Certified Unsolvability for SAT Planning with Property Directed Reachability

Abstract

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.

Compiling HTN Plan Verification Problems into HTN Planning Problems

“…To provide a meaningful explanation on why verification failed, one could incorporate explanations for the unsolvability of the generated planning problem. Providing certificates for unsolvability of planning problems is an active field of research, at least in classical planning (Eriksson, Röger, and Helmert 2017;Eriksson and Helmert 2020). I.e., like for the solvers, we benefit from established research directions in planning and their future progress.…”

Can LLMs Fix Issues with Reasoning Models? Towards More Likely Models for AI Planning

“…This is because when a model is unsolvable, there is no artifact (such as an outputted plan) to look at for debugging purposes. While there have been a lot of efforts, including an ongoing competition (Muise and Lipovetzky 2023), to detect unsolvability of planning tasks up-front to speed up calls to a planning module (Bäckström, Jonsson, and Ståhlberg 2013;Moreira and Ralha 2017), and attempts to compute or even learn heuristics (Hoffmann, Kissmann, and Torralba 2014;Ståhlberg 2017;Ståhlberg, Francès, and Seipp 2021) and produce certificates Helmert 2017, 2018;Eriksson and Helmert 2020) for unsolvable tasks, to make this process as efficient as possible, these do not help to fix the issues with the model that make it unsolvable in the first place.…”

Formally Verified SAT-Based AI Planning

“…the verified SAT solver by Blanchette et al is one to two orders of magnitude slower than Minisat (Eén and Sörensson 2003), and the verified unsatisfiability certificate checker GRAT (Lammich 2017) is faster than DRAT-trim (Wetzler, Heule, and Jr 2014). Lastly, the problem of increasing trustworthiness of 'traditional' SATbased planning was most recently raised by Eriksson and Helmert (2020). They stated, as an open problem, certifying that an unsatisfiable SAT formula encoding a planning problem indeed shows a lower bound on the solution length.…”