 
Summary: Testing Boolean Function Isomorphism
Noga Alon1,
and Eric Blais2
1
Schools of Mathematics and Computer Science, Sackler Faculty of Exact Sciences,
Tel Aviv University, Tel Aviv 69978, Israel. Email: nogaa@tau.ac.il.
2
School of Computer Science, Carnegie Mellon University, Pittsburgh 15213, USA.
Email: eblais@cs.cmu.edu.
Abstract. 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 nonadaptive query complexity of the isomorphism testing prob
lem is ~(n). In fact, we show that the lower bound of (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
