Iskanje po repozitoriju

Opis: Let a group of automorphisms lift along a regular covering projection of connected graphs given combinatorially by means of voltages. The data that determine the lifted group and its action are then conveniently encoded in terms of voltages as well. Along these lines, an algorithm for testing whether the lifted group is a split extension of the group of covering transformations has recently been proposed in the case when the group of covering transformations is solvable. It consists of decomposing the covering into a series of coverings with elementary abelian groups of covering transformations, and inductively solving the problem at every elementary abelian step. Although the explicit construction of the lifted group is not needed, it still involves time and space consuming constructions of certain subgroups in the lifted group at every step except at the final one. In this paper, an improved version that completely avoids such constructions is presented. From voltage distribution we first compute the weak action and the factor set that determine the lifted group, and we then carry out the test by extracting the necessary information only from the corresponding weak actions and factor sets at every step. An experimental comparison is made against the previous version.
Ključne besede: algorithm, graph, group extension, lifting automorphisms, regular covering projection, voltages
Objavljeno v RUP: 03.01.2022; Ogledov: 763; Prenosov: 17
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Ključne besede: quantum algorithms, cryptanalysis of block ciphers, postquantum analysis, Simon's algorithm, Grover's algorithm, Bernstein-Vazirani's algorithm, Kuperberg's algorithm, Feistel network, SPN, FX
Objavljeno v RUP: 18.10.2021; Ogledov: 1296; Prenosov: 35
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Ključne besede: I-graphs, double generalized Petersen graphs, folded cubes, recognition algorithm, cycle regularity
Objavljeno v RUP: 18.10.2021; Ogledov: 1111; Prenosov: 23
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Ključne besede: graph diameter, blocker problem, polynomial algorithm, NP-complete problem
Objavljeno v RUP: 04.06.2021; Ogledov: 908; Prenosov: 57
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Ključne besede: Simon's algorithm, Grover's algorithm, generalized Feistel network, SMS4 block cipher, quantum cryptanalysis
Objavljeno v RUP: 17.12.2020; Ogledov: 1206; Prenosov: 34
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