Heminga attālums permutācijām
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Latvijas Universitāte
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Abstract
Bakalaura darbs izstrādāts ar mērķi pētīt un analizēt maksimāla izmēra permutāciju grupas, kuru permutācijām ir pietiekami liels minimālais Heminga attālums. Šādas permutāciju grupas, praksē tiek izmantotas, dažādu efektīvu algoritmu izstrādē. Darbā permutāciju grupas aplūkotas, kā matemātisks instruments, lai pierādītu, ka varbūtiskam kvantu galīgam automātam ir supereksponenciāli mazāk stāvokļu, kā determinētam kvantu galīgam automātam.
The goal of the bachelor research is to explore and analyze permutation groups of maximal order and having reasonable minimal Hamming distance between any two group permutations. This kind of permutation groups is very often used for practical porpoises – developing of different efficient algorithms. Permutation groups in this work is more studied as a mathematical instrument for proving that quantum finite state automate with mixed states has super-exponentially less states than determined quantum finite state automata.
The goal of the bachelor research is to explore and analyze permutation groups of maximal order and having reasonable minimal Hamming distance between any two group permutations. This kind of permutation groups is very often used for practical porpoises – developing of different efficient algorithms. Permutation groups in this work is more studied as a mathematical instrument for proving that quantum finite state automate with mixed states has super-exponentially less states than determined quantum finite state automata.