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**1 - 2**of**2**### On the Isomorphism Problem for Decision Trees and Decision Lists

"... 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(lg s) O(1) time algorithm for isomorphism testing of decision trees of size s. Additionally, we show: • Isomorphism testing of rank-1 decision tr ..."

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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 √ 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 polynomialtime equivalent to Graph Isomorphism. As a consequence we obtain a 2 √ 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.

### Around and Beyond the Isomorphism Problem for Interval Graphs

"... Ever since Reingold’s deterministic logspace algorithm [66] for undirected graph reachability, logspace algorithms for various combinatorial problems have been discovered and it is now a flourishing area of research. Notable examples include special cases of directed graph reachability and planar gr ..."

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Ever since Reingold’s deterministic logspace algorithm [66] for undirected graph reachability, logspace algorithms for various combinatorial problems have been discovered and it is now a flourishing area of research. Notable examples include special cases of directed graph reachability and planar graph isomorphism [23]. In this interesting article, Johannes Köbler, Sebastian Kuhnert and Oleg Verbitsky discuss the structural properties of interval graphs and other technical ingredients that go into their recent logspace isomorphism algorithm for interval graphs, along with some generalizations and new directions.