Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Monotonicity testing over general poset domains
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Improved Testing Algorithms for Monotonicity
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
A lower bound for testing juntas
Information Processing Letters
Journal of Computer and System Sciences - Special issue on FOCS 2002
The Difficulty of Testing for Isomorphism against a Graph That Is Given in Advance
SIAM Journal on Computing
Testing for Concise Representations
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Probabilistic computations: Toward a unified measure of complexity
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
SIAM Journal on Computing
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Property Testing: A Learning Theory Perspective
Foundations and Trends® in Machine Learning
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Algorithmic and Analysis Techniques in Property Testing
Foundations and Trends® in Theoretical Computer Science
Lower Bounds for Testing Function Isomorphism
CCC '10 Proceedings of the 2010 IEEE 25th Annual Conference on Computational Complexity
Untestable properties in the kahr-moore-wang class
WoLLIC'11 Proceedings of the 18th international conference on Logic, language, information and computation
Information Processing Letters
Nearly tight bounds for testing function isomorphism
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Isomorphism testing of boolean functions computable by constant-depth circuits
LATA'12 Proceedings of the 6th international conference on Language and Automata Theory and Applications
| Hi-index | 0.00 |
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 &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 Θ(2n/2). The bound in this result holds for both adaptive and non-adaptive testing algorithms.