Automatic Verification for Soundness of Bounded QNP Abstractions for Generalized Planning

Generalized planning (GP) studies the computation of general solutions for a set of planning problems. Computing general solutions with correctness guarantee has long been a key issue in GP. Abstractions are widely used to solve GP problems. For example, a popular abstraction model for GP is qualitative numeric planning (QNP), which extends classical planning with non-negative real variables that can be increased or decreased by some arbitrary amount. The refinement of correct solutions of sound abstractions are solutions with correctness guarantees for GP problems. More recent literature proposed a uniform abstraction framework for GP and gave model-theoretic definitions of sound and complete abstractions for GP problems. In this paper, based on the previous work, we explore automatic verification of sound abstractions for GP. Firstly, we present a proof-theoretic characterization for sound abstractions. Secondly, based on the characterization, we give a sufficient condition for sound abstractions with deterministic actions. Then we study how to verify the sufficient condition when the abstraction models are bounded QNPs where integer variables can be incremented or decremented by one. To this end, we develop methods to handle counting and transitive closure, which are often used to define numerical variables. Finally, we implement a sound bounded QNP abstraction verification system and report experimental results on several domains.