On Computation Complexity of True Proof Number Search
Chao Gao · arXiv (Cornell University) · 2021
We point out that the computation of true \emph{proof} and \emph{disproof} numbers for proof number search in arbitrary directed acyclic graphs is NP-hard, an important theoretical result for proof number search. The proof requires a reduction from SAT, which demonstrates that finding true proof/disproof number for arbitrary DAG is at least as hard as deciding if arbitrary SAT instance is satisfiable, thus NP-hard.