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Applications of Ramsey's theorem to decision tree complexity

1985
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Journal of the ACM
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Combinatorial techniques for extending lower bound results for decision trees to general types of queries are presented. Problems that are defined by simple inequalities between inputs, called order invariant problems, are considered. A decision tree is called k-bounded if each query depends on at most k variables. No further assumptions on the type of queries are made. It is proved that one can replace the queries of any k-bounded decision tree that solves an order-invariant problem over a

doi:10.1145/4221.4259
fatcat:twqmzjpvpzbs5k2kjnyeekqbwq