Two boolean functions f, g : {0,1} n →{0,1} are isomorphic if they are identical up to relabeling of the input variables. We consider the problem of testing whether two functions are isomorphic or far from being isomorphic with as few queries as possible.

In the setting where one of the functions is known in advance, we show that the non-adaptive query complexity of the isomorphism testing problem is \(\tilde{\Theta}(n)\). In fact, we show that the lower bound of Ω(n) queries for testing isomorphism to g holds for almost all functions g.

In the setting where both functions are unknown to the testing algorithm, we show that the query complexity of the isomorphism testing problem is \(\tilde{\Theta}(2^{n/2})\). The bound in this result holds for both adaptive and non-adaptive testing algorithms.


Boolean Function Query Complexity Property Testing Testing Algorithm Graph Isomorphism 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Noga Alon
    • 1
  • Eric Blais
    • 2
  1. 1.Schools of Mathematics and Computer Science, Sackler Faculty of Exact SciencesTel Aviv UniversityTel AvivIsrael
  2. 2.School of Computer ScienceCarnegie Mellon UniversityPittsburghUSA

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