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"State Space Exploration: Principles, Algorithms and Applications"

Final Report Summary - SSX (State Space Exploration: Principles, Algorithms and Applications)

State-space search, i.e. finding paths in huge, implicitly given graphs, is a fundamental problem in artificial intelligence and other areas of computer science. State-space search algorithms like A*, IDA* and greedy best-first search are major success stories in artificial intelligence. However, despite their success, these algorithms have deficiencies that have not been sufficiently addressed in the past:

1. They explore a monolithic model of the world rather than applying a factored perspective.

2. They are unable to formally reason about the structure and state spaces, which makes them rather opaque. This is particularly apparent in cases where an algorithm reports a problem to be unsolvable, in which case a user has no way to independently verify the correctness of the computation.

3. The major satisficing (i.e. suboptimal) search algorithms like greedy best-first search are based on rather ad-hoc intuitions and poorly understood from a theoretical perspective.

The project has targeted the first deficiency by developing a theory of reasoning about factored state spaces in terms of declarative statements in tractable constraint languages, along with accompanying algorithms for synthesizing distance estimators that are provably best among all functions of the same mathematical shape.

It has targeted the second deficiency by developing two general formal models for representing certificates of unsolvability for factored state-space search algorithms, along with certifying planning algorithms and an independent certificate verifier.

Finally, it has targeted the third deficiency by providing a thorough theoretical understanding of the nature of greedy best-first search, including its episodic nature as a sequence of essentially disconnected searches between so-called "progress states", necessary and sufficient criteria for node expansion, proofs of NP-completeness for determining the minimum or maximum number of expanded nodes under varying tie-breaking strategies, and tractability results for the case of undirected state spaces.