Learning decision trees from random examples needed for learning
Information and Computation
Hypergraph isomorphism and structural equivalence of Boolean functions
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
On the isomorphism of expressions
Information Processing Letters
Machine Learning
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
The Boolean isomorphism problem
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Isomorhism of Hypergraphs of Low Rank in Moderately Exponential Time
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
The computational complexity of equivalence and isomorphism problems
The computational complexity of equivalence and isomorphism problems
The isomorphism problem for k-trees is complete for logspace
Information and Computation
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We study the complexity of isomorphism testing for Boolean functions that are represented by decision trees or decision lists. Our results include a $2^{\sqrt{s}(\lg s)^{O(1)}}$ time algorithm for isomorphism testing of decision trees of size s. Additionally, we show: · Isomorphism testing of rank-1 decision trees is complete for logspace. · For r≥2, isomorphism testing for rank-r decision trees is polynomial-time equivalent to Graph Isomorphism. As a consequence we obtain a ${2^{\sqrt{s}(\lg s)^{O(1)}}}$ time algorithm for isomorphism testing of decision trees of size s. · 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.