We study the complexity of isomorphism testing for Boolean functions that are represented by decision trees or decision lists. Our results include a 2 s~(1/2)(ls s)~(O(1)) time algorithm for isomorphism testing of decision trees of size s. Additionally, we show:1. Isomorphism testing of rank-1 decision trees is complete for logspace.2. For r ≥ 2, isomorphism testing for rank-r decision trees is polynomial-time equivalent to Graph Isomorphism. As a consequence we obtain a 2 s~(1/2)(lg s)~(O(1)) time algorithm for isomorphism testing of decision trees of size s.3. The isomorphism problem for decision lists admits a Schaefer-type dichotomy: depending on the class of base functions, the isomorphism problem is either in polynomial time, or equivalent to Graph Isomorphism, or coNP-hard.
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