate validation tool. Experiments show that the overhead for producing such certificates is tolerable and that their validation is practically feasible

On Producing Shortest Cost-Optimal Plans

Cost-optimal planning is at the heart of planning research, with many existing planners that produce provably optimal solutions. While some applications pose additional restrictions, such as producing shortest (in the number of actions) among the cost-optimal plans, standard cost-optimal planning does not provide such a guarantee. We discuss two possible approaches to produce provably the shortest among the costoptimal plans, one corresponding to an instantiation of costalgebraic A∗, the other based on a cost transformation. We formally prove that the new cost-transformation method indeed produces the shortest among the cost-optimal plans and empirically compare the performance of the approaches in different configurations

Cost Partitioning Heuristics for Stochastic Shortest Path Problems

In classical planning, cost partitioning is a powerful method which allows to combine multiple admissible heuristics while retaining an admissible bound. In this paper, we extend the theory of cost partitioning to probabilistic planning by generalizing from deterministic transition systems to stochastic shortest path problems (SSPs). We show that fundamental results related to cost partitioning still hold in our extended theory. We also investigate how to optimally partition costs for a large class of abstraction heuristics for SSPs. Lastly, we analyze occupation measure heuristics for SSPs as well as the theory of approximate linear programming for reward-oriented Markov decision processes. All of these fit our framework and can be seen as cost-partitioned heuristics

A Proof System for Unsolvable Planning Tasks

While traditionally classical planning concentrated on finding plans for solvable tasks, detecting unsolvable instances has recently attracted increasing interest. To preclude wrong results, it is desirable that the planning system provides a certificate of unsolvability that can be independently verified. We propose a rule-based proof system for unsolvability where a proof establishes a knowledge base of verifiable basic statements and applies a set of derivation rules to infer the unsolvability of the task from these statements. We argue that this approach is more flexible than a recent proposal of inductive certificates of unsolvability and show how our proof system can be used for a wide range of planning techniques

Optimal planning in the presence of conditional effects : extending LM-Cut with context-splitting

The LM-Cut heuristic is currently the most successful heuristic in optimal STRIPS planning but it cannot be applied in the presence of conditional effects. Keyder, Hoffmann and Haslum recently showed that the obvious extensions to such effects ruin the nice theoretical properties of LM-Cut. We propose a new method based on context splitting that preserves these properties

Inductive Certificates of Unsolvability for Domain-Independent Planning

If a planning system outputs a solution for a given problem, it is simple to verify that the solution is valid. However, if a planner claims that a task is unsolvable, we currently have no choice but to trust the planner blindly. We propose a sound and complete class of certificates of unsolvability, which can be verified efficiently by an independent program. To highlight their practical use, we show how these certificates can be generated for a wide range of state-of-the-art planning techniques with only polynomial overhead for the planner

On the expressive power of non-linear Merge-and-Shrink representations

We prove that general merge-and-shrink representations are strictly more powerful than linear ones by showing that there exist problem families that can be represented compactly with general merge-and-shrink representations but not with linear ones. We also give a precise bound that quantifies the necessary blowup incurred by conversions from general merge-and-shrink representations to linear representations or BDDs/ADDs. Our theoretical results suggest an untapped potential for non-linear merging strategies and for the use of non-linear merge-and-shrink-like representations within symbolic search