Unsolvability Certificates for Classical Planning

Abstract

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.

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.…”

A Proof System for Unsolvable Planning Tasks

“…Following our model from Eriksson et al (2017), we use restricted classes of logical formulas and formula-like structures to obtain compact set representations, where a formula ϕ over the state variables represents all states that are satisfying assignments for ϕ. Specifically, we consider the following four representations for state sets:…”

“…For (4a) and (4b), Theorem 4 of Eriksson et al (2017) describes how to express the test ϕ [{a}] ⊆ ψ as an entailment test of the form α(ϕ, a) |= ψ, where α(ϕ, a) is a BDD/Horn formula/2CNF formula if ϕ is and can be computed in polynomial time. They do not consider an arbitrary formula ψ, but the proof generalizes directly to this case.…”

“…All unsolvability certificates in our previous approach are based on inductive sets, which are sets S of states that are closed under progression, i.e., S[A] ⊆ S. The most basic version are inductive certificates. Definition 4 (Inductive Certificate, Eriksson, Röger, and Helmert 2017). An inductive certificate for a state s of task Π is given by a set S ⊆ S(Π) of states such that 1. s ∈ S, 2.…”

“…In the SAT community it is common practice that a solver that identifies a formula as unsolvable can generate a proof of unsolvability that can be verified independently by another program. In our previous work (Eriksson, Röger, and Helmert 2017) we introduced a similar notion of unsolvability certificates for planning problems. These so-called inductive certificates have several desirable properties: they are complete in the sense that for every unsolvable task there exists a certificate that certifies unsolvability; they are efficiently verifiable in the sense that an independent verifier can validate certificates in polynomial time in the certificate size; and they are fairly general in the sense that a number of commonly used planning techniques can be modified to generate certificates of the required form with polynomial overhead.…”