A general model of abstraction of graphs

Christer Bäckström, Peter Jonsson, A framework for analysing state-abstraction methods, Artificial Intelligence, Volume 302, 2022 DOI: 10.1016/j.artint.2021.103608.

Abstraction has been used in combinatorial search and action planning from the very beginning of AI. Many different methods and formalisms for state abstraction have been proposed in the literature, but they have been designed from various points of view and with varying purposes. Hence, these methods have been notoriously difficult to analyse and compare in a structured way. In order to improve upon this situation, we present a coherent and flexible framework for modelling abstraction (and abstraction-like) methods based on graph transformations. The usefulness of the framework is demonstrated by applying it to problems in both search and planning. We model six different abstraction methods from the planning literature and analyse their intrinsic properties. We show how to capture many search abstraction concepts (such as avoiding backtracking between levels) and how to put them into a broader context. We also use the framework to identify and investigate connections between refinement and heuristics—two concepts that have usually been considered as unrelated in the literature. This provides new insights into various topics, e.g. Valtorta’s theorem and spurious states. We finally extend the framework with composition of transformations to accommodate for abstraction hierarchies, and other multi-level concepts. We demonstrate the latter by modelling and analysing the merge-and-shrink abstraction method.

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