TY - GEN
T1 - Junto-symmetric functions, hypergraph isomorphism and crunching
AU - Chakraborty, Sourav
AU - Fischer, Eldar
AU - Gacía-Soriano, David
AU - Matsliah, Arie
PY - 2012
Y1 - 2012
N2 - We make a step towards characterizing the boolean functions to which isomorphism can be efficiently tested. Specifically, we prove that isomorphism to any boolean function on {0, 1} n with a polynomial number of distinct permutations can be tested with a number of queries that is independent of n. We also show some partial results in the converse direction, and discuss related problems: testing isomorphism up to linear transformations, and testing isomorphism against a uniform (hyper)graph that is given in advance. Our results regarding the latter topic generalize a theorem of Fischer (SICOMP 2005), and in the process we also provide a simpler proof of his original result which avoids the use of Szemerédi's regularity lemma.
AB - We make a step towards characterizing the boolean functions to which isomorphism can be efficiently tested. Specifically, we prove that isomorphism to any boolean function on {0, 1} n with a polynomial number of distinct permutations can be tested with a number of queries that is independent of n. We also show some partial results in the converse direction, and discuss related problems: testing isomorphism up to linear transformations, and testing isomorphism against a uniform (hyper)graph that is given in advance. Our results regarding the latter topic generalize a theorem of Fischer (SICOMP 2005), and in the process we also provide a simpler proof of his original result which avoids the use of Szemerédi's regularity lemma.
KW - Function Isomorphism
KW - Hypergraph Isomorphism
KW - Poly-symmetric functions
KW - Property Testing
UR - http://www.scopus.com/inward/record.url?scp=84866490472&partnerID=8YFLogxK
U2 - https://doi.org/10.1109/CCC.2012.28
DO - https://doi.org/10.1109/CCC.2012.28
M3 - منشور من مؤتمر
SN - 9780769547084
T3 - Proceedings of the Annual IEEE Conference on Computational Complexity
SP - 148
EP - 158
BT - Proceedings - 2012 IEEE 27th Conference on Computational Complexity, CCC 2012
T2 - IEEE Computer Society Technical Committee on Mathematical Foundations of Computing
Y2 - 26 June 2012 through 29 June 2012
ER -