Testing Boolean function isomorphism

Noga Alon; Eric Blais

doi:10.1007/978-3-642-15369-3_30

Testing Boolean function isomorphism

Noga Alon, Eric Blais

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

18 Scopus citations

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 non-adaptive query complexity of the isomorphism testing problem is Θ(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(2^n/2). The bound in this result holds for both adaptive and non-adaptive testing algorithms.

Original language	English (US)
Title of host publication	Approximation, Randomization, and Combinatorial Optimization
Subtitle of host publication	Algorithms and Techniques - 13th International Workshop, APPROX 2010 and 14th International Workshop, RANDOM 2010, Proceedings
Pages	394-405
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-642-15369-3_30
State	Published - 2010
Externally published	Yes
Event	13th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2010 and 14th International Workshop on Randomization and Computation, RANDOM 2010 - Barcelona, Spain Duration: Sep 1 2010 → Sep 3 2010

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	6302 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	13th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2010 and 14th International Workshop on Randomization and Computation, RANDOM 2010
Country/Territory	Spain
City	Barcelona
Period	9/1/10 → 9/3/10

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-642-15369-3_30

Cite this

Alon, N., & Blais, E. (2010). Testing Boolean function isomorphism. In Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 13th International Workshop, APPROX 2010 and 14th International Workshop, RANDOM 2010, Proceedings (pp. 394-405). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6302 LNCS). https://doi.org/10.1007/978-3-642-15369-3_30

Alon, Noga ; Blais, Eric. / Testing Boolean function isomorphism. Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 13th International Workshop, APPROX 2010 and 14th International Workshop, RANDOM 2010, Proceedings. 2010. pp. 394-405 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Testing Boolean function isomorphism",

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 non-adaptive query complexity of the isomorphism testing problem is Θ(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.",

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Alon, N & Blais, E 2010, Testing Boolean function isomorphism. in Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 13th International Workshop, APPROX 2010 and 14th International Workshop, RANDOM 2010, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6302 LNCS, pp. 394-405, 13th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2010 and 14th International Workshop on Randomization and Computation, RANDOM 2010, Barcelona, Spain, 9/1/10. https://doi.org/10.1007/978-3-642-15369-3_30

Testing Boolean function isomorphism. / Alon, Noga; Blais, Eric.
Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 13th International Workshop, APPROX 2010 and 14th International Workshop, RANDOM 2010, Proceedings. 2010. p. 394-405 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6302 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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N2 - 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 Θ(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.

AB - 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 Θ(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.

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Alon N, Blais E. Testing Boolean function isomorphism. In Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 13th International Workshop, APPROX 2010 and 14th International Workshop, RANDOM 2010, Proceedings. 2010. p. 394-405. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-15369-3_30

Testing Boolean function isomorphism

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