Certifying planning systems : witnesses for unsolvability

Classical planning tackles the problem of finding a sequence of actions that leads from an initial state to a goal. Over the last decades, planning systems have become significantly better at answering the question whether such a sequence exists by applying a variety of techniques which have become more and more complex. As a result, it has become nearly impossible to formally analyze whether a planning system is actually correct in its answers, and we need to rely on experimental evidence. One way to increase trust is the concept of certifying algorithms, which provide a witness which justifies their answer and can be verified independently. When a planning system finds a solution to a problem, the solution itself is a witness, and we can verify it by simply applying it. But what if the planning system claims the task is unsolvable? So far there was no principled way of verifying this claim. This thesis contributes two approaches to create witnesses for unsolvable planning tasks. Inductive certificates are based on the idea of invariants. They argue that the initial state is part of a set of states that we cannot leave and that contains no goal state. In our second approach, we define a proof system that proves in an incremental fashion that certain states cannot be part of a solution until it has proven that either the initial state or all goal states are such states. Both approaches are complete in the sense that a witness exists for every unsolvable planning task, and can be verified efficiently (in respect to the size of the witness) by an independent verifier if certain criteria are met. To show their applicability to state-of-the-art planning techniques, we provide an extensive overview how these approaches can cover several search algorithms, heuristics and other techniques. Finally, we show with an experimental study that generating and verifying these explanations is not only theoretically possible but also practically feasible, thus making a first step towards fully certifying planning systems

Certified Unsolvability for SAT Planning with Property Directed Reachability

While classical planning systems can usually detect if a task is unsolvable, only recent research introduced a way to verify such a claim. These methods have already been applied to a variety of explicit and symbolic search algorithms, but so far no planning technique based on SAT has been covered with them. We fill this gap by showing how property directed reachability can produce proofs while only minimally altering the framework by allowing to utilize certificates for unsolvable SAT queries within the proof. We additionally show that a variant of the algorithm that does not use SAT calls can produce proofs that fit into the existing framework without requiring any changes

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

Detecting Unsolvability Based on Separating Functions

While the unsolvability IPC sparked a multitude of planners proficient in detecting unsolvable planning tasks, there are gaps where concise unsolvability arguments are known but no existing planner can capture them without prohibitive computational effort. One such example is the sliding tiles puzzle, where solvability can be decided in polynomial time with a parity argument. We introduce separating functions, which can prove that one state is unreachable from another, and show under what conditions a potential function over any nonzero ring is a separating function. We prove that we can compactly encode these conditions for potential functions over features that are pairs, and show in which cases we can efficiently synthesize functions satisfying these conditions. We experimentally evaluate a domain-independent algorithm that successfully synthesizes such separating functions from PDDL representations of the sliding tiles puzzle, the Lights Out puzzle, and Peg Solitaire

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

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

Gibberellin A1 Metabolism Contributes to the Control of Photoperiod-Mediated Tuberization in Potato

Some potato species require a short-day (SD) photoperiod for tuberization, a process that is negatively affected by gibberellins (GAs). Here we report the isolation of StGA3ox2, a gene encoding a GA 3-oxidase, whose expression is increased in the aerial parts and is repressed in the stolons after transfer of photoperiod-dependent potato plants to SD conditions. Over-expression of StGA3ox2 under control of constitutive or leaf-specific promoters results in taller plants which, in contrast to StGA20ox1 over-expressers previously reported, tuberize earlier under SD conditions than the controls. By contrast, StGA3ox2 tuber-specific over-expression results in non-elongated plants with slightly delayed tuber induction. Together, our experiments support that StGA3ox2 expression and gibberellin metabolism significantly contribute to the tuberization time in strictly photoperiod-dependent potato plants

Optimality Certificates for Classical Planning

Algorithms are usually shown to be correct on paper, but bugs in their implementations can still lead to incorrect results. In the case of classical planning, it is fortunately straightforward to check whether a computed plan is correct. For optimal planning however, plans are additionally required to have minimal cost, which is significantly more difficult to verify. While some domain-specific approaches exists, we lack a general tool to verify optimality for arbitrary problems. We bridge this gap and introduce two approaches based on the principle of certifying algorithms, which provide a computer-verifiable certificate of correctness alongside their answer. We show that both approaches are sound and complete, analyze whether they can be generated and verified efficiently, and show how to apply them to concrete planning algorithms. The experimental evaluation shows that verifying optimality comes with a cost but is still practically feasible. Furthermore it confirms that the tested planner configurations provide optimal plans on the given instances, as all certificates were verified successfully